CN105303535A - Global subdivision pyramid model based on wavelet transformation - Google Patents
Global subdivision pyramid model based on wavelet transformation Download PDFInfo
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Abstract
The invention provides a global subdivision pyramid model based on wavelet transformation and belongs to the technical field of image processing. The invention aims to adopt the wavelet transformation technology to construct an image pyramid for remote sensing images large in data size. Image wavelet decomposition comprises the steps of: (1) wavelet transformation; (2) multi-resolution analysis and Mallat algorithm calculation; (3) two-dimensional Mallat algorithm calculation; and (4) wavelet decomposition of the images. Then, the pyramid model is constructed based on wavelet transformation. The wavelet transformation technology performs well in the field of image processing and has good capability for representing signal local characteristics in both a time domain and a frequency domain, so that an effective mathematic tool is provided for image processing. In addition, the multi-resolution analysis characteristic of wavelet transformation is naturally similar to the image pyramid model. With regard to the improved pyramid model, data redundancy is effectively reduced, the data amount of network transmission is simultaneously reduced, and the progressive transmission and display mode is supported.
Description
Technical field
The invention belongs to technical field of image processing.
Background technology
Multiresolution image pyramid model is that one multiresolution carrys out organization and management significantly image effectively simple spatial hierarchy.By generating multiresolution image pyramid to remote sensing image resource, without the need to real-time resampling, can according to different displays and application demand, the image of the multiple resolution of quick obtaining, the fast roaming realizing mass remote sensing image is browsed and Zoom display.When zoom operations, seamless switching can also be realized.
For traditional multiresolution image pyramid model, its conventional method built is: using the bottom of image the highest for resolution as pyramid model, then carry out piecemeal to it, be defined as the 0th layer of Block matrix.On the basis of the bottom, travel through adjacent 2 successively
×2 image blocks, and to resampling after these 4 image blocks splicings, set up the image blocks that a series of resolution only has the 0th layer of half, form the 1st layer of Block matrix, but the scope that whole picture represents remains unchanged.Generation the 2nd layer of Block matrix that use the same method is adopted again on the basis of the 1st layer.So go down, generate image the 3rd, 4,5 ... layer, till the resolution of the final top image data set up meets the demands, forms whole image pyramid.Because its each layer image is all Block matrix distribution, therefore this pyramid model is generally also referred to as tile pyramid.
Theoretically, although the image pyramid model that said method builds can increase by the storage space of about 1/3, but for a large amount of remote sensing image data amounts, the reading of data, transmission and display efficiency can be significantly improved, and there is good data buffering characteristic and good parallel characteristics, be a kind of conceptual model of typically trading space for time.
Because the data volume of remote sensing image is huge, as direct construction image pyramid, storing, scheduling and transmission time the Time and place that expends all very large, sometimes or even be difficult to accept, therefore, the resampling that adopts of image pyramid and compression algorithm just seem extremely important.
Summary of the invention
The object of the invention is to adopt wavelet transformation technique to build the global subdivision pyramid model based on wavelet transformation of image pyramid to the remote sensing image that data volume is huge.
Image wavelet decomposition step of the present invention is:
(1) wavelet transformation: by square-integrable real number space
in a function
by a mother wavelet
after flexible and translation in time domain, resolve into a series of subband signal superposition with different spatial resolutions, different frequency characteristic and directivity characteristics;
If
, its Fourier transform
meet admissibility condition:
(3.1)
Namely
bounded, now,
be called as a mother wavelet or wavelet mother function, will
through stretching and after translation, obtaining a wavelet sequence:
(3.2)
Wherein,
be called as contraction-expansion factor or scale parameter,
be called as translation location parameter;
Function
?
space is about mother wavelet
continuous wavelet transform be defined as follows:
(3.3)
Will
integrated form expand into discrete and form, then function
?
wavelet transform is spatially defined as:
(3.4)
Wherein,
,
,
; Conventional is dyadic wavelet, namely
,
, now,
;
If
orthonormal, coefficient
just be expressed as by inner product:
(3.5)
(2) multiresolution analysis and Mallat algorithm:
If
in a series of subspaces
meet following condition, then can be called
one two enter multiresolution:
A. monotonicity:
,
;
B. Approximation:
,
;
C. retractility:
,
;
D. translation invariance:
,
;
E.Riesz base existence: existence function
, make
form
riesz base;
Then certainly exist coefficient sequence
, following equation is set up:
(3.6)
Wherein,
it is metric space
canonical orthogonal basis function, be called scaling function;
For wavelet space
, then have following equation to set up:
(3.7)
Wherein,
it is wavelet space
canonical orthogonal basis function, be called wavelet function;
For any given function
, it is projected to respectively
with
space, then have:
(3.8)
Wherein,
be called scale coefficient,
being called wavelet coefficient, can obtaining through deriving:
(3.9)
(3.10)
Formula (3.9) and formula (3.10) are brought into, obtains respectively
with
the scale coefficient in space and wavelet coefficient:
(3.11)
For any given one-dimensional discrete signal
, often once decompose the part that will produce two length and reduce by half,
be decomposed into
,
...,
with
, concrete formula is:
(3.12)；
(3) two-dimentional Mallat algorithm:
If
for two dimensional image signal, resolution filter first carries out once " OK " to image and decomposes, and then carries out once " row " decomposition, each decomposition generation four subbands
,
,
with
, it is the low frequency sub-band produced in previous stage that next stage decomposes
basis on to carry out;
Two dimension Mallat decomposition algorithm is as follows:
（3.13)
Wherein,
with
be respectively given low-pass filter and the coefficient of Hi-pass filter;
Two dimension Mallat restructuring procedure is then the inverse process of above-mentioned decomposable process,
（3.14）；
(4) wavelet decomposition of image:
According to two-dimentional Mallat algorithm, take original image as initial value, first wavelet transformation is carried out to each row of image, respectively filtering is carried out to each row of image with low-pass filter and Hi-pass filter, and decimation, keep data volume constant, obtain H and L two parts, then use the same method and a wavelet transformation is carried out to each row obtaining image again, like this after one deck wavelet transformation, picture breakdown is four subband LL, HL, LH, HH, low-frequency information in the corresponding upper level image of they difference is with vertical, the information of level and diagonal, from multiresolution analysis, each is decomposed again to the low frequency subgraph picture of upper level, obtain LL
2, HL
2, LH
2, HH
2, the rest may be inferred, carries out multi-level decomposition to image, carries out
secondary decomposition just can obtain
individual subband.
The step that the present invention is based on wavelet transformation structure pyramid model is:
(1) according to the highest resolution of original remote sensing image data, obtain total number of plies J of image pyramid, determined by table 3.1, then be the relation of 2 times according to resolution between adjacent layer, determine the pyramid level L that the remote sensing image of existing N kind resolution is corresponding, the corresponding from high to low level of resolution is respectively L
1, L
2,
, L
n , L
n, the L that resolution is the highest
1corresponding 0th layer;
Table 3.1 pyramid level and highest resolution, bottom image blocks quantity corresponding relation
(2) according to the resolution of existing remote sensing image, determined the subdivision level of its global subdivision graticule mesh by table 3.2, carry out subdivision process according to split surface blade unit size, form remote sensing image dough sheet;
Corresponding relation between table 3.2 subdivision progression and image resolution
(3) number of times that existing remote sensing image needs wavelet decomposition is calculated respectively
:
(3.15)
(4) number of times is determined
after, existing remote sensing image is carried out respectively
secondary wavelet decomposition, utilizes the multiresolution analysis characteristic of small echo, and each " existing layer " obtains a low frequency sub-band
with a series of high-frequency sub-band
,
,
,
,
,
,
;
(5) by low frequency sub-band that existing remote sensing image decomposes out
fill it in image pyramid corresponding the
layer, first order high-frequency sub-band
,
,
be 2 in spatial domain cutting
×after 2 equal portions, put into image pyramid
the relevant position of layer, each Block matrix of this layer stores three high-frequency sub-band simultaneously
,
,
corresponding fritter after cutting, second level high-frequency sub-band
,
,
be 4 in spatial domain cutting
×image pyramid is put into after 4 equal portions
the relevant position of layer, the like, until fill up whole image pyramid.
Wavelet transformation technique of the present invention, in image processing field exhibits excellent, all has the ability of good characterization signal local feature in time domain and frequency domain, for image procossing provides effective mathematical tool.In addition, the multiresolution analysis feature of wavelet transformation and image pyramid model also have natural similarity.The pyramid model improved significantly reduces data redundancy, reduces the data volume of Internet Transmission simultaneously, and supports progressive transmission and display.
Accompanying drawing explanation
Fig. 1 is Mallat algorithm decomposable process schematic diagram;
Fig. 2 is Mallat algorithm restructuring procedure schematic diagram;
Fig. 3 is Mallat algorithm two-dimensional wavelet transformation decomposing schematic representation;
Fig. 4 is Mallat algorithm two-dimensional wavelet transformation reconstruct schematic diagram;
Fig. 5 is the wavelet decomposition schematic diagram of image, and wherein (a) is raw video, and (b) is 1 grade of wavelet decomposition schematic diagram, and (c) is 2 grades of wavelet decomposition schematic diagram;
Fig. 6 is original remote sensing image;
Fig. 7 is the wavelet decomposition of remote sensing image, wherein (a) be remote sensing image 1 grade of wavelet decomposition, 2 grades of wavelet decomposition that (b) is remote sensing image;
Fig. 8 is the basic building flow process of the global subdivision gold word model based on wavelet transformation;
Fig. 9 is the layering building process of image pyramid spatial domain cutting;
Figure 10 is the layering building process of image pyramid;
Figure 11 is three width test remote sensing images;
Figure 12 is that testing image is decomposed and the image reconstructed by different wavelet basis, (a) testing image, b () haar decomposes and the image reconstructed, c () db2 decomposes and the image reconstructed, d () db4 decomposes and the image reconstructed, e () bior2.2 decomposes and the image reconstructed, (f) bior4.4 decomposes and the image reconstructed;
Figure 13 is two kinds of pyramid model construction method contrasts, (a) traditional image pyramid construction method, the image pyramid construction method that (b) improves;
Figure 14 is the design sketch of image blocks progressive transmission, (a) the 3rd layer image, the image of (b) the 2nd, 3 layers reconstruct, the image of (c) the 1st, 2,3 layers reconstruct, the image of (d) the 0th, 1,2,3 layer reconstruct;
Data volume comparison diagram during Figure 15 two kinds of pyramid model transmission images.
Embodiment
Image wavelet decomposition step of the present invention is:
(1) wavelet transformation: the small echo in wavelet transformation is exactly little waveform, so-called " little " refers to that its Decay Rate, " ripple " refer to its undulatory property.By square-integrable real number space
in a function
by a mother wavelet
after flexible and translation in time domain, resolve into a series of subband signal superposition with different spatial resolutions, different frequency characteristic and directivity characteristics;
If
, its Fourier transform
meet admissibility condition:
(3.1)
Namely
bounded, now,
be called as a mother wavelet or wavelet mother function, will
through stretching and after translation, obtaining a wavelet sequence:
(3.2)
Wherein,
be called as contraction-expansion factor or scale parameter, it determines the frequency span of wave filter, thus determines the frequency information in wavelet transformation.
be called as translation location parameter, which determine the time-domain information in transformation results.
Function
?
space is about mother wavelet
continuous wavelet transform be defined as follows:
(3.3)
In actual applications, usually need form original signal being decomposed into discrete superposition, i.e. summation instead of integration, namely will
integrated form expand into discrete and form, then function
?
wavelet transform is spatially defined as:
(3.4)
Wherein,
,
,
; Conventional is dyadic wavelet, namely
,
, now,
;
If
orthonormal, coefficient
just be expressed as by inner product:
(3.5)。
(2) multiresolution analysis and Mallat algorithm:
Multiresolution analysis (MRA) is exactly at function space
in, will
be decomposed into a series of sequence of subspaces with different resolution
, the limit of these sequences of subspaces is exactly
, then by space
in function
be described as the limit of a series of approximate function, that is function can be shown in space
in approximate representation
the limit.These are similar to and all obtain on different scale, and multiresolution analysis is gained the name thus.
If
in a series of subspaces
meet following condition, then can be called
one two enter multiresolution:
A. monotonicity:
,
.
B. Approximation:
,
.
C. retractility:
,
.
D. translation invariance:
,
.
E.Riesz base existence: existence function
, make
form
riesz base;
According to above-mentioned theory, define one to space
the sequence of subspaces approached gradually
, then coefficient sequence is certainly existed
, following equation is set up:
(3.6)
Wherein,
it is metric space
canonical orthogonal basis function, be called scaling function; This is because
, and
form
a Riesz base.
According to multiresolution analysis theory, the subdivision step by step of metric space
, have
,
,
,
,
, wherein
for
?
in the orthogonal complement space, contain from
layer arrives
the detailed information of layer.For wavelet space
, then have following equation to set up:
(3.7)
Wherein,
it is wavelet space
canonical orthogonal basis function, be called wavelet function;
The mathematical relation that what formula (3.6) and formula (3.7) described is between adjacent two metric space basis functions, is called two-scale equation.
Under the theoretical frame of multiresolution analysis, bank of filters is combined with wavelet conversion coefficient by Mallat, utilizes the characteristic of QMF compression in multiresolution analysis theory, proposes the fast algorithm of wavelet transform, i.e. Mallat algorithm.
For any given function
, it is projected to respectively
with
space, then have:
(3.8)
Wherein,
be called scale coefficient,
being called wavelet coefficient, can obtaining through deriving:
(3.9)
(3.10)
Formula (3.6) and formula (3.7) are carried out flexible and translation to the time, and formula (3.9) and formula (3.10) are brought into, obtain respectively
with
the scale coefficient in space and wavelet coefficient:
(3.11)
Above formula illustrates,
the scaling function in space and
the wavelet function in space can be by
the scaling function in space is through wave filter
with
be weighted summation to obtain, thus obtain the decomposition on any metric space, formula (3.11) is exactly QMF compression algorithm.
For any given one-dimensional discrete signal
, the low frequency component of a reflection upper level signal general picture
, the high fdrequency component of another reflection upper level signal detail
.Concrete decomposable process as shown in Figure 1, often once decomposes the part that will produce two length and reduce by half,
be decomposed into
,
...,
with
, as shown in Figure 2, concrete formula is its restructuring procedure:
(3.12)。
(3) two-dimentional Mallat algorithm:
By Mallat algorithm application in remote sensing image process field, just it must be generalized to two-dimensional space from one dimension.If
for two dimensional image signal, resolution filter first carries out once " OK " to image and decomposes, and then carries out once " row " decomposition, this completes the once decomposition to signal of video signal, each decomposition generation four subbands
,
,
with
, it is the low frequency sub-band produced in previous stage that next stage decomposes
basis on to carry out; The decomposable process of two dimension Mallat algorithm as shown in Figure 3, wherein
represent in every two row (column) and take out a row (column).
Two dimension Mallat decomposition algorithm is as follows:
（3.13)
Wherein,
with
be respectively given low-pass filter and the coefficient of Hi-pass filter; Under each yardstick,
comprise the low-frequency information of this time decomposing, and
,
,
comprise the level of this time decomposing, vertical and edge detail information to angular direction respectively.For
the image of pixel, can decompose at most
it is secondary,
, wherein
for rounding downwards.
Two dimension Mallat restructuring procedure is then the inverse process of above-mentioned decomposable process, formula as shown in (3.14), detailed process as shown in Figure 4, wherein
represent and insert a row (column) between every two row (column).
（3.14）；
Wavelet transformation has good frequency-domain and time-domain analytical characteristics simultaneously, and effectively can isolate high fdrequency component and the low frequency component of raw video, low frequency component comprises the main information of image, carries higher energy; And high fdrequency component mainly comprises the details of image, edge and profile information, the energy carried is lower.
(4) wavelet decomposition of image:
According to two-dimentional Mallat algorithm, take original image as initial value, first wavelet transformation is carried out to each row of image, respectively filtering is carried out to each row of image with low-pass filter and Hi-pass filter, and decimation, keep data volume constant, obtain H and L two parts, then use the same method and a wavelet transformation is carried out to each row obtaining image again, like this after one deck wavelet transformation, picture breakdown is four subband LL, HL, LH, HH, low-frequency information in the corresponding upper level image of they difference is with vertical, the information of level and diagonal, from multiresolution analysis, each is decomposed again to the low frequency subgraph picture of upper level, obtain LL
2, HL
2, LH
2, HH
2, the rest may be inferred, carries out multi-level decomposition to image, carries out
secondary decomposition just can obtain
individual subband.Figure 5 shows that 1,2 grade of wavelet decomposition schematic diagram.
In Fig. 5 (b), low frequency sub-band LL, comprise substance and the principal character of original image, but lose the detailed information such as some edges, texture and profile, these information have been assigned in other three sub-band images, and high-frequency sub-band HL, LH, HH comprise the detailed information of image in level, vertical and diagonal respectively.
Fig. 6 is original remote sensing image, and Fig. 7 carries out to Fig. 6 the image that 1,2 grade of wavelet decomposition obtains, and that adopt here is wave filter db4 corresponding to Daubechies small echo.
Thus show that in fact every one-level wavelet decomposition of image is exactly the low-frequency information of upper level divided meticulousr, form the image of multiple resolution.The multiresolution analysis characteristic of small echo provides possibility for building multiresolution image pyramid based on wavelet transformation.
Although traditional pyramid simple structure, be convenient to realize, be data model conventional in the practice of huge image data management engineering, also have that following some is not enough:
1. remote sensing image is compressed into independently different resolution Block matrix by traditional image pyramid in advance, is stored in pyramidal different layers, causes correlativity between different layers higher, there is certain data redundancy.
2. because the image blocks of different resolution is between layers separate, user is when Zoom display, the data of different layers can only be called as required, cannot utilize and transmit and the image data obtained, generally also not support embedded bitstream and progressive transmission.
3. current, overwhelming majority tile image pyramid is based upon on the basis of plane projection, when processing global image data, subregion (as high latitude area) has larger error, distance under Global Scale, orientation and areal calculation out of true, spatial data is discontinuous, is also difficult to realize browsing based on the seamless of sphere.
Therefore, in order to overcome the deficiency of traditional image pyramid, realize browsing based on continuous, the gradual roaming of global sphere, convergent-divergent, reduce data redundancy, utilize the advantage of global subdivision graticule mesh and wavelet transformation herein, they are combined with multiresolution image pyramid, propose a kind of pyramid model of improvement---based on the global subdivision pyramid model of wavelet transformation, improve the management of mass remote sensing image data, scheduling, the efficiency of transmission and visual effect.
Express to realize spatial data that is global seamless, rule, need first to complete pretreated remote sensing image and carry out subdivision according to global subdivision graticule mesh, the progression of subdivision model can be determined by the resolution of remote sensing image, and image resolution and subdivision progression are generally just like the corresponding relation shown in table 3.2.
There are two kinds of situations when building image pyramid, if original remote sensing image only has a kind of resolution, then obtain pyramidal each layer by carrying out process to this layer data; If original remote sensing image comprises the data source of multiple resolution, as the Landsat7ETM image of the IKONOS image of the WorldView image of 0.5 meter of resolution, 1 meter of resolution, the SPOT image of 10 meters of resolution and 15 meters of resolution, these existing image datas itself can form the respective layer of image pyramid respectively, and other layer data pyramidal then obtain by existing data Layer nearest below it.
Based on above consideration, multiple resolution is had below for original remote sensing image, the conventional method of image pyramid model construction is optimized and is improved, discuss the structure flow process of the global subdivision pyramid model based on wavelet transformation designed herein, as shown in Figure 8, detailed process is as follows for basic procedure:
The step that the present invention is based on wavelet transformation structure pyramid model is:
(1) according to the highest resolution of original remote sensing image data, obtain total number of plies J of image pyramid, determined by table 3.1, then be the relation of 2 times according to resolution between adjacent layer, determine the pyramid level L that the remote sensing image of existing N kind resolution is corresponding, the corresponding from high to low level of resolution is respectively L
1, L
2,
, L
n , L
n, the L that resolution is the highest
1corresponding 0th layer;
Table 3.1 pyramid level and highest resolution, bottom image blocks quantity corresponding relation
(2) according to the resolution of existing remote sensing image, determined the subdivision level of its global subdivision graticule mesh by table 3.2, carry out subdivision process according to split surface blade unit size, form remote sensing image dough sheet;
Corresponding relation between table 3.2 subdivision progression and image resolution
(3) number of times that existing remote sensing image needs wavelet decomposition is calculated respectively
:
(3.15)
(4) number of times is determined
after, existing remote sensing image is carried out respectively
secondary wavelet decomposition, utilizes the multiresolution analysis characteristic of small echo, and each " existing layer " obtains a low frequency sub-band
with a series of high-frequency sub-band
,
,
,
,
,
,
;
(5) by low frequency sub-band that existing remote sensing image decomposes out
fill it in image pyramid corresponding the
layer, first order high-frequency sub-band
,
,
be 2 in spatial domain cutting
×after 2 equal portions, put into image pyramid
the relevant position of layer, each Block matrix of this layer stores three high-frequency sub-band simultaneously
,
,
corresponding fritter after cutting, second level high-frequency sub-band
,
,
be 4 in spatial domain cutting
×image pyramid is put into after 4 equal portions
the relevant position of layer, the like, until fill up whole image pyramid.Its layering building process as shown in Figure 9.
In Fig. 10, suppose the remote sensing image of existing Resolutions, be respectively
,
, in the corresponding pyramid of its resolution difference
with
layer.According to above-mentioned theory, the number of times of wavelet decomposition is needed to be respectively
,
.Then after wavelet decomposition, insert each layer of image pyramid to existing image subdivision, in this example, each layer of image pyramid is respectively:
what store is
low frequency sub-band
,
what store is
one-level high-frequency sub-band
,
,
,
what store is
secondary high-frequency sub-band
,
,
,
what store is
low frequency sub-band
,
what store is
secondary high-frequency sub-band
,
,
.
The image pyramid model formed by above-mentioned construction strategy, the present invention is called the global subdivision pyramid model based on wavelet transformation.Due to the wavelet decomposition that this remote sensing image pyramid model is original image data, the different frequency of the corresponding original image of each layer, therefore, effectively can reduce correlativity between each layer of pyramid, reduce the data redundancy between pyramid each level, and substantially can eliminate increase when traditional image pyramid builds about
data volume.
To image by entirety to local roaming, browse time, as needed the remote sensing image data of certain the high resolving power level in image pyramid, can according to reality, read and transmit low frequency component and the high fdrequency component of corresponding level between them of the image data nearest to its resolution, then being obtained by wavelet inverse transformation reconstruct.Such pyramid model is applicable to the stream transmission of image data very much.When user's convergent-divergent is browsed, existing low resolution image data (low frequency sub-band) can be utilized, only need the high-frequency sub-band that transmission is corresponding, thus reduce the data traffic of transmission.
The data structure of image blocks:
According to correlation theory and the above-mentioned construction strategy of image pyramid, the present invention devises the related data structures towards the remote sensing image pyramid model improved, and the data structure false code of each image blocks is described below:
typedefstructpyramidTILE_struct
{
Inti_r, i_c; // image blocks size, is respectively the pixel count in row, column direction here
Doubleres_r, res_c; // image blocks is expert at, the resolution of column direction, the longitude and latitude number of degrees that every pixel represents
DoubleLeftup_L, Leftup_B; The longitude and latitude of // image blocks top left corner pixel
DoubleRightdown_L, Rightdown_B; The longitude and latitude of // image blocks lower right corner pixel
IntPyramid_lvl; The pyramidal level in // place
StringWavelet_Name; The wavelet basis title that // wavelet transformation uses
IntWavelet_lvl; The progression of // wavelet decomposition
}
Above-mentioned data structure just contains the essential information of image blocks, also can add the data such as image blocks ID, wave band, channel bit number in practical application.The data structure of the just single image blocks more than provided itself.
The selection of wavelet basis in pyramid model:
When according to above-mentioned the Theory Construction image pyramid, during wavelet decomposition, the selection of wavelet basis is extremely important, the performance of different wavelet basiss in image reconstruction effect and computation complexity is different, also will finally have influence on performance and the effect of visualization of image pyramid.
The mathematical characteristic of wavelet basis comprises the aspects such as linear phase feature (i.e. orthogonality), compactly support characteristic, symmetry, regularity and vanishing moment.In actual applications, the selection of wavelet basis mainly consider following some:
1. the regularity of wavelet basis is higher, and small echo is more level and smooth, and blocking artifact is more not obvious;
2. the wavelet basis that vanishing moment is larger, the energy after conversion is more concentrated, and the ratio of compression of image is also higher, but calculated amount can increase;
3. the width of compactly support can have influence on the localization property of small echo, and compactly support width is less, and localization property is better, and the complexity of calculating is also lower, is convenient to quick realization;
4., although biorthogonal wavelet sacrifices a part of orthogonality, its other performances are better than orthogonal wavelet;
5. should consider the relation between each mathematical property of wavelet basis, choose applicable wavelet basis.
In sum, the present invention have chosen 5 conventional wavelet basiss and tests, comprise haar, db2, db4, bior2.2 and bior4.4, analyzed their performance and effect by contrast experiment, table 3.3 gives orthogonality, symmetry, the parameter such as bearing length and vanishing moment of these 5 wavelet basiss.
The mathematical characteristic of wavelet basis commonly used by table 3.3
The present invention has selected 3 width remote sensing images so that the impact of different wavelet basis on image reconstruction effect and efficiency to be described, 3 width testing images as shown in figure 11.
The 5 groups of wavelet basiss chosen with the present invention remote sensing image different to above-mentioned 3 width carries out wavelet decomposition, decomposing level is 6, but do not carry out quantizing and entropy code, simultaneously for making test effect comparatively obvious, here larger 15% is only retained in wavelet coefficient, filling with 0 of other, is then reconstructed image.Experiment adopts Y-PSNR (PSNR) as the objective evaluation standard of the quality of image, obtain often kind of wavelet basis respectively to decompose 3 width remote sensing images and the Y-PSNR reconstructed and the time expended, often group is tested in triplicate and is averaged, and experimental result is as shown in table 3.4.
Table 3.4 three width remote sensing image is to the signal to noise ratio (S/N ratio) of different wavelet basis and contrast consuming time
Figure 12 (a) is the width raw video in test remote sensing image, and Figure 12 (b), (c), (d), (e), (f) are decomposed and the result reconstructed by different wavelet basis for testing image (a).
As can be seen from the above experimental data, the Y-PSNR of bior4.4 small echo is the highest, and edge details is all better than other wavelet basis in the same circumstances, and visual effect is best, but it is longer to expend time in.Because mass remote sensing image management mainly solves efficiency when image scheduling, transmission, display, so the present invention selects Y-PSNR lower slightly, but the bior2.2 small echo expending time in shorter.
Experimental result and analysis:
According to the global subdivision pyramid model based on wavelet transformation of the present invention's design, now test with the remote sensing image in certain region, the disk space shared by test builds image pyramid and the data volume needed for image transmission.The total size of remote sensing image is 833.40MB, and total pixel number is 131072 × 65536 pixels, and subdivision is the image blocks of every 256 × 256 pixels, totally 131072 pieces.
Utilize the remote sensing image block of subdivision, use the method for classic method and improvement to build image pyramid respectively.The hierarchy schematic diagram that Figure 13 (a) is traditional image pyramid, Figure 13 (b) is the image pyramid layering building process schematic diagram improved.According to total pixel number and the resolution of testing image, determine that pyramidal level needs 9 grades altogether, traditional pyramid model adopts value-taking mean value process to carry out the resampling of image, and the pyramid model of improvement selects bior2.2 wavelet basis to decompose image.In building process, record the data volume of two kinds of each layers of pyramid model respectively.
The image pyramid total amount of data of two kinds of method structures is respectively 1103.98MB and 863.87MB, and each layer data amount is as shown in table 3.5.Data experiment result proves, what the present invention proposed improves one's methods shared disk space compared with traditional image pyramid model, decrease the data volume of 28.81%, significantly reduce inter-layer data redundancy, essentially eliminate the about 1/3 data increment problem of traditional image pyramid model.
The disk space that takies of table 3.5 two kinds of image pyramid models contrasts
Because the pyramid model improved make use of the characteristic of the multiresolution analysis of wavelet transformation, when reading and reconstruct high-resolution remote sensing image, the high-resolution data obtained can be utilized, only need transmit corresponding high-frequency sub-band, high-resolution remote sensing image is obtained by wavelet reconstruction, and carry out renewal display, obtain the progressive transmission effect that resolution as shown in figure 14 improves gradually, shorten the time that user waits for.
For comparative analysis improve pyramid model read at image from traditional pyramid model, transmit time data volume different, the present invention is according to pyramid grade, in two kinds of pyramid models, the remote sensing image that resolution increases gradually is successively obtained from high level to low layer, read range size is 1024 × 1024 pixels, record each layer in two kinds of pyramid models respectively to need to read and the data volume transmitted, comparative analysis as shown in figure 15, wherein solid line is the image pyramid model improved, and dotted line is traditional image pyramid model.
As can be seen from Figure 15, the pyramid model of improvement effectively reduces data volume when image reads and transmits, and particularly there is obvious advantage when big data quantity, is very beneficial for the net distribution of remote sensing image data.But the image pyramid model of improvement, in image display process, just can obtain high resolution image because user also needs to carry out wavelet reconstruction after getting high frequency component data, make the process of reconstruction of image comparatively complicated.
Claims (2)
1., based on a global subdivision pyramid model for wavelet transformation, it is characterized in that: image wavelet decomposition step is:
(1) wavelet transformation: by square-integrable real number space
in a function
by a mother wavelet
after flexible and translation in time domain, resolve into a series of subband signal superposition with different spatial resolutions, different frequency characteristic and directivity characteristics;
If
, its Fourier transform
meet admissibility condition:
(3.1)
Namely
bounded, now,
be called as a mother wavelet or wavelet mother function, will
through stretching and after translation, obtaining a wavelet sequence:
(3.2)
Wherein,
be called as contraction-expansion factor or scale parameter,
be called as translation location parameter;
Function
?
space is about mother wavelet
continuous wavelet transform be defined as follows:
(3.3)
Will
integrated form expand into discrete and form, then function
?
wavelet transform is spatially defined as:
(3.4)
Wherein,
,
,
; Conventional is dyadic wavelet, namely
,
, now,
;
If
orthonormal, coefficient
just be expressed as by inner product:
(3.5)
(2) multiresolution analysis and Mallat algorithm:
If
in a series of subspaces
meet following condition, then can be called
one two enter multiresolution:
A. monotonicity:
,
;
B. Approximation:
,
;
C. retractility:
,
;
D. translation invariance:
,
;
E.Riesz base existence: existence function
, make
form
riesz base;
Then certainly exist coefficient sequence
, following equation is set up:
(3.6)
Wherein,
it is metric space
canonical orthogonal basis function, be called scaling function;
For wavelet space
, then have following equation to set up:
(3.7)
Wherein,
it is wavelet space
canonical orthogonal basis function, be called wavelet function;
For any given function
, it is projected to respectively
with
space, then have:
(3.8)
Wherein,
be called scale coefficient,
being called wavelet coefficient, can obtaining through deriving:
(3.9)
(3.10)
Formula (3.9) and formula (3.10) are brought into, obtains respectively
with
the scale coefficient in space and wavelet coefficient:
(3.11)
For any given one-dimensional discrete signal
, often once decompose the part that will produce two length and reduce by half,
be decomposed into
,
...,
with
, concrete formula is:
(3.12)；
(3) two-dimentional Mallat algorithm:
If
for two dimensional image signal, resolution filter first carries out once " OK " to image and decomposes, and then carries out once " row " decomposition, each decomposition generation four subbands
,
,
with
, it is the low frequency sub-band produced in previous stage that next stage decomposes
basis on to carry out;
Two dimension Mallat decomposition algorithm is as follows:
（3.13)
Wherein,
with
be respectively given low-pass filter and the coefficient of Hi-pass filter;
Two dimension Mallat restructuring procedure is then the inverse process of above-mentioned decomposable process,
（3.14）；
(4) wavelet decomposition of image:
According to two-dimentional Mallat algorithm, take original image as initial value, first wavelet transformation is carried out to each row of image, respectively filtering is carried out to each row of image with low-pass filter and Hi-pass filter, and decimation, keep data volume constant, obtain H and L two parts, then use the same method and a wavelet transformation is carried out to each row obtaining image again, like this after one deck wavelet transformation, picture breakdown is four subband LL, HL, LH, HH, low-frequency information in the corresponding upper level image of they difference is with vertical, the information of level and diagonal, from multiresolution analysis, each is decomposed again to the low frequency subgraph picture of upper level, obtain LL
2, HL
2, LH
2, HH
2, the rest may be inferred, carries out multi-level decomposition to image, carries out
secondary decomposition just can obtain
individual subband.
2. the global subdivision pyramid model based on wavelet transformation according to claim 1, is characterized in that: the steps include:
(1) according to the highest resolution of original remote sensing image data, obtain total number of plies J of image pyramid, determined by table 3.1, then be the relation of 2 times according to resolution between adjacent layer, determine the pyramid level L that the remote sensing image of existing N kind resolution is corresponding, the corresponding from high to low level of resolution is respectively L
1, L
2,
, L
n , L
n, the L that resolution is the highest
1corresponding 0th layer;
Table 3.1 pyramid level and highest resolution, bottom image blocks quantity corresponding relation
(2) according to the resolution of existing remote sensing image, determined the subdivision level of its global subdivision graticule mesh by table 3.2, carry out subdivision process according to split surface blade unit size, form remote sensing image dough sheet;
Corresponding relation between table 3.2 subdivision progression and image resolution
(3) number of times that existing remote sensing image needs wavelet decomposition is calculated respectively
:
(3.15)
(4) number of times is determined
after, existing remote sensing image is carried out respectively
secondary wavelet decomposition, utilizes the multiresolution analysis characteristic of small echo, and each " existing layer " obtains a low frequency sub-band
with a series of high-frequency sub-band
,
,
,
,
,
,
;
(5) by low frequency sub-band that existing remote sensing image decomposes out
fill it in image pyramid corresponding the
layer, first order high-frequency sub-band
,
,
be 2 in spatial domain cutting
×after 2 equal portions, put into image pyramid
the relevant position of layer, each Block matrix of this layer stores three high-frequency sub-band simultaneously
,
,
corresponding fritter after cutting, second level high-frequency sub-band
,
,
be 4 in spatial domain cutting
×image pyramid is put into after 4 equal portions
the relevant position of layer, the like, until fill up whole image pyramid.
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