CN101082987B - Column diagram comparability measurement method based on average difference between windows - Google Patents

Abstract

The invention discloses a histogram similarity gauging method based on average difference among windows in the image analyzing technical domain, which comprises the following steps: calculating average difference after making the window distance as power value to powering through statisticallizing value difference between two same histogram windows and the value difference between two different distant windows; adopting the average difference as the standard to estimate the similarity of two histograms; displaying superior gauging property to traditional gauging method under deviation condition for gray histogram; providing reliable reference to index the image based on histogram.

Description

Histogram method for measuring similarity based on mean difference between window

Technical field

The invention belongs to the image analysis technology field, be specifically related to a kind of histogram method for measuring similarity based on mean difference between window.

Technical background

Histogram is one of key character of digital picture, the population distribution information of characteristics such as the gray scale of reflection piece image (or wherein a part is regional), color, texture.Histogram feature is widely used in aspects [1] [2] such as image retrieval, target following.In concrete the application, the similarity between two width of cloth histograms is very important evaluation criterion.Existing histogram similarity measurement mainly is based on Euclidean distance or some criterion distance after the conversion between two width of cloth histograms, like L ₁Distance, L _pDistance, χ ²Distance etc.These methods are when estimating the histogram similarity; All be that value through calculating two histogram corresponding positions is as standard; Calculate simpler; But histogram is had the situation of certain deformation (skew, compression, stretching etc.), and for example image receives factor affecting such as noise, illumination variation, and some just can not reflect its similarity well.When adopting these modules; Piece image and its receive the histogram similarity between the image behind certain noise, the illumination effect may be significantly less than the histogram similarity between this width of cloth image and another the incoherent image, and this is very disadvantageous in concrete the application.The L of some improved methods such as cumulative histogram ₁The relation between the histogram diverse location has been considered in [3] [4] such as distance, but shortcoming is to have lost histogrammic local message.Other some histogram comparative approach have good effect, but on ubiquity, have certain deficiency like histogram peak matching method [5], each rank square relative method parameterized methods such as [6] of histogram under some application-specific.And to these not enough EMD that propose (EarthMover ' s Distance) method [7] [8] situation such as histogram skew can better be solved; But because coupling will solve an optimization problem between two width of cloth histograms; Complexity is higher, in the application such as image retrieval of big data quantity, comes with some shortcomings.The present invention proposes a kind of new histogram method for measuring similarity based on mean difference between window; Through calculating the value difference and the weighted sum of different windows distance between two width of cloth histograms; Obtaining between a window mean difference measures and estimates two histogrammic similaritys; Algorithm is simple, general, has solved some problems that previous method exists preferably.

Summary of the invention

The object of the present invention is to provide the histogram method for measuring similarity that a kind of computation complexity is lower, average error rate is also low.

The histogram method for measuring similarity that the present invention proposes is a kind of measure based on the window mean difference.

Introduce existing histogram similarity evaluation standard below earlier

Existing histogram similarity evaluation mainly is based on the comparison of the value at two width of cloth histogram uniform window places, like L ₁Distance, L _pDistance, χ ²Distance etc.These distances and all can regard the Euclidean distance under the certain parameter as through the distance after some simple transformation (like the cosine distance etc.), more greatly then the histogram similarity is more little for distance.

Simple and be without loss of generality, consider the one dimension histogram here, and with L ₁Distance, L _pDistance, χ ²Distance is an example.If two width of cloth histograms are respectively G={g (j) | j=0,1 ... R} and H={h (k) | k=0,1 ... R}, wherein j, k represent position of window in the histogram, r is that (j, k just represent gray-scale value to the maximum label of window for the grey level histogram of image; The r value is 255), g (j) expression histogram G is in the value at window j place, and h (k) expression histogram H is in the value at window k place.Two histogrammic all kinds of distance definitions are:

The greatest problem that these measures exist is exactly the relation of only having calculated between the value at two width of cloth histogram uniform window places, does not consider the correlativity between the different windows.Explain as shown in Figure 1 with a simple example.Shown the histogram distribution situation that three width of cloth are different among the figure; Wherein the Y histogram is the certain compression of X histogram process result's (for example gray level image being made compressed transform between a gray area) afterwards, and subjective judgement can draw these two histogrammic similaritys of X and Y obviously will be higher than the similarity between X and the Z.But owing to calculate L ₁Distance, L _pDistance, χ ²Apart from the time only consider can draw the difference of the corresponding value in uniform window position these two histogrammic similaritys of X and Y and be less than the similarity between X and the Z.The example of another real image is following: the even number (between 0 to 254) that each point gray-scale value in the piece image is all become the minimum that is not more than former gray-scale value; And the gray-scale value of another width of cloth image each point to be first width of cloth image corresponding position gray-scale value add 1 (promptly complete be odd number); At this moment the grey level histogram of two width of cloth images is not 0 in the value of even number value part and odd number value part only respectively; Has no common factor; Therefore the above three analogous column diagrams distance of being obtained is all very big, can draw the complete dissimilar conclusion of this two width of cloth figure.And in fact this two width of cloth figure does not almost have difference, and histogram shape is also just the same, just translation a window.Certainly this problem is enlarging window size or can obtain solution to a certain degree through histogram after level and smooth, but such loss that can cause statistical information again, and still possibly have problems to the situation of some other conversion.These examples can explain because the value at each window place of histogram has certain correlativity, and the difference of only considering uniform window place value is estimated the histogram similarity and had certain limitation.

The mean difference measure is following between the histogram window that the present invention proposes:

Consider between the value at each window place of histogram correlativity, establish two width of cloth histograms and be respectively G={g (j) | j=0,1;, r} and H={h (k) | k=0,1;, r}, wherein j, k represent position of window in the histogram; R is the maximum label of window, and g (j) expression histogram G is at the statistical value at window j place, and h (k) expression histogram H is at the statistical value at window k place.If G, H satisfy the equal condition of always counting, i.e. ∑ (g (j))=∑ (h (k)), define among two width of cloth histogram G and the H between different windows apart from d=|j-k|, then mean difference tolerance is tried to achieve according to following method between histogram window:

(a) set a histogram maximized window apart from d _Max, as the loop termination sign, greater than d _MaxWindow distance all regard d as _Max

(b) get d=0, obtain n ₀=∑ (min (g (i), h (i))) is promptly added up the common factor at two width of cloth histogram uniform window places.Statistical value with two each window place of width of cloth histogram all deducts corresponding common factor part then, generates the new histogram of two width of cloth, i.e. g (i) '=g (i)-min (g (i), h (i)), h (i) '=h (i)-min (g (i), h (i)).This moment this two width of cloth histogram uniform window place to correct to rare 1 be 0.

(c) get d=1; The histogram new to two width of cloth; M=0 begins from the window's position; Search m=r-d from small to large: if on the width of cloth histogram on m window and another width of cloth histogram the value of m+d window (promptly corresponding window is apart from being the window of d) all be not 0, then establishing less in two values one is p _m, the value at two window places is respectively deducted p _m, generate the histogram that two width of cloth upgrade.After accomplishing all search, the p of value will be arranged _mAdd up the statistical value n that obtains counting ₁, it is defined as window apart from the histogram value difference that is at 1 o'clock.

(d) to d from 1 to d _MaxCarry out operation successively, just can obtain between two width of cloth histograms different windows apart from the value difference n of d like step (c) ₁To n _Max, in conjunction with before the n that tries to achieve ₀, histogrammic mean difference D between different windows is defined as:

$D=\frac{\underset{i=0}{\overset{d\max }{\mathrm{\Σ}}}{n}_i\·i}{\underset{i=0}{\overset{d\max }{\mathrm{\Σ}}}{n}_i}---\left(4\right)$

Wherein, molecule is the weighted sum (is weights with the window) of the histogram value difference of corresponding variant window distance, and denominator is always counting in the width of cloth histogram.

D has represented mean difference between the window between two width of cloth histograms, and the similarity between more little expression two width of cloth histograms of D value is big more.

The acquiring method of bright D for instance below.Two width of cloth histogram A and B (as shown in Figure 2) always count and are 30, owing to have only 6 windows altogether, maximized window is apart from d _MaxBe made as 5.

A：(7，2，8，2，9，2)

B：(0，2，4，6，8，10)

(A, B)=(0,2,4,2,8,2), d always counts to obtain the common factor min of A, B ₀=18; A, B obtain after deducting common factor respectively:

A1：(7，0，4，0，1，0)

B1：(0，0，0，4，0，8)

From left to right search for window among A1, the B1 apart from r be 1 and window place value all be not 0 point, and deduct one less in two values respectively: promptly A1, B1 become (7,0,0,0,1,0) and (0,0,0,0,0,8) at first respectively; Become (7,0,0,0,0,0) and (0,0,0,0,0,7) then respectively; D is at last always counted ₁=4+1=5;

A2：(7，0，0，0，0，0)

B2：(0，0，0，0，0，7)

Increase deviation r and continue search, obtain d successively ₂=0; d ₃=0; d ₄=0; d ₅=7;

Calculate D=1.333 according to formula (4)

The comparison of several kinds of histogram method for measuring similarity performances

Chosen 10 width of cloth natural images (as shown in Figure 3) in the standard picture storehouse here, the image size is 128 pixels * 128 pixels (always count is 16384).Obtain they reach each other and separately image receive the similarity measurement between the grey level histogram after noise, grayscale shift etc. influence, with mean difference tolerance (d between the window that proposes _MaxGet 40) and classical L ₁Distance, L _pDistance (p gets 2) and χ ²Distance metric compares.Ask according to (1), (2), (3) formula these three apart from the time, the distance of trying to achieve divided by total window number (256), is obtained the result's (because relative size relatively just, so the normalization operation is to not influence of result) here after the equalization.The conversion of image being carried out for emulating image influenced by noise, grayscale shift etc. comprises: 1, add the 15dB Gaussian noise; 2, the each point gray scale becomes original 90%; 3, the each point gray scale becomes original 110%.The influence of these transfer pair images itself and histogram shape thereof is not very big; No matter to the subjective feeling of image or histogram shape still from the requirement of application such as image retrieval, piece image and its histogram similarity through the image after the above-mentioned conversion generally should be less than the histogram similaritys between this image and another width of cloth image.And can find out from actual specific result, adopt these distance metrics to estimate the histogram similarity under the certain situation, can obtain opposite conclusion.

The result that (being altogether 45 groups of situation) reaches separately and four kinds of similarity measurements of employing are estimated between the image after its conversion between any two adds up and can know to 10 width of cloth images, adopts L ₁Distance, L _pDistance (p gets 2) and χ ²The error rate of distance metric is higher, is respectively 7 groups, 14 groups and 18 groups.And mean difference metrology error rate is minimum between the window that employing the present invention proposes, and only goes wrong under 3 groups of situation therein, and under these 3 groups of situation, adopts other three kinds of distance metrics also all can not correctly estimate.Thus it is clear that, with the histogram method for evaluating similarity (L of classics ₁Distance, L _pDistance and χ ²Distance) compare, mean difference tolerance receives factor affecting such as noise, illumination condition and takes place under the situation of histogram skew better effect is arranged between window at image.

Description of drawings

Fig. 1, histogram similarity example.

Mean difference metric calculation method example between Fig. 2, window.

Fig. 3, be used for the gray-scale map image set (yardstick: 128 pixels * 128 pixels) of comparison.

Fig. 4, the gray level image that is used for comparison and histogram thereof.First row from left to right is followed successively by this two width of cloth image and first width of cloth image and adds that 15dB Gaussian noise, gray scale become original 90% and gray scale and become the image after original 110%, and the next line correspondence position then is the grey level histogram of every width of cloth figure.

Embodiment

Contrast with the image of ' woman2 ' and ' crowd ' by name in the selected image is example (Fig. 4).Fig. 4 first row from left to right is respectively this two width of cloth image and ' woman2 ' image and adds that 15dB Gaussian noise, gray scale become original 90% and gray scale and become the image after original 110%, and the next line correspondence position then is the grey level histogram of every width of cloth figure.According to formula (1), (2), (3) and (4), adopt L ₁Distance, L _pDistance (p gets 2), χ ²Mean difference tolerance (is represented d between distance and window with AD in the hereinafter table _MaxGet 40) to (a) with (b), (a) with (c), (a) with (d) with (a) compare with (e) histogram similarity, the result is as shown in table 1.

Wherein, (a) and the L (b) ₁Distance (32.2) basically and (c) near (a), (a) and (d), (a) and (e) between L ₁Distance (being respectively 32.3,29.3,29.1) is not easy to judge the size of similarity each other.(a) and the L (b) _pThe distance (47.5) then be significantly less than (a) and (c), (a) and (d), (a) and (e) between L _pDistance (being respectively 61.0,71.7,69.0).Similarly, (a) and the χ (b) ²The distance (10.9) be significantly less than (a) and (c), (a) and (d), (a) and (e) between χ ²Distance (being respectively 32.6,43.7,34.9).Adopt these two kinds of distance metrics can draw (a) and (b) the bigger conclusion of histogram similarity, this and actual observation to image and histogram situation all do not meet.Thus it is clear that, if utilize L ₁Distance, L _pDistance (p gets 2) or χ ²The measured histogram similarity of distance is carried out image retrieval to (a), then possible errors ground (b) figure as result for retrieval, but not (c), (d) or (e).

By contrast; Adopt mean difference tolerance between the window that the present invention proposes then can draw mean difference (7.9) between (a) and histogram window (b) obviously and (c) greater than (a), (a) and (d), (a) and (e) between histogram window between mean difference (being respectively 4.9,3.6,3.4); Promptly (a) and the less conclusion of histogram similarity (b) meet truth more.

Table 1, Fig. 4 adopt distinct methods to carry out the result of histogram similarity measurement

In sum, mean difference is measured the histogram similarity between the histogram window that this paper proposes, and receives factor affecting such as noise, illumination condition at image and takes place that performance is superior to classical histogram method for measuring similarity under the situation of histogram skew.This method is calculated simple and clear, and has good versatility, is expected to be applied to the various fields based on the histogram similarity, like image retrieval, target following etc.

List of references

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Claims (1)

1. histogram method for measuring similarity based on mean difference between window; It is characterized in that adding up value difference and the value difference between the different distance window between two width of cloth histogram uniform windows; Obtaining with the window distance is the mean difference after weights carry out weighting; As the standard of estimating this two width of cloth histogram similarity, concrete steps are following with it:

If two width of cloth histograms are respectively G={g (j) | j=0,1 ... R} and H={h (k) | k=0,1 ... R}, wherein j, k represent position of window in the histogram, r is the maximum label of window; G (j) expression histogram G is at the statistical value at window j place, and h (k) expression histogram H is at the statistical value at window k place; If G, H satisfy the equal condition of always counting, i.e. ∑ (g (j))=∑ (h (k)), define among two width of cloth histogram G and the H between different windows apart from d=|j-k|, abbreviate the window distance as, then mean difference tolerance is tried to achieve according to following method between histogram window:

(a) set a histogram maximized window apart from d _Max, as the loop termination sign, greater than d _MaxWindow distance all regard d as _Max

(b) get d=0, add up the common factor at two width of cloth histogram uniform window places; Obtain n ₀=∑ (min (g (i), h (i))); Statistical value with two each window place of width of cloth histogram all deducts corresponding common factor part then; Generate the new histogram of two width of cloth: i.e. g (i) '=g (i)-min (g (i); H (i)); H (i) '=h (i)-min (g (i), h (i)), this moment this two width of cloth histogram g (i) ' and h (i) ' uniform window place to correct to rare 1 be 0;

(c) get d=1, to the new histogram of described two width of cloth, m=0 begins from the window's position, searches m=r-d from small to large: if on the width of cloth histogram on m window and another width of cloth histogram value of m+d window all be not 0, then establishing less in two values one is p _m, the value at two window places is respectively deducted p _m, generate the histogram that two width of cloth upgrade; After accomplishing all search, the p of value will be arranged _mAdd up the statistical value n that obtains counting ₁, it is defined as window apart from the histogram value difference that is at 1 o'clock;

(d) to d from 2 to d _MaxCarry out successively searching the concrete operations of m=r-d from small to large, obtain between two width of cloth histograms different windows apart from the value difference n of d as beginning from the window's position m=0 in the step (c) ₂To n _Max, in conjunction with before the n that tries to achieve ₀And n ₁, between different windows histogrammic mean difference D be:

$D=\frac{\underset{i=0}{\overset{d\max }{\mathrm{\Σ}}}{n}_i\·i}{\underset{i=0}{\overset{d\max }{\mathrm{\Σ}}}{n}_i}$

Wherein, molecule is the weighted sum of the histogram value difference of corresponding variant window distance, and denominator is always counting in the width of cloth histogram; Similarity between more little expression two width of cloth histograms of D value is big more.

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