CN102231099A - Method for correcting per-pixel response brightness in multi-projector auto-stereoscopic display - Google Patents

Abstract

The invention discloses a method for correcting per-pixel response brightness in multi-projector auto-stereoscopic display, which belongs to the technical field of large-screen high-resolution display in multi-projector combination display. The method is characterized by comprising the following steps of: taking projections of all projectors corresponding to the same viewpoint image after geometries and brightness are corrected as a projection of a virtual projector; measuring a brightness response function of each point in the virtual projector; and according to different brightness response functions of each point, pre-converting the brightness of an input image, wherein the problem of inconsistent brightness in the whole display region resulted from the conjoining display of each viewpoint image in a multi-projector auto-stereoscopic display system through a plurality of projectors can be resolved; consistent seamless conjoining large-screen high-resolution display brightness of each viewpoint image in the multi-projector auto-stereoscopic display system is realized; according to the method, the problem of different brightness response functions of each point on the screen in the multi-projector auto-stereoscopic display system resulted from specific optical properties of the screen can be resolved; and the brightness correction result is more uniform and consistent.

Description

The brightness correcting method that the multi-projector free stereo shows by pixel response

Technical field

The present invention relates to the combination demonstration that the multi-projector free stereo shows, realize the brightness unanimity of the giant-screen high resolving power demonstration that the multi-projector free stereo shows.

Background technology

In recent years, the stereoscopic vision based on binocular parallax is widely used in every field such as film, recreation, emulation, virtual reality.Now, free 3 D display technology has also been obtained major technological breakthrough, and it makes the beholder need not to wear anaglyph spectacles just can see (right and left eyes) image corresponding to different points of view by eyes, thereby produces strong three-dimensional stereoscopic visual effect.Present auto-stereoscopic display is subjected to the restrictions such as resolution of individual monitor, can only hold less spectators and watch in the zone of certain appointment, and this has limited its promotion and application.A plurality of visual point images are shown and can address the above problem effectively with the combination that a plurality of projector carry out the free stereo demonstration.But the screen characteristic that the multi-projector free stereo shows makes geometry correction and brightness correcting method that conventional combination shows be difficult to use.Traditional brightness correcting method mainly comprises brightness fusion method and brightness decay method.

The brightness fusion method utilizes the projector space that geometry correction obtains and the coordinate transformation relation of screen space to calculate the overlapping view field in projector space, and in the overlapping region in projector space, calculate from 0 to the 1 brightness decay factor of transition gradually, make that the brightness decay factor sum of all projector of the every bit correspondence on the screen space is 1.The brightness fusion method is simple and be easy to calculating, but can only solve the luminance difference of projector overlapping region, and the luminance difference between projector inside and the projector is ignored.

The brightness decay method is carried out gamma correction by luminosity response function and maximum, the minimum brightness response curved surface of measuring each projector.This method is only measured a luminosity response function to each projector.Adopt special optical screen in order to obtain the free stereo display effect in the multi-projector auto-stereo display system.The special optical character of these screens has caused the luminosity response function each point difference of projector.So, in the multi-projector auto-stereo display system, use the brightness decay method and carry out gamma correction and can not obtain good gamma correction effect.

Summary of the invention

The objective of the invention is to solve in the multi-projector auto-stereo display system and all use a plurality of projector splicings to show the inconsistent problem of brightness of the whole viewing area of causing, realized the brightness unanimity that the seamless spliced giant-screen high resolving power of each visual point image shows in the multi-projector auto-stereo display system each visual point image.

The invention is characterized in, contain following steps successively:

Step (1): set up a variable resolution multi-projector auto-stereo display system with two visual point images of I=2, comprise: an array of rear-projectors, an auto-stereoscopic display screen curtain, be called for short screen, a digital camera, a server and a plurality of client computer below, wherein, array of rear-projectors is made up of 24 DLP projector, each visual point image is pressed the capable Nc row of Nr with Nr * Nc DLP projector on the auto-stereoscopic display screen curtain mode tiled display, Nr=3, Nc=4; Client computer has 12, two described DLP projector of every client computer control;

Step (2): described server carries out geometry correction to described multi-projector auto-stereo display system, and step is as follows:

Step (2.1): show the image of forming by the unique point of the equidistant distribution of setting respectively in the projector space of each projector frame buffer by each client, form projector space initial mesh meshp _Ij, i represents the sequence number of viewpoint, i=1, and 2, j represents the sequence number of pairing described DLP projector among each viewpoint i, j=1,2 ..., 11,12; Obtain the screen characteristics dot image that the unique point image projection of corresponding each the described DLP projector of each viewpoint forms respectively with described digital camera on described screen again, form the initial mesh meshd of screen space _Ij

Step (2.2): be calculated as follows j the correcting area dispW of projector on described screen in described i the viewpoint _Ij,

dispW _ij＝I(dispA _ij，rect)，i＝0，1，j＝1，2，…，11，12 (1)

Wherein, dispA _IjBe j the viewing area of projector on screen in i the viewpoint, rect is the zone that combination shows on the described screen,

$\mathrm{rect}=I_{i=1}^{\mathrm{Nv}}\left(\mathrm{inrect}\left(U_{j=1}^{\mathrm{Nr}\×\mathrm{Nc}}{\mathrm{dispA}}_{\mathrm{ij}}\right)\right)---\left(2\right)$

In i viewpoint the summation of totally 12 DLP projector viewing areas on described screen use

Expression, one of inrect asks the function that connects rectangle in the given area;

Step (2.3): j correcting area dispW that the DLP projector shows on described screen in i viewpoint _IjIn regenerate by the unique point of described equidistant setting and be organized into described correcting area dispW _IjCalibration grid meshnd at described screen space _IjAgain according to the calibration grid meshnd of described screen space _IjThe coordinate (D of summit D _U,, D _v) calculate its corresponding projector free-air correction grid meshnp _IjCoordinate (the D of point D ' _x', D _y');

Calibration grid meshnd when described screen space _IjSummit D (D _U,, D _v) area coordinate be (m, k, in the time of w),

$m=\frac{S\left(\mathrm{\ΔABD}\right)}{S\left(\mathrm{\ΔABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& B_u& D_u\\ A_v& B_v& D_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},k=\frac{S\left(\mathrm{\ΔDBC}\right)}{S\left(\mathrm{\ΔABC}\right)}=\frac{\left|\begin{array}{ccc}{D}_u& B_u& C_u\\ D_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},w=\frac{S\left(\mathrm{\ΔADC}\right)}{S\left(\mathrm{\ΔABC}\right)}\frac{\left|\begin{array}{ccc}{A}_u& D_u& C_u\\ A_v& D_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}---\left(3\right)$

Wherein, Δ ABC is that the D point is at described initial mesh meshd _IjThe triangle at middle place, m is the interior triangle Δ ABD of Δ ABC and the ratio of the area of this triangle Δ ABC, k is the interior triangle Δ DBC of Δ ABC and the ratio of the area of this triangle Δ ABC, and w is the interior triangle Δ ADC of Δ ABC and the ratio of the area of this triangle Δ ABC, (A _u, A _v), (B _u, B _v) and (C _u, C _v) be three apex coordinates of Δ ABC;

Described projector free-air correction grid meshnp _IjCoordinate (the D of point D ' _x', D _y') be

$\left\{\begin{array}{c}{D}_x^{\′}=m\×A_x^{\′}+k\×B_x^{\′}+w\×C_x^{\′}\\ D_y^{\′}=m\×A_y^{\′}+k\×B_y^{\′}+w\×C_y^{\′}\end{array}\right.---\left(4\right)$

Wherein, Δ A ' B ' C ' is at described grid meshp _IjIn with described grid meshd _IjThe pairing triangle of Δ ABC, three apex coordinates of Δ A ' B ' C ' are respectively (A _x', A _y'), (B _x', B _y'), (C _x', C _y').

Step (2.4): be calculated as follows described server is distributed to j DLP projector in i the viewpoint by each client calibration grid meshnp _IjThe reference position (x of image ^Ij _Start, y ^Ij _Start), wide high width _IjAnd height _Ij, and distribute to described calibration grid meshnp _IjThe texture coordinate (xx on e summit _Ije, yy _Ije);

$\left\{\begin{array}{c}{x^{\mathrm{ij}}}_{\mathrm{start}}=[({u^{\mathrm{ij}}}_{\min }-u_{\min })/(u_{\max }-u_{\min })]\×\mathrm{wd}\\ {y^{\mathrm{ij}}}_{\mathrm{start}}=[({v^{\mathrm{ij}}}_{\min }-v_{\min })/(v_{\max }-v_{\min })]\×\mathrm{hd}\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{\mathrm{width}}_{\mathrm{ij}}=[({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })/(u_{\max }-u_{\min })]\×\mathrm{wd}\\ {\mathrm{height}}_{\mathrm{ij}}=[({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })/(v_{\max }-v_{\min })]\×\mathrm{hd}\end{array}\right.---\left(6\right)$

$\left\{\begin{array}{c}{\mathrm{xx}}_{\mathrm{ije}}=(u_{\mathrm{ije}}-{u^{\mathrm{ij}}}_{\min })/({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })\\ {\mathrm{yy}}_{\mathrm{ije}}=(v_{\mathrm{ije}}-{v^{\mathrm{ij}}}_{\min })/({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })\end{array}\right.---\left(7\right)$

Wherein, width _IjAnd height _IjBe the calibration grid meshnp that described server-assignment is given j DLP projector in i the viewpoint _IjImage wide and high, wd and hd are image wide and high before projection of wanting tiled display on the described screen, (u _Min, v _Min) and (u _Max, v _Max) be the lower left corner of combination viewing area rect on the described screen and the apex coordinate in the upper right corner, u ^Ij _Min, u ^Ij _Max, v ^Ij _MinAnd v ^Ij _MaxBe respectively correcting area dispW _IjFour apex coordinates in minimum, the maximal value of minimum, maximal value and ordinate of horizontal ordinate, (u _Ije, v _Ije) be calibration grid meshnp _IjIn the coordinate of screen space of screen of e summit correspondence, i=1,2, j=1,2 ..., Nr*Nc;

Step (2.5): server will make up each client in the program each width of cloth image of demonstration, (2.4) reference position of calculating, the corresponding subimage of size intercepting are distributed to the clients corresponding computing machine set by step, so that the subimage that distributes is mapped to corresponding geometry correction grid meshnp by the described texture coordinate that calculates _IjOn, again with projector projection output, on described screen, obtain the splicing effect of geometric alignment;

Step (3): adopt the brightness fusion method that transkit attenuation is carried out in the brightness at the edge of each DLP projector overlapping region on the screen described in the described multi-projector auto-stereo display system successively according to the following steps;

Step (3.1): the projector space each point (x, the intensity correction values A that y) locates that are calculated as follows j projector in i the viewpoint _Ij(x y), is combined into the gamma correction template of this j projector:

$A_{\mathrm{ij}}(x,y)={\left(\frac{a_{\mathrm{ij}}(u,v)}{{\mathrm{\Σ}}_{j^{\′}=1}^{\mathrm{Nr}\×\mathrm{Nc}}{a}_{{\mathrm{ij}}^{\′}}(u,v)}\right)}^{1/\mathrm{\γ}}---\left(8\right)$

Wherein, (u, v) be j DLP projector of i viewpoint the projector space (x, y) Dui Ying screen space coordinates, i=1,2, j=1,2 ..., Nr*Nc, γ=2.4, a _Ij(u v) is the correcting area dispW of j projector of i viewpoint _IjIn the screen space point (u, v) arrive its four borders apart from minimum value, j '=1,2 ..., Nr*Nc, but j ' ≠ j and correcting area dispW _IjWith correcting area dispW _{Ij '}The overlapping region is arranged, a _{Ij '}(u v) is the correcting area dispW of i the individual projector of viewpoint j ' _{Ij '}In the screen space point (u, v) arrive its four borders apart from minimum value, at Non-overlapping Domain a _{Ij '}(u, v)=0;

Step (3.2): projection output again after the value correspondence of every bit in the value of the every bit of image after the projector geometry correction and the gamma correction template multiplied each other, thus the combination that obtains the brightness decay of projector overlapping region shows;

Step (3.3): (1) and step (2) are carried out projector image behind geometry and the gamma correction as the projected image of a virtual projection instrument set by step relevant all the DLP projector of each viewpoint;

Step (4): the irradiance value of calculating corresponding each sampling brightness input on each location of pixels of each described virtual projection instrument successively according to the following steps;

Step (4.1): get K sampled point by certain interval in the interval [0,255] of brightness value, for the ease of the storage computation of back, equilibration time and precision are got K=30, are calculated as follows the brightness value SL of 30 sampled points _k,

${\mathrm{SL}}_k=\left\{\begin{array}{cc}8\&times;(k-1)& 1\&le;k\&le;15\\ 8\&times;(k+2)& 15<k\&le;29\\ 255& k=30\end{array}\right.,$ k＝1，2…K (9)

Step (4.2): generating size is K the image of xRes x yRes, K=30, wherein, xRes=1024, yRes=768; K image l _kIn every brightness identical, all be k sampling brightness value SL _k, k=1,2 ... K; Between 0.02s-2.0s, get S time shutter Δ t _s, s=1,2 ..., S, wherein S=16;

Step (4.3): all images to all virtual projection instrument and the generation of second step repeats following step (4.3.1)～step (4.3.2), obtains the irradiance value of corresponding each sampling brightness input on each pixel in each virtual projection instrument;

Step (4.3.1): for k image I of the generation of i the virtual projection instrument step display (4.2) described in the step (3.3) _kProjection result on screen is Δ t camera being set the time shutter respectively _s, s=1,2 ..., S, after take pictures, obtaining the individual size of S ' is the image of xcRes x ycRes, wherein, S '=S, xcRes and ycRes are respectively the wide and high of camera image, xcRes=2288, ycRes=1520;

Step (4.3.2): with setting time shutter Δ t _sThe take pictures brightness value Z of p point in the described image of obtaining step (4.3.1) of camera _PsIrradiance E with this point _p,

$\ln E_p=\frac{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(z_{\mathrm{ps}}\right)(g\left(Z_{\mathrm{ps}}\right)-\ln \mathrm{\&Delta;}{t}_S)}{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)},$ p＝1，2...P (10)

Wherein, P is the number of pixels in each image, P=2288*1520, function g (Z _Ps) be Z _PsAnd E _pWith Δ t _sThe mapping relations of logarithmic function,

g(Z _ps)＝lnE _p+lnΔt _s (11)

W (Z _Ps) be to distribute to brightness Z _PsWeight,

$w\left(Z_{\mathrm{ps}}\right)=\left\{\begin{array}{cc}{Z}_{\mathrm{ps}}-Z_{\min }& Z_{\mathrm{ps}}\&le;Z_{\mathrm{mid}}\\ Z_{\max }-Z_{\mathrm{ps}}& Z_{\mathrm{ps}}>Z_{\mathrm{mid}}\end{array}\right.---\left(12\right)$

Step (4.3.3): in order to obtain exporting one to one at screen space with the input position of described virtual projection instrument, on each described irradiance image mapped to a grid of the correspondence that each described DLP projector is calculated step (4.3.2), and the irradiance image overlay on these grids is obtained together the output of virtual projection instrument; The coordinate on each summit on the grid (x, y) and texture coordinate (tex_x tex_y) is respectively

$\left\{\begin{array}{c}x=(D_u-\min x)/(\max x-\min x)*\mathrm{xRes}\\ y=(D_v-\min y)/(\max y-\min y)*\mathrm{yRes}\end{array}\right.---\left(13\right)$

$\left\{\begin{array}{c}\mathrm{tex}\_x=D_u/\mathrm{xcRes}\\ \mathrm{tex}\_y=D_v/\mathrm{ycRes}\end{array}\right.---\left(14\right)$

Wherein, (D _u, D _v) be that summit on the calibration grid of each projector is at the coordinate of screen space, (minx, miny) and (maxx, maxy) be the upper left corner of whole correcting area and the lower right corner coordinate respectively at screen space, xRes and yRes divide the wide and high of the image that maybe make up demonstration, and xcRes and ycRes are respectively the wide and high of camera image;

Step (5): on each pixel of virtual projection instrument, generate K some P _k, k=0,1 ... K-1, K=30, wherein, k some P _kHorizontal ordinate be k+1 at this pixel place sampling brightness value, the irradiance value that ordinate calculates the brightness value input of should sampling for this pixel place; In order to obtain the corresponding relation of continuous input and output brightness, calculate being three Uniform B-spline interpolation curves of this K point, and obtain the reference mark of B-spline curves by following formula,

$\left[\begin{array}{cccccc}6& -6& & & & 0\\ 1& 4& 1& & & \\ & 1& 4& 1& & \\ & & \mathrm{<figure-callout\; id="1"\; label="O\; O\; O"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">O</figure-callout>}& O& O& \\ & & & 1& 4& 1\\ 0& & & & -6& 6\end{array}\right]\left[\begin{array}{c}{V}_0\\ V_1\\ V_2\\ M\\ V_K\\ V_{K+1}\end{array}\right]=\left[\begin{array}{c}0\\ P_0\\ P_1\\ M\\ P_{K-1}\\ 0\end{array}\right]---\left(15\right)$

Wherein, V ₀, V ₁..., V _K+1It is the reference mark.Find the solution tri-diagonal matrix equation in the following formula with chasing method, obtain the reference mark V of three Uniform B-spline interpolation curves ₀, V ₁..., V _K+1

Step (6): (u, the brightness value of v) locating is more arbitrarily in the minimum brightness curved surface of vision unanimity in the calculating screen space

$L^{\&prime;}(u,v)=\max (L\min (u,v),\mathrm{\&lambda;}\&times;\frac{|L\min (u,v)-L\min (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(16\right)$

Wherein, (u v) shows minimum sampling brightness SL for the virtual projection instrument to Lmin _MinThe brightness output image of correspondence is in that ((u ', v ') is that (Lmin (u ', v ') shows the sampling brightness SL of minimum for the virtual projection instrument for u, neighbor point v) for u, the v) brightness at coordinate place during the image that generates _MinThe brightness output image of correspondence is in the brightness at (u ', v ') coordinate place during the image that generates, and λ is the visually-perceptible coefficient, λ=50, and max is the function of maximizing;

(u, the brightness value of v) locating is more arbitrarily in the high-high brightness curved surface of vision unanimity in the calculating screen space

$L^{\&prime;\&prime;}(u,v)=\min (L\max (u,v),\mathrm{\&lambda;}\&times;\frac{|L\max (u,v)-L\max (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(17\right)$

Wherein, (u v) shows maximum sampling brightness SL for the virtual projection instrument to Lmax _MaxThe brightness output image of correspondence is in that ((u ', v ') is that (Lmax (u ', v ') shows the sampling brightness SL of maximum for the virtual projection instrument for u, neighbor point v) for u, the v) brightness at coordinate place during the image that generates _MaxThe brightness output image of correspondence is in the brightness at (u ', v ') coordinate place during the image that generates;

Step (7): successively according to the following steps according to virtual projection instrument every bit (x, the process of the input brightness of this point of the brightness calculation of the image of y) locating that will show on the B-spline curves of correspondence is as follows:

Step (7.1): the reference mark of the B-spline curves of each location of pixels is packaged into little texture respectively, with the synthetic big reference mark texture of these all little textures; Each B-spline curves is calculated 32 reference mark; The horizontal ordinate at each reference mark and ordinate account for a passage in the texture respectively; For the 2 d texture of 4 passages, the texture size of 32 reference mark needs is 32*2/4=16; For the ease of the calculating of texture coordinate, little texture is stored by the mode of 4 row, 4 row.Large texture is stored each little texture by the mode of the capable xRes row of yRes, and wherein, xRes*yRes is the resolution of display device; So the size of big reference mark texture is (xRes*4) * (yRes*4);

Step (7.2): (x y) locates, and step (the 7.2.1)～step (7.2.4) below repeating obtains the brightness input behind the every bit gamma correction at each location of pixels of virtual projection instrument; By changing the brightness value of input, obtain consistent brightness output;

Step (7.2.1): the output brightness range that will put is compressed to the minimum of vision unanimity and high-high brightness curved surface on the interval between the brightness value of this point, obtain the vision unanimity brightness output Wl (x, y),

Wl(x，y)＝Lmin(x，y)+Ol(x，y)/255.0*(Lmax(x，y)-Lmin(x，y))

(18)

Wherein, (x is to make up the brightness of the image of demonstration at this some y) to Ol, and (x y) shows minimum sampling brightness SL for the virtual projection instrument to Lmin _MinThe brightness output image of correspondence is in the brightness of this some during the image that generates, and (x is that the virtual projection instrument shows maximum sampling brightness SL y) to Lmax _MaxThe brightness output image of correspondence is in the brightness of this some during the image that generates;

Step (7.2.2): according to previous calculations obtain (two end points P of the c section function of three Uniform B-spline curves are calculated at x, the reference mark of three Uniform B-spline curves y) with following formula _c(0) and P _c(1),

$P_c\left(t\right)=\left[\begin{array}{cccc}1& t& t^2& {\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">t</figure-callout>}}^3\end{array}\right]\frac{1}{6}\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{V}_c\\ V_{c+1}\\ V_{c+2}\\ V_{c+3}\end{array}\right],$ 0≤t≤1，c＝0，1，...，K-1 (19)

Wherein, t is the coefficient parameter of B-spline curves, and c is the call number of function segment, P _c(t) be each point between the c section function region of B-spline curves, V _c, V _C+1, V _C+2, V _C+3The call number that is B-spline curves respectively is for being respectively c, c+1, c+2, the reference mark of c+3; According to these end points P _c(0) and P _c(1), find the call number c between function region, (x is y) in the formed interval of ordinate value of two end points of c section function to make Wl;

Step (7.2.3): with dichotomy calculate (x, the input brightness Nl after y) some brightness is proofreaied and correct (x, y): with [0,1] is between the parametric t original area, by getting interval mid point tm, original interval is divided into two; The ordinate E of the point during with formula (19) calculating parameter t=tm on the B-spline curves _pIf E _p(x y), is a half-interval on the left side between the newly developed area to＜Wl; If E _p(x y), is a half-interval on the right between the newly developed area to＞Wl; Constantly the interval is divided into two, the iteration said process is up to the error amount of interval range less than a setting; Getting parametric t is the midrange that iterates to last resulting interval, calculates the abscissa value of the point on the B-spline curves with formula (18), this value be exactly Wl (x, y) Dui Ying input brightness Nl (x, y);

(x y) multiply by the gamma correction template that obtains to step (7.2.4): Nl in step (3), obtain the final brightness input of each projector; By changing the brightness value of input, obtain consistent brightness output.

The invention has the advantages that, luminosity response function according to every bit in the projector carries out brightness transition, solved the different problem of each point luminosity response function on the screen that the special optical character of screen in the multi-projector auto-stereo display system causes, relevant how much of all projector of same visual point image and the projection behind the gamma correction projection as a virtual projection instrument, quicken to make the measurements and calculations of luminosity response function speed up by B-spline curves match and GPU, obtain the gamma correction effect of uniformity more.

Description of drawings

Fig. 1 is the synoptic diagram of scalable high resolving power multi-projector auto-stereo display system.

Fig. 2 is the initial mesh in projector space.

Fig. 3 is the initial mesh of screen space.

Fig. 4 is the calibration grid of screen space.

Fig. 5 is the calibration grid in projector space.

Fig. 6 is the coordinate conversion in screen space and projector space.

Fig. 7 is the program flow chart of display system.

Embodiment

The present invention is achieved by the following technical programs: form a scalable high resolving power multi-projector auto-stereo display system with array of rear-projectors, auto-stereoscopic display screen curtain, digital camera, server and client side's computing machine.Fig. 1 is the synoptic diagram of scalable high resolving power multi-projector auto-stereo display system, wherein, and Nv=2, Nr=3, Nc=4.The image that Nv viewpoint arranged in the system, each visual point image are pressed the mode tiled display of the capable Nc row of Nr on the auto-stereoscopic display screen curtain with Nr * Nc DLP projector.Server calculates the geometry correction and the brightness correction parameter of each projector, and sends to the client of control homolographic projection instrument.Two projector of each client control.The projector that re-sends to its control after the image that the parameter that geometry correction that client calculates according to server and edge merge will show each width of cloth is out of shape carries out projection, thereby obtains seamless spliced display result on screen.In order to obtain the seamless spliced demonstration of a plurality of visual point images, the projection of a virtual projection instrument is used as in the projection after all projector geometry corrections that the present invention is at first relevant with a viewpoint and edge merge; Then, the luminosity response function of every bit in the measurements and calculations virtual projection instrument; At last, import for the brightness that obtains identical brightness output needs, on giant-screen, obtain the brightness unanimity by the brightness input of revising the virtual projection instrument according to the luminosity response function calculation of virtual projection instrument every bit.

Because the anisotropic reflectivity properties of auto-stereoscopic display screen curtain, making screen have high light belt produces, and luminosity response function each point difference, this makes the brightness decay method of only measuring a luminosity response function can not obtain good gamma correction effect in auto-stereo display system.The present invention solves the gamma correction problem of multi-projector auto-stereo display system by the luminosity response function by every bit in the pixel measuring projector.Optical measuring apparatus such as photometer are measured accurately, but can only measure the color of a point at every turn.Obtain the luminosity response function that projector has a few and to utilize the HDR method.This method is measured its brightness output respectively to 255 brightness inputs of each projector.Set a series of time shutter for brightness output each time respectively with digital camera and take pictures, the image with a plurality of different exposure time synthesizes the brightness output of a panel height dynamic image as reduction then.Need very many sample image data owing to measure the luminosity response function, the time of calculating the luminosity response function from image is also very long.About 5 minutes of the computing time of each luminosity response function in the classic method.If measure scalable high resolving power multi-projector free stereo show in the luminosity response function of every bit in 24 projector, will calculate 24*1024*768 luminosity response function, computing time is long.Because the luminosity response function difference of every bit, gamma correction stage every bit calculates according to different brightness look-up tables.The computing velocity that realizes the brightness look-up table in CPU is very slow, and the finite space of video memory makes the while be difficult to realize the calculating of 1024*768 brightness look-up table on GPU.

At the speed issue that brings by the luminosity response function of pixel measuring projector every bit, the present invention sets about improving performance from the following aspects: (1) is relevant how much of all projector of same visual point image and the projection behind the gamma correction projection as a virtual projection instrument.The input of this virtual projection instrument is that relevant viewpoint will make up the image of demonstration, and output is that combination shows the projection of back on giant-screen.Pursue the luminosity response function that pixel is measured this virtual projection instrument, this virtual projection instrument is carried out gamma correction, avoided the measurement repeatedly and synthetic calculating of overlapping region.(2) quicken to reduce measurements and calculations time of luminosity response function by B-spline curves and GPU.Import corresponding output on giant-screen with camera measure portion sampling luminance picture, and quicken reduction output brightness by GPU with the HDR method.Then, all calculate the B-spline curves of the input and output point of all sampling brightness of a mistake at each location of pixels of virtual projection instrument, thereby obtain continuous luminosity response function at every bit.(3) in order to make the brightness range behind the gamma correction big as far as possible, minimum and maximum brightness curved surface is carried out the minimum and maximum luminosity response curved surface that smoothing processing obtains the vision unanimity respectively, make brightness section behind the every bit gamma correction between the brightness value of the correspondence position of the minimum and maximum luminosity response curved surface of vision unanimity.(4) utilize B-spline function, realize that the GPU of the brightness look-up table that each pixel is different calculates, and be applied in the gamma correction.

Relevant how much of all projector of each viewpoint and the projection behind the gamma correction projection as a virtual projection instrument.The luminosity response function of measuring every bit in the virtual projection instrument carries out gamma correction.The input of this virtual projection instrument is that relevant viewpoint will make up the image of demonstration, and output is that combination shows the projection of back on giant-screen.The process of measuring the luminosity response function of virtual projection instrument every bit and carrying out gamma correction according to these luminosity response functions is as follows:

(1) server adopts the secondary geometric correction method that the multi-projector auto-stereo display system is carried out geometry correction.

The first step: the image that shows the unique point composition of equidistant distribution as shown in Figure 2 in each projector frame buffer space respectively.Obtain each projector respectively with digital camera and be projected in unique point image on the screen.With the projector space characteristics point of j projector in i the viewpoint and project to unique point on the screen and be organized into as shown in Figure 2 projector space initial mesh meshp respectively _IjThe initial mesh meshd of screen space as shown in Figure 3 _IjWherein, i represents the sequence number of viewpoint, i=1, and 2, j represents the sequence number of pairing described DLP projector among each viewpoint i, j=1,2 ..., 11,12.

Second step: calculate the correcting area of j projector on screen in i the viewpoint

dispW _ij＝I(dispA _ij，rect)，i＝0，1，j＝1，2，…，11，12 (1)

Wherein, dispA _IjBe j the viewing area of projector on screen in i the viewpoint, rect is the zone that combination shows on the screen,

$\mathrm{rect}=I_{i=1}^{\mathrm{Nv}}\left(\mathrm{inrect}\left(U_{j=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}{\mathrm{dispA}}_{\mathrm{ij}}\right)\right)---\left(2\right)$

One of inrect asks the function that connects rectangle in the given area.

The 3rd step: at correcting area dispW _IjIn regenerate equidistant unique point as shown in Figure 4 and be organized into screen space calibration grid meshnd _IjAccording to meshnd _IjEach summit calculate its corresponding projector spatial point.And these projector spatial point are organized into as shown in Figure 5 projector free-air correction grid meshnp _IjAccording to meshnd _IjEach summit D (D _u, D _v) calculate the coordinate (D of its corresponding projector spatial point D ' _x', D _y') method as follows.

At first, be calculated as follows described screen space point D (D _U,, D _v) area coordinate (m, k, w),

$m=\frac{S\left(\mathrm{\&Delta;ABD}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& B_u& D_u\\ A_v& B_{\mathrm{<figure-callout\; id="1"\; label="v\; D\; v"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">v</figure-callout>}}& D_v{}_{}\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_{\mathrm{<figure-callout\; id="1"\; label="v\; C\; v"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">v</figure-callout>}}& C_v{}_{}\\ 1& 1& 1\end{array}\right|},k=\frac{S\left(\mathrm{\&Delta;DBC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{D}_u& B_u& C_u\\ D_v& B_{\mathrm{<figure-callout\; id="1"\; label="v\; C\; v"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">v</figure-callout>}}& C_v{}_{}\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_{\mathrm{<figure-callout\; id="1"\; label="v\; C\; v"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">v</figure-callout>}}& C_v{}_{}\\ 1& 1& 1\end{array}\right|},w=\frac{S\left(\mathrm{\&Delta;ADC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}\frac{\left|\begin{array}{ccc}{A}_u& D_u& C_u\\ A_v& D_{\mathrm{<figure-callout\; id="1"\; label="v\; C\; v"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">v</figure-callout>}}& C_v{}_{}\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_{\mathrm{<figure-callout\; id="1"\; label="v\; C\; v"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">v</figure-callout>}}& C_v{}_{}\\ 1& 1& 1\end{array}\right|}---\left(3\right)$

Wherein, Δ ABC is that the D point is at grid meshd _IjThe triangle (as shown in Figure 6) at middle place, m is the interior triangle Δ ABD of Δ ABC and the ratio of the area of this triangle Δ ABC, k is the interior triangle Δ DBC of Δ ABC and the ratio of the area of this triangle Δ ABC, and w is the interior triangle Δ ADC of Δ ABC and the ratio of the area of this triangle Δ ABC, (A _u, A _v), (B _u, B _v) and (C _u, C _v) be three apex coordinates of Δ ABC, (D _u, D _v) be the D point coordinate;

Then, be calculated as follows the coordinate (D of the some D ' in projector space _x', D _y'),

$\left\{\begin{array}{c}{D}_x^{\&prime;}=m\&times;A_x^{\&prime;}+k\&times;B_x^{\&prime;}+w\&times;C_x^{\&prime;}\\ D_y^{\&prime;}=m\&times;A_y^{\&prime;}+k\&times;B_y^{\&prime;}+w\&times;C_y^{\&prime;}\end{array}\right.---\left(4\right)$

Wherein, Δ A ' B ' C ' is at grid meshp _IjIn with grid meshd _IjThe pairing triangle of Δ ABC (as shown in Figure 6), (A _x', A _y'), (B _x', B _y'), (C _x', C _y') be three apex coordinates of Δ A ' B ' C '.

The 4th step: the server dispensed is given the reference position (x of the image of j projector in i the viewpoint ^Ij _Start, y ^Ij _Start), the size (width _Ij, height _Ij) and distribute to calibration grid meshnp _IjThe texture coordinate (xx on e summit _Ije, yy _Ije);

$\left\{\begin{array}{c}{x^{\mathrm{ij}}}_{\mathrm{start}}=[({u^{\mathrm{ij}}}_{\min }-u_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {y^{\mathrm{ij}}}_{\mathrm{start}}=[({v^{\mathrm{ij}}}_{\min }-v_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{\mathrm{width}}_{\mathrm{ij}}=[({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {\mathrm{height}}_{\mathrm{ij}}=[({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(6\right)$

$\left\{\begin{array}{c}{\mathrm{xx}}_{\mathrm{ije}}=(u_{\mathrm{ije}}-{u^{\mathrm{ij}}}_{\min })/({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })\\ {\mathrm{yy}}_{\mathrm{ije}}=(v_{\mathrm{ije}}-{v^{\mathrm{ij}}}_{\min })/({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })\end{array}\right.---\left(7\right)$

Wherein, width _IjAnd heigh _IjBe image wide and high of distributing to j projector in i the viewpoint, wd and hd are wide and high before projection of the image of wanting tiled display, (u _Min, v _Min) and (u _Max, v _Max) be the lower left corner of combination viewing area rect on the giant-screen and the apex coordinate in the upper right corner, u ^Ij _Min, u ^Ij _Max, v ^Ij _MinAnd v ^Ij _MaxBe respectively correcting area dispW _IjFour apex coordinates in minimum, the maximal value of minimum, maximal value and ordinate of horizontal ordinate, (u _Ije, v _Ije) be calibration grid meshnp _IjIn the coordinate of screen space of giant-screen of e summit correspondence, i=1 ..., Nv, j=1,2 ..., Nr*Nc.

The 5th step: server will make up each width of cloth image of demonstration, distribute to client computer by the reference position that calculates, the corresponding subimage of size intercepting, client computer is mapped to geometry correction grid meshnp with the subimage that distributes by the texture coordinate that calculates _IjOn, use projector projection output again, thereby on screen, obtain the splicing effect of geometric alignment.

(2) adopting the brightness fusion method that the multi-projector auto-stereo display system is carried out the edge merges.

The first step: the gamma correction template that adopts each projector in the brightness calculating fusion multi-projector auto-stereo display system.Be calculated as follows projector space each point (x, the intensity correction values A that y) locates of j projector in i the viewpoint _Ij(x y), is combined into the gamma correction template of this j projector:

$A_{\mathrm{ij}}(x,y)={\left(\frac{a_{\mathrm{ij}}(u,v)}{{\mathrm{\&Sigma;}}_{j^{\&prime;}=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}{a}_{{\mathrm{ij}}^{\&prime;}}(u,v)}\right)}^{1/\mathrm{\&gamma;}}---\left(8\right)$

Wherein, (u, v) be j DLP projector of i viewpoint the projector space (x, y) Dui Ying screen space coordinates, i=1,2, j=1,2 ..., Nr*Nc, γ=2.4, a _Ij(u v) is the correcting area dispW of j projector of i viewpoint _IjIn the screen space point (u, v) arrive its four borders apart from minimum value, j '=1,2 ..., Nr*Nc, but j ' ≠ j and correcting area dispW _IjWith correcting area dispW _{Ij '}The overlapping region is arranged, a _{Ij '}(u v) is the correcting area dispW of i the individual projector of viewpoint j ' _{Ij '}In the screen space point (u, v) arrive its four borders apart from minimum value, at Non-overlapping Domain a _{Ij '}(u, v)=0.

Second step: projection output again after the value correspondence of every bit in image after the projector geometry correction and the gamma correction template multiplied each other.Such brightness that gets the projector overlapping region obtains decay, and the combination that obtains merging at the edge shows.

The 3rd step: the projection of the projection of relevant all projector of each viewpoint after as a virtual projection instrument by how much of top methods and gamma correction.

(3) calculate the irradiance output of corresponding each sampling brightness input on each location of pixels of each virtual projection instrument.

The first step: get K sampled point by certain interval in the interval [0,255] of brightness value, for the ease of the storage computation of back, equilibration time and precision are got K=30, are calculated as follows the brightness value SL of 30 sampled points _k,

${\mathrm{SL}}_k=\left\{\begin{array}{cc}8\&times;(k-1)& 1\&le;k\&le;15\\ 8\&times;(k+2)& 15<k\&le;29\\ 255& k=30\end{array}\right.,$ k＝1，2…K (9)

Second step: generating size is K the image of xRes x yRes, wherein, and xRes=1024, yRes=768.K image I _kIn every brightness identical, all be k sampling brightness value SL _k, k=1,2 ... K.Between 0.02s-2.0s, get S time shutter Δ t _s, s=1,2 ..., S, wherein, S=16.

The 3rd step: all images to all virtual projection instrument and the generation of second step repeated for fourth, fifth and six steps, obtained the irradiance output that corresponding each sampling brightness is imported on each pixel in each virtual projection instrument.

The 4th step: show k the image I that second step generated for i virtual projection instrument _kProjection result on screen, it is Δ t that camera is set the time shutter respectively _s, s=1,2 ..., S, after take pictures, obtain S the size be the image of xcRes x ycRes, wherein, xcRes and ycRes are respectively the wide and high of camera image, xcRes=2288, ycRes=1520.

The 5th step: with setting time shutter Δ t _sThe take pictures brightness value Z of p point in the image that obtains of camera _PsIrradiance E with this point _pBetween have following relation,

Z _ps＝f(E _pΔt _s)，p＝1，2...P (10)

Wherein, f reflects take pictures Nonlinear Mapping relation between the brightness of the image that generates of the brightness of actual scenery and camera, and P is the number of pixels in the synthetic image, P=2288 x 1520.If use f ^-1The inverse function of expression f, then

f ^-1(Z _ps)＝E _pΔt _s (11)

Take the logarithm in both sides,

lnf ^-1(Z _ps)＝lnE _p+lnΔt _s (12)

Make function g (Z _Ps) expression Z _PsAnd E _pWith Δ t _sThe mapping relations of logarithmic function, g=lnf ^-1, so

g(Z _ps)＝lnE _p+lnΔt _s (13)

E in the following formula _pWith function g the unknown, by finding the solution the least square solution of following formula, the minimum value of just finding the solution following formula obtains,

$\mathrm{\&Omega;}=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\left\{w\left(Z_{\mathrm{ps}}\right)\right[g\left(Z_{\mathrm{ps}}\right)-\ln E_p-\ln \mathrm{\&Delta;}{t}_s\left]\right\}}^2+\mathrm{\&lambda;}\underset{z=Z_{\min }+1}{\overset{Z_{\max }-1}{\mathrm{\&Sigma;}}}{\left[w\left(z\right)g^{\&prime;\&prime;}\left(z\right)\right]}^2---\left(14\right)$

Wherein, w (Z _Ps) be to distribute to brightness Z _PsWeight, λ=50 are smoothing factor, g " (z) be the second derivative of g (z),

$w\left(Z_{\mathrm{ps}}\right)=\left\{\begin{array}{cc}{Z}_{\mathrm{ps}}-Z_{\min }& Z_{\mathrm{ps}}\&le;Z_{\mathrm{mid}}\\ Z_{\max }-Z_{\mathrm{ps}}& Z_{\mathrm{ps}}>Z_{\mathrm{mid}}\end{array}\right.---\left(15\right)$

$w\left(Z\right)=\left\{\begin{array}{cc}z-Z_{\min }& z\&le;Z_{\mathrm{mid}}\\ Z_{\max }-z& z>Z_{\mathrm{mid}}\end{array}\right.---\left(16\right)$

g″(z)＝g(z-1)-2g(z)+g(z+1) (17)

Wherein, Z _MinBe the brightness minimum value of all pixels in S the image, Z _MaxBe the brightness maximal value of all pixels in S the image, Z _Mid=(Z _Max+ Z _Max)/2.

For the robustness of calculating, obtain the irradiance E of p point by the image of a plurality of time shutter _p,

$\ln E_p=\frac{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(z_{\mathrm{ps}}\right)(g\left(Z_{\mathrm{ps}}\right)-\ln \mathrm{\&Delta;}{t}_S)}{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)},$ p＝1，2...P (18)

The 6th step: in order to obtain exporting one to one at screen space with the input position of described virtual projection instrument, on each described irradiance image mapped to a grid of the correspondence that each described DLP projector is calculated previous step, and the irradiance image overlay on these grids is obtained together the output of virtual projection instrument.The coordinate on each summit on the grid (x, y) and texture coordinate (tex_x tex_y) is respectively

$\left\{\begin{array}{c}x=(D_u-\min x)/(\max x-\min x)*\mathrm{xRes}\\ y=(D_v-\min y)/(\max y-\min y)*\mathrm{yRes}\end{array}\right.---\left(19\right)$

$\left\{\begin{array}{c}\mathrm{tex}\_x=D_u/\mathrm{xcRes}\\ \mathrm{tex}\_y=D_v/\mathrm{ycRes}\end{array}\right.---\left(20\right)$

Wherein, (D _u, D _v) be the screen space coordinates on the summit on the calibration grid of each projector, (minx, miny) and (maxx, maxy) be the screen space coordinates in the upper left corner and the lower right corner of whole correcting area respectively, xRes and yRes divide the wide and high of the image that maybe make up demonstration, and xcRes and ycRes are respectively the wide and high of camera image.

(4) on each pixel of virtual projection instrument, obtain the luminosity response function that B-spline curves are represented.

On each pixel of virtual projection instrument, generate K some P _k, k=0,1 ... K-1, wherein, k some P _kHorizontal ordinate be k+1 at this pixel place sampling brightness value, the irradiance output that ordinate calculates the brightness value input of should sampling for this pixel place.In order to obtain the corresponding relation of continuous input and output brightness, calculate being three Uniform B-spline interpolation curves of this K point, and obtain the reference mark of B-spline curves by following formula,

$\left[\begin{array}{cccccc}6& -6& & & & 0\\ 1& 4& 1& & & \\ & 1& 4& 1& & \\ & & \mathrm{<figure-callout\; id="1"\; label="O\; O\; O"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">O</figure-callout>}& O& O& \\ & & & 1& 4& 1\\ 0& & & & -6& 6\end{array}\right]\left[\begin{array}{c}{V}_0\\ V_1\\ V_2\\ M\\ V_K\\ V_{K+1}\end{array}\right]=\left[\begin{array}{c}0\\ P_0\\ P_1\\ M\\ P_{K-1}\\ 0\end{array}\right]---\left(21\right)$

Wherein, V ₀, V ₁..., V _K+1It is the reference mark.Find the solution tri-diagonal matrix equation in the following formula with chasing method, obtain the reference mark V of three Uniform B-spline interpolation curves ₀, V ₁..., V _K+1

(5) the minimum and maximum brightness curved surface of computation vision unanimity.According to visual theory, the output brightness range of each point of virtual projection instrument is compressed in the different intervals.Calculating can reach the minimum and maximum brightness curved surface of vision unanimity, then the brightness range of each point is compressed to the minimum of vision unanimity and high-high brightness curved surface on the interval between the brightness value of this point.So both increased brightness range, the vision unanimity of each some brightness of the virtual projection instrument output of having got back.(u, the brightness value of v) locating is more arbitrarily in the minimum brightness curved surface of vision unanimity

$L^{\&prime;}(u,v)=\max (L\min (u,v),\mathrm{\&lambda;}\&times;\frac{|L\min (u,v)-L\min (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(22\right)$

Wherein, (u v) shows minimum sampling brightness SL for the virtual projection instrument to Lmin _MinThe brightness output image of correspondence is in that ((u ', v ') is that (Lmin (u ', v ') shows the sampling brightness SL of minimum for the virtual projection instrument for u, neighbor point v) for u, the v) brightness at coordinate place during the image that generates _MinThe brightness output image of correspondence is in the brightness at (u ', v ') coordinate place during the image that generates, and λ is the visually-perceptible coefficient, λ=50, and max is the function of maximizing.

(u, the brightness value of v) locating is more arbitrarily in the high-high brightness curved surface of vision unanimity

$L^{\&prime;\&prime;}(u,v)=\min (L\max (u,v),\mathrm{\&lambda;}\&times;\frac{|L\max (u,v)-L\max (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(23\right)$

Wherein, (u v) shows maximum sampling brightness SL for the virtual projection instrument to Lmax _MaxThe brightness output image of correspondence is in that ((u ', v ') is that (Lmax (u ', v ') shows the sampling brightness SL of maximum for the virtual projection instrument for u, neighbor point v) for u, the v) brightness at coordinate place during the image that generates _MaxThe brightness output image of correspondence is in the brightness at (u ', v ') coordinate place during the image that generates.

(6) according to virtual projection instrument every bit (x, the process of the input brightness of this point of the brightness calculation of the image of y) locating that will show on the B-spline curves of correspondence is as follows:

The first step: the reference mark of the B-spline curves of each location of pixels is packaged into little texture respectively, with the synthetic big reference mark texture of these all little textures.In our experiment each B-spline curves is calculated 32 reference mark.The horizontal ordinate at each reference mark and ordinate account for a passage in the texture respectively.For the 2 d texture of 4 passages, the texture size of 32 reference mark needs is 32*2/4=16.For the ease of the calculating of texture coordinate, little texture is stored by the mode of 4 row, 4 row.Large texture is stored each little texture by the mode of the capable xRes row of yRes, and wherein, xRes*yRes is the resolution of display device.So the size of big reference mark texture is (xRes*4) * (yRes*4).

Second step: (x y) locates, and the 3rd below repeating went on foot for the 6th step, obtains the brightness input behind the every bit gamma correction at each location of pixels of virtual projection instrument.By changing the brightness value of input, obtain consistent brightness output.

The 3rd step: the output brightness range that will put is compressed to the minimum of vision unanimity and high-high brightness curved surface on the interval between the brightness value of this point, the brightness that obtains the vision unanimity export Wl (x, y),

Wl(x，y)＝Lmin(x，y)+Ol(x，y)/255.0*(Lmax(x，y)-Lmin(x，y))

(24)

Wherein, (x is to make up the brightness of the image of demonstration at this some y) to Ol, and (x y) shows minimum sampling brightness SL for the virtual projection instrument to Lmin _MinThe brightness output image of correspondence is in the brightness of this some during the image that generates, and (x is that the virtual projection instrument shows maximum sampling brightness SL y) to Lmax _MaxThe brightness output image of correspondence is in the brightness of this some during the image that generates.

The 4th step: according to previous calculations obtain (x, the reference mark of three Uniform B-spline curves y) is with two end points P of the c section function of three Uniform B-spline curves of following formula calculating _c(0) and P _c(1),

$P_c\left(t\right)=\left[\begin{array}{cccc}1& t& t^2& {\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">t</figure-callout>}}^3\end{array}\right]\frac{1}{6}\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{V}_c\\ V_{c+1}\\ V_{c+2}\\ V_{c+3}\end{array}\right],$ 0≤t≤1，c＝0，1，...，K-1 (25)

Wherein, t is the coefficient parameter of B-spline curves, and c is the call number of function segment, and Pc (t) is each point between the c section function region of B-spline curves, Vc, Vc+1, Vc+2, Vc+3 are respectively that the call number of B-spline curves is for being respectively c, c+1, c+2, the reference mark of c+3; According to these end points Pc (0) and Pc (1), find the call number c between function region, (x is y) in the formed interval of ordinate value of two end points of c section function to make Wl.

The 5th step: with dichotomy calculate (x, the input brightness Nl after y) some brightness is proofreaied and correct (x, y).With [0,1] is between the parametric t original area, by getting interval mid point tm, original interval is divided into two.The ordinate E of the point during with formula (25) calculating parameter t=tm on the B-spline curves _pIf E _p(x y), is a half-interval on the left side between the newly developed area to＜Wl.If E _p(x y), is a half-interval on the right between the newly developed area to＞Wl.Constantly the interval is divided into two, the iteration said process is up to the error amount of interval range less than a setting.Getting parametric t is the midrange that iterates to last resulting interval, calculates the abscissa value of the point on the B-spline curves with formula (18), this value be exactly Wl (x, y) Dui Ying input brightness Nl (x, y).

(x y) multiply by the gamma correction template that obtains to the 6th step: Nl in (2) step, obtain the final brightness input of each projector.By changing the brightness value of input, obtain consistent brightness output.

Claims (1)

1. the brightness correcting method by pixel response of multi-projector free stereo demonstration is characterized in that, contains following steps successively:

Step (1): set up a variable resolution multi-projector auto-stereo display system with two visual point images of I=2, comprise: an array of rear-projectors, an auto-stereoscopic display screen curtain, be called for short screen, a digital camera, a server and a plurality of client computer below, wherein, array of rear-projectors is made up of 24 DLP projector, each visual point image is pressed the capable Nc row of Nr with Nr * Nc DLP projector on the auto-stereoscopic display screen curtain mode tiled display, Nr=3, Nc=4; Client computer has 12, two described DLP projector of every client computer control;

Step (2): described server carries out geometry correction to described multi-projector auto-stereo display system, and step is as follows:

Step (2.1): show the image of forming by the unique point of the equidistant distribution of setting respectively in the projector space of each projector frame buffer by each client, form projector space initial mesh meshp _Ij, i represents the sequence number of viewpoint, i=1, and 2, j represents the sequence number of pairing described DLP projector among each viewpoint i, j=1,2 ..., 11,12; Obtain the screen characteristics dot image that the unique point image projection of corresponding each the described DLP projector of each viewpoint forms respectively with described digital camera on described screen again, form the initial mesh meshd of screen space _Ij

Step (2.2): be calculated as follows j the correcting area dispW of projector on described screen in described i the viewpoint _Ij,

dispW _ij＝I(dispA _ij，rect)，i＝0，1，j＝1，2，…，11，12 (1)

Wherein, dispA _IjBe j the viewing area of projector on screen in i the viewpoint, rect is the zone that combination shows on the described screen,

$\mathrm{rect}=I_{i=1}^{\mathrm{Nv}}\left(\mathrm{inrect}\left(U_{j=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}{\mathrm{dispA}}_{\mathrm{ij}}\right)\right)---\left(2\right)$

In i viewpoint the summation of totally 12 DLP projector viewing areas on described screen use

Expression, one of inrect asks the function that connects rectangle in the given area;

Step (2.3): j correcting area dispW that the DLP projector shows on described screen in i viewpoint _IjIn regenerate by the unique point of described equidistant setting and be organized into described correcting area dispW _IjCalibration grid meshnd at described screen space _IjAgain according to the calibration grid meshnd of described screen space _IjThe coordinate (D of summit D _U,, D _v) calculate its corresponding projector free-air correction grid meshnp _IjCoordinate (the D of point D ' _x', D _y');

Calibration grid meshnd when described screen space _IjSummit D (D _U,, D _v) area coordinate be (m, k, in the time of w),

$m=\frac{S\left(\mathrm{\&Delta;ABD}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& B_u& D_u\\ A_v& B_v& D_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},k=\frac{S\left(\mathrm{\&Delta;DBC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{D}_u& B_u& C_u\\ D_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},w=\frac{S\left(\mathrm{\&Delta;ADC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}\frac{\left|\begin{array}{ccc}{A}_u& D_u& C_u\\ A_v& D_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}---\left(3\right)$

Wherein, Δ ABC is that the D point is at described initial mesh meshd _IjThe triangle at middle place, m is the interior triangle Δ ABD of Δ ABC and the ratio of the area of this triangle Δ ABC, k is the interior triangle Δ DBC of Δ ABC and the ratio of the area of this triangle Δ ABC, and w is the interior triangle Δ ADC of Δ ABC and the ratio of the area of this triangle Δ ABC, (A _u, A _v), (B _u, B _v) and (C _u, C _v) be three apex coordinates of Δ ABC;

Described projector free-air correction grid meshnp _IjCoordinate (the D of point D ' _x', D _y') be

$\left\{\begin{array}{c}{D}_x^{\&prime;}=m\&times;A_x^{\&prime;}+k\&times;B_x^{\&prime;}+w\&times;C_x^{\&prime;}\\ D_y^{\&prime;}=m\&times;A_y^{\&prime;}+k\&times;B_y^{\&prime;}+w\&times;C_y^{\&prime;}\end{array}\right.---\left(4\right)$

Wherein, Δ A ' B ' C ' is at described grid meshp _IjIn with described grid meshd _IjThe pairing triangle of Δ ABC, three apex coordinates of Δ A ' B ' C ' are respectively (A _x', A _y'), (B _x', B _y'), (C _x', C _y').

Step (2.4): be calculated as follows described server is distributed to j DLP projector in i the viewpoint by each client calibration grid meshnp _IjThe reference position (x of image ^IjStart, y ^IjStart), wide high width _IjAnd height _Ij, and distribute to described calibration grid meshnp _IjThe texture coordinate (xx on e summit _Ije, yy _Ije);

$\left\{\begin{array}{c}{x^{\mathrm{ij}}}_{\mathrm{start}}=[({u^{\mathrm{ij}}}_{\min }-u_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {y^{\mathrm{ij}}}_{\mathrm{start}}=[({v^{\mathrm{ij}}}_{\min }-v_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{\mathrm{width}}_{\mathrm{ij}}=[({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {\mathrm{height}}_{\mathrm{ij}}=[({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(6\right)$

$\left\{\begin{array}{c}{\mathrm{xx}}_{\mathrm{ije}}=(u_{\mathrm{ije}}-{u^{\mathrm{ij}}}_{\min })/({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })\\ {\mathrm{yy}}_{\mathrm{ije}}=(v_{\mathrm{ije}}-{v^{\mathrm{ij}}}_{\min })/({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })\end{array}\right.---\left(7\right)$

Wherein, width _IjAnd heigh _IjBe the calibration grid meshnp that described server-assignment is given j DLP projector in i the viewpoint _IjImage wide and high, wd and hd are image wide and high before projection of wanting tiled display on the described screen, (u _Min, v _Min) and (u _Max, v _Max) be the lower left corner of combination viewing area rect on the described screen and the apex coordinate in the upper right corner, u ^Ij _Min, u ^Ij _Max, v ^Ij _MinAnd v ^Ij _MaxBe respectively correcting area dispW _IjFour apex coordinates in minimum, the maximal value of minimum, maximal value and ordinate of horizontal ordinate, (u _Ije, v _Ije) be calibration grid meshnp _IjIn the coordinate of screen space of screen of e summit correspondence, i=1,2, j=1,2 ..., Nr*Nc;

Step (2.5): server will make up each client in the program each width of cloth image of demonstration, (2.4) reference position of calculating, the corresponding subimage of size intercepting are distributed to the clients corresponding computing machine set by step, so that the subimage that distributes is mapped to corresponding geometry correction grid meshnp by the described texture coordinate that calculates ^IjOn, again with projector projection output, on described screen, obtain the splicing effect of geometric alignment;

Step (3): adopt the brightness fusion method that transkit attenuation is carried out in the brightness at the edge of each DLP projector overlapping region on the screen described in the described multi-projector auto-stereo display system successively according to the following steps;

Step (3.1): the projector space each point (x, the intensity correction values A that y) locates that are calculated as follows j projector in i the viewpoint _Ij(x y), is combined into the gamma correction template of this j projector:

$A_{\mathrm{ij}}(x,y)={\left(\frac{a_{\mathrm{ij}}(u,v)}{{\mathrm{\&Sigma;}}_{j^{\&prime;}=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}{a}_{{\mathrm{ij}}^{\&prime;}}(u,v)}\right)}^{1/\mathrm{\&gamma;}}---\left(8\right)$

Wherein, (u, v) be j DLP projector of i viewpoint the projector space (x, y) Dui Ying screen space coordinates, i=1,2, j=1,2 ..., Nr*Nc, γ=2.4, a _Ij(u v) is the correcting area dispW of j projector of i viewpoint _IjIn the screen space point (u, v) arrive its four borders apart from minimum value, j '=1,2 ..., Nr*Nc, but j ' ≠ j and correcting area dispW _IjWith correcting area dispW _{Ij '}The overlapping region is arranged, a _{Ij '}(u v) is the correcting area dispW of i the individual projector of viewpoint j ' _{Ij '}In the screen space point (u, v) arrive its four borders apart from minimum value, at Non-overlapping Domain a _{Ij '}(u, v)=0;

Step (3.2): projection output again after the value correspondence of every bit in the value of the every bit of image after the projector geometry correction and the gamma correction template multiplied each other, thus the combination that obtains the brightness decay of projector overlapping region shows;

Step (3.3): (1) and step (2) are carried out projector image behind geometry and the gamma correction as the projected image of a virtual projection instrument set by step relevant all the DLP projector of each viewpoint;

Step (4): the irradiance value of calculating corresponding each sampling brightness input on each location of pixels of each described virtual projection instrument successively according to the following steps;

Step (4.1): get K sampled point by certain interval in the interval [0,255] of brightness value, for the ease of the storage computation of back, equilibration time and precision are got K=30, are calculated as follows the brightness value SL of 30 sampled points _k,

${\mathrm{SL}}_k=\left\{\begin{array}{cc}8\&times;(k-1)& 1\&le;k\&le;15\\ 8\&times;(k+2)& 15<k\&le;29\\ 255& k=30\end{array}\right.,$ k＝1，2…K

(9)

Step (4.2): generating size is K the image of xRes x yRes, K=30, wherein, xRes=1024, yRes=768; K image I _kIn every brightness identical, all be k sampling brightness value SL _k, k=1,2 ... K; Between 0.02s-2.0s, get S time shutter Δ t _s, s=1,2 ..., S, wherein S=16;

Step (4.3): all images to all virtual projection instrument and the generation of second step repeats following step (4.3.1)～step (4.3.2), obtains the irradiance value of corresponding each sampling brightness input on each pixel in each virtual projection instrument;

Step (4.3.1): for k image I of the generation of i the virtual projection instrument step display (4.2) described in the step (3.3) _kProjection result on screen is Δ t camera being set the time shutter respectively _s, s=1,2 ..., S, after take pictures, obtaining the individual size of S ' is the image of xcRes x ycRes, wherein, S '=S, xcRes and ycRes are respectively the wide and high of camera image, xcRes=2288, ycRes=1520;

Step (4.3.2): with setting time shutter Δ t _sThe take pictures brightness value Z of p point in the described image of obtaining step (4.3.1) of camera _PsIrradiance E with this point _p,

$\ln E_p=\frac{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(z_{\mathrm{ps}}\right)(g\left(Z_{\mathrm{ps}}\right)-\ln \mathrm{\&Delta;}{t}_S)}{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)},$ p＝1，2...P (10)

Wherein, P is the number of pixels in each image, P=2288*1520, function g (Z _Ps) be Z _PsAnd E _pWith Δ t _sThe mapping relations of logarithmic function,

g(Z _ps)＝lnE _p+lnΔt _s (11)

W (Z _Ps) be to distribute to brightness Z _PsWeight,

$w\left(Z_{\mathrm{ps}}\right)=\left\{\begin{array}{cc}{Z}_{\mathrm{ps}}-Z_{\min }& Z_{\mathrm{ps}}\&le;Z_{\mathrm{mid}}\\ Z_{\max }-Z_{\mathrm{ps}}& Z_{\mathrm{ps}}>Z_{\mathrm{mid}}\end{array}\right.---\left(12\right)$

Step (4.3.3): in order to obtain exporting one to one at screen space with the input position of described virtual projection instrument, on each described irradiance image mapped to a grid of the correspondence that each described DLP projector is calculated step (4.3.2), and the irradiance image overlay on these grids is obtained together the output of virtual projection instrument; The coordinate on each summit on the grid (x, y) and texture coordinate (tex_x tex_y) is respectively

$\left\{\begin{array}{c}x=(D_u-\min x)/(\max x-\min x)*\mathrm{xRes}\\ y=(D_v-\min y)/(\max y-\min y)*\mathrm{yRes}\end{array}\right.---\left(13\right)$

$\left\{\begin{array}{c}\mathrm{tex}\_x=D_u/\mathrm{xcRes}\\ \mathrm{tex}\_y=D_v/\mathrm{ycRes}\end{array}\right.---\left(14\right)$

Wherein, (D _u, D _v) be that summit on the calibration grid of each projector is at the coordinate of screen space, (minx, miny) and (maxx, maxy) be the upper left corner of whole correcting area and the lower right corner coordinate respectively at screen space, xRes and yRes divide the wide and high of the image that maybe make up demonstration, and xcRes and ycRes are respectively the wide and high of camera image;

Step (5): on each pixel of virtual projection instrument, generate K some P _k, k=0,1 ... K-1, K=30, wherein, k some P _kHorizontal ordinate be k+1 at this pixel place sampling brightness value, the irradiance value that ordinate calculates the brightness value input of should sampling for this pixel place; In order to obtain the corresponding relation of continuous input and output brightness, calculate being three Uniform B-spline interpolation curves of this K point, and obtain the reference mark of B-spline curves by following formula,

$\left[\begin{array}{cccccc}6& -6& & & & 0\\ 1& 4& 1& & & \\ & 1& 4& 1& & \\ & & O& O& O& \\ & & & 1& 4& 1\\ 0& & & & -6& 6\end{array}\right]\left[\begin{array}{c}{V}_0\\ V_1\\ V_2\\ M\\ V_K\\ V_{K+1}\end{array}\right]=\left[\begin{array}{c}0\\ P_0\\ P_1\\ M\\ P_{K-1}\\ 0\end{array}\right]---\left(15\right)$

Wherein, V ₀, V ₁..., V _K+1It is the reference mark.Find the solution tri-diagonal matrix equation in the following formula with chasing method, obtain the reference mark V of three Uniform B-spline interpolation curves ₀, V ₁..., V _K+1

Step (6): (u, the brightness value of v) locating is more arbitrarily in the minimum brightness curved surface of vision unanimity in the calculating screen space

$L^{\&prime;}(u,v)=\max (L\min (u,v),\mathrm{\&lambda;}\&times;\frac{|L\min (u,v)-L\min (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(16\right)$

Wherein, (u v) shows minimum sampling brightness SL for the virtual projection instrument to Lmin _MinThe brightness output image of correspondence is in that ((u ', v ') is that (Lmin (u ', v ') shows the sampling brightness SL of minimum for the virtual projection instrument for u, neighbor point v) for u, the v) brightness at coordinate place during the image that generates _MinThe brightness output image of correspondence is in the brightness at (u ', v ') coordinate place during the image that generates, and λ is the visually-perceptible coefficient, λ=50, and max is the function of maximizing;

(u, the brightness value of v) locating is more arbitrarily in the high-high brightness curved surface of vision unanimity in the calculating screen space

$L^{\&prime;\&prime;}(u,v)=\min (L\max (u,v),\mathrm{\&lambda;}\&times;\frac{|L\max (u,v)-L\max (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(17\right)$

Wherein, (u v) shows maximum sampling brightness SL for the virtual projection instrument to Lmax _MaxThe brightness output image of correspondence is in that ((u ', v ') is that (Lmax (u ', v ') shows the sampling brightness SL of maximum for the virtual projection instrument for u, neighbor point v) for u, the v) brightness at coordinate place during the image that generates _MaxThe brightness output image of correspondence is in the brightness at (u ', v ') coordinate place during the image that generates;

Step (7): successively according to the following steps according to virtual projection instrument every bit (x, the process of the input brightness of this point of the brightness calculation of the image of y) locating that will show on the B-spline curves of correspondence is as follows:

Step (7.1): the reference mark of the B-spline curves of each location of pixels is packaged into little texture respectively, with the synthetic big reference mark texture of these all little textures; Each B-spline curves is calculated 32 reference mark; The horizontal ordinate at each reference mark and ordinate account for a passage in the texture respectively; For the 2 d texture of 4 passages, the texture size of 32 reference mark needs is 32*2/4=16; For the ease of the calculating of texture coordinate, little texture is stored by the mode of 4 row, 4 row.Large texture is stored each little texture by the mode of the capable xRes row of yRes, and wherein, xRes*yRes is the resolution of display device; So the size of big reference mark texture is (xRes*4) * (yRes*4);

Step (7.2): (x y) locates, and step (the 7.2.1)～step (7.2.4) below repeating obtains the brightness input behind the every bit gamma correction at each location of pixels of virtual projection instrument; By changing the brightness value of input, obtain consistent brightness output;

Step (7.2.1): the output brightness range that will put is compressed to the minimum of vision unanimity and high-high brightness curved surface on the interval between the brightness value of this point, obtain the vision unanimity brightness output Wl (x, y),

Wl(x，y)＝Lmin(x，y)+Ol(x，y)/255.0*(Lmax(x，y)-Lmin(x，y)) (18)

Wherein, (x is to make up the brightness of the image of demonstration at this some y) to Ol, and (x y) shows minimum sampling brightness SL for the virtual projection instrument to Lmin _MinThe brightness output image of correspondence is in the brightness of this some during the image that generates, and (x is that the virtual projection instrument shows maximum sampling brightness SL y) to Lmax _MaxThe brightness output image of correspondence is in the brightness of this some during the image that generates;

Step (7.2.2): according to previous calculations obtain (two end points P of the c section function of three Uniform B-spline curves are calculated at x, the reference mark of three Uniform B-spline curves y) with following formula _c(0) and P _c(1),

$P_c\left(t\right)=\left[\begin{array}{cccc}1& t& t^2& t^3\end{array}\right]\frac{1}{6}\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{V}_c\\ V_{c+1}\\ V_{c+2}\\ V_{c+3}\end{array}\right],$ 0≤t≤1，c＝0，1，...，K-1 (19)

Wherein, t is the coefficient parameter of B-spline curves, and c is the call number of function segment, P _c(t) be each point between the c section function region of B-spline curves, V _c, V _C+1, V _C+2, V _C+3The call number that is B-spline curves respectively is for being respectively c, c+1, c+2, the reference mark of c+3; According to these end points P _c(0) and P _c(1), find the call number c between function region, (x is y) in the formed interval of ordinate value of two end points of c section function to make Wl;

Step (7.2.3): with dichotomy calculate (x, the input brightness Nl after y) some brightness is proofreaied and correct (x, y): with [0,1] is between the parametric t original area, by getting interval mid point tm, original interval is divided into two; The ordinate E of the point during with formula (19) calculating parameter t=tm on the B-spline curves _pIf (x y), is a half-interval on the left side between the newly developed area to Ep＜Wl; If (x y), is a half-interval on the right between the newly developed area to Ep＞Wl; Constantly the interval is divided into two, the iteration said process is up to the error amount of interval range less than a setting; Getting parametric t is the midrange that iterates to last resulting interval, calculates the abscissa value of the point on the B-spline curves with formula (18), this value be exactly Wl (x, y) Dui Ying input brightness Nl (x, y);

(x y) multiply by the gamma correction template that obtains to step (7.2.4): Nl in step (3), obtain the final brightness input of each projector; By changing the brightness value of input, obtain consistent brightness output.

Images