COLOR CORRELATION-BASED MATCHING

S. Chambon∗ and A. Crouzil∗

Abstract

In the context of computer vision, stereo matching can be done us-ing correlation measures. Few papers deal with color correlation-based matching so the underlying problem of this paper is abouthow it can be adapted to color images. The goals of this work areto help choosing a color space and to generalize the correlationmeasures to color. Nine color spaces and three different meth-ods have been investigated to evaluate their suitability for stereomatching. The results show us to what extent stereo matchingcan be improved with color.

Key Words

Color, correlation, matching.

1. Introduction

Matching is an important task in computer vision be-cause the accuracy of the 3D reconstruction depends onthe accuracy of the matching. A lot of matching algo-rithms have been proposed [1, 2]; the present paper fo-cuses on matching using correlation measures [3] whosemain hypothesis is based on the similarity of the neigh-borhoods of the corresponding pixels. Hence, in thiscontext, we consider that a correlation measure evalu-ates the similarity between two pixel sets. In our previ-ous work [4], the commonly used correlation measuresare classified into five families and, as we are particularlyconcerned with the occlusion problems, new correlationmeasures that are robust near occlusions are proposed.This work was done with gray level images.

Although the use of color images is more and morefrequent in computer vision [5] and can improve the ac-curacy of stereo matching [6], few papers present cor-relation measures using color images [6, 7]. The mostcommon approach is to compute the mean of the threecolor components [8]. In this paper, our purpose is alsoto take into account color in dense matching using cor-relation and to adapt our previous work [4]. Here, themain novelty is a generalization strategy that enables tochoose a color space and to adapt the correlation mea-sures from gray level to color.

∗IRIT – TCI, Universite Paul Sabatier, 118 route de Narbonne,31062 Toulouse Cedex 4, France

Nine color spaces are evaluated and three methodsare proposed: to compute the correlation with each colorcomponent and then to merge the results; to process aprincipal component analysis and then to compute thecorrelation with the first principal component; to com-pute the correlation directly with colors. Moreover, anevaluation protocol which enables to study the behaviorof each method with each color space is required to high-light the best way to adapt correlation measures to colorand the improvement of the efficiency of correlation-based matching.

The paper is structured as follows. Firstly, the mostused color spaces are presented. Secondly, gray levelcorrelation-based matching is defined. Thirdly, colorcorrelation-based matching is described. Fourthly, weshow our evaluation protocol. Finally, the results arediscussed and conclusions are drawn.

2. Color spaces

A color space is a mean by which color can be speci-fied, created and visualized. The choice of color spaceis important and a lot of color spaces have been pro-posed [9, 10, 11]. Here, the color spaces that are mostused are distinguished into four families [12] (table 1):

• Primary systems: RGB, XY Z [12];• Luminance-chrominance systems: L∗u∗v∗ [11],

L∗a∗b∗ [11], AC1C2 [13] and Y C1C2 [10];• Perceptual system: HSI [7];• Statistical independent component systems: I1I2I3

[14] and H1H2H3 [9].The two next sections present gray level correlation-

based matching and color correlation-based matching.We call gray level correlation measures, the “1D mea-sures” and color correlation measures, the “3D mea-sures”.

3. Gray level correlation-based matching

The three steps of the basic algorithm are, for each pixel,p

i,jl , in the left image (fig. 1):1. The search area, Ar, the region of the image where

we expect to find the corresponding pixel, is deter-mined in the right image;

2. For each pixel, ps,tr , in the search area, the correla-

tion score is evaluated;

3. The pixel, ps,tr , giving the best score is the corre-

sponding pixel.

1

Table 1The nine color spaces investigated.

Name Definition

XY Z

XYZ

=

0.607 0.174 0.200

0.299 0.587 0.114

0.000 0.066 1.116

RGB

L∗u∗v∗

L∗ =

{

116 (Y/Yw)13 − 16 if Y/Yw > 0.01

903.3 Y/Yw otherwise

u∗ = 13L∗(u′ − u′w) with u′ = 4X

X+15Y +3Z

v∗ = 13L∗(v′ − v′w) with v′ = 9Y

X+15Y +3ZXw, Yw, Zw: white reference components

L∗a∗b∗

a∗ = 500(f(X/Xw) − f(Y/Yw))b∗ = 200(f(Y/Yw) − f(Z/Zw))

f(x) =

{

x1/3 if x > 0.008856

7.787x + 16116 otherwise

AC1C2

AC1

C2

=

13

13

13√

32

−√

32 0

−12

−12 1

RGB

Y C1C2

YC1

C2

=

13

13

13

1 −12

−12

0 −√

32

√3

2

RGB

HSI

I = R+G+B3 , S = 1 − 3min(R,G,B)

R+G+B

H =

{

arccos H1 if B ≤ G

2π − arccos H1 otherwise

H1 = (R−G)+(R−B)

2√

(R−G)2+(R−B)(G−B)

I1I2I3

I1

I2

I3

=

13

13

13

12 0 −1

2−14

−14

12

RGB

H1H2H3

H1

H2

H3

=

1 1 01 −1 0−12 0 −1

2

RGB

The left and right images are denoted by Iv, v = l, r,and the following notations are used:• The size of the correlation windows is (2n + 1) ×

(2m + 1) and N = (2n + 1)(2m + 1), n, m ∈ IN∗.• The number of pixels in the search area, Ar, is M .• The gray level of the pixel in the image Iv at coor-

dinates (i, j) is noted Ii,jv .

• The vectors fv, v = l, r, contain the gray levels ofthe pixels in the left and right correlation windows:fv = (· · · Ii+p,j+q

v · · · )T = (· · · fkv · · · )T , where fk

v isthe element k of vector fv, p ∈ [−n;n], q ∈ [−m;m],k ∈ [0;N − 1].

• The ordered values of vector f are noted(f)0:N−1 ≤ . . . ≤ (f)N−1:N−1.

(a)

fr

Left image Right image

i

j

Search area = Ar

Correlation windowsfl

pi,j

lps,t

rt

s

(b)

fl

scores

1D measure

(see (c))

C

S1

...

SM

the

score

best

Compute

using

Select

Ar

(c)

...

......

S1

SM

fl

fMr

f1

r

Ar

1D

measure

1D

measure

Figure 1. Gray level correlation-based matching(S = Score, C = Correspondent) – (a) Search area andcorrelation windows. (b) Search the corresponding pixelusing a 1D measure. (c) Details for computing the scoresusing a 1D measure.

4. Color correlation-based matching

In the sequel, we use coordinates x, y and z for the threecomponents. We introduce the following notations:

• ckv = (xk

v ykv zk

v )T , v = l, r, are the colors of theelements k in the correlation windows;

• Matrices Fv, v = l, r, contain the colors of the pix-els in the left and right correlation windows:Fv = (· · · ck

v · · · )T , k ∈ [0;N − 1].

The three different methods for adapting gray levelcorrelation-based matching to color are presented.

4.1 Fusion

4.1.1 Score fusion

For method fusion-score (fig. 2), the correlationmeasures with each component are computed and

2

merged:

Mc(Fl,Fr) = γ(Mg(xl,xr),Mg(yl,yr),Mg(zl, zr))

γ ∈ {min,max,med,mean,belli}. (1)

Mc is a color correlation and Mg a gray level correlation.The vectors xv, yv, zv, v = l, r, contain all the compo-nents of the colors in the correlation windows and thefusion of Belli [15] is defined by

Mc(Fl,Fr) =Mg(xl,xr)2+Mg(yl,yr)2+Mg(zl,zr)2

Mg(xl,xr)+Mg(yl,yr)+Mg(zl,zr). (2)

S2

1

S3

1

...

S1

1

...S1

......

...

S1

M

S2

M

S3

M

SM

C

scores

1D measure

scores

1D measure

scores

1D measure

using

Compute

Compute

using

Compute

using

the

best

score

SelectFl

Ar

Fusion

Fusion

Figure 2. Method fusion-score (S = Score, C = Cor-respondent) – Search the corresponding pixel using threecomponents and fusion of the scores (see fig. 1(c)).

4.1.2 Disparity map fusion

For method fusion-map (fig. 3), three disparity mapsare computed (one for each component) and merged:• If at least two of the disparity maps give the

same corresponding pixel, then this correspondentis kept.

• If each map gives a different correspondent then thecorresponding pixel which obtain the best score iskept.

4.2 PCA

The principle of method pca is to process a principalcomponent analysis, PCA, like Cheng [16], and then tocompute the correlation measure using the first principalcomponent. The PCA can be done on the whole image(pca-ima, figure 4) or on the correlation windows (pca-

win,figure 5) and in this latter:

Mc(Fl,Fr) = Mg(PCA(Fl),PCA(Fr)). (3)

S2

1

S3

1

...

S1

...

S2

M

S3

M

Cthe

best

score

SelectFl

Ar

Compute

scores

using

score1D measure

1D measure

using best

scores

Compute

1D measure

using

thescores

Compute Select

Select

Select

the

best

best

score

the

score

S3

S2

S1

M

S1

1

...

Figure 3. Method fusion-map (S = Score, C = Corre-spondent) – Search the corresponding pixel using threecomponents and fusion of the disparities (see fig. 1(c)).

C

SM

...

S1

scores

1D measure

the

best

scoreApcar

f pca

lCompute

using

Select

Figure 4. Method pca-ima (S = Score, C = Corre-spondent, see fig. 1(c)). The terms fPCA

l and APCAr are

obtained from the first principal component of a PCA.

4.3 1D measure generalization

The goal of method corr is to compute the correlationmeasure directly using colors. So, we have to transformthe 1D measures into 3D measures. The four next sec-tions give the different rules for this adaptation.

4.3.1 Generalization of the basic operators

• LP norm with P ∈ IN∗ defined by

‖fv‖P =

(N−1∑

k=0

|fkv |P) 1

P

becomes

‖Fv‖P =

(N−1∑

k=0

‖ckv‖P

P

) 1P

with

‖ckv‖P

P=(xk

v)P

+ (ykv )

P+ (zk

v )P

.

(4)

Euclidean and Frobenius norms are respectivelynoted ‖fv‖ = ‖fv‖2 and ‖Fv‖ = ‖Fv‖2.

3

(a)

C

SM

...

S1

Compute Select

scores using

1D measure

(see (b)) score

the

bestAr

Fl

PCA and

(b)

...

......

S1

SM

measure

measure

1D

1D

Fl

Ar

fl

f1

r

fl

fMr

PCA

PCA

PCA

PCAFMr

F1

r

Figure 5. Method pca-win (S = Score, C = Corre-spondent) – (a) Search the corresponding pixel using thePCA and a 1D measure. (b) Details for computing thescores using the PCA and a 1D measure.

• Scalar product defined by

fl · fr =

N−1∑

k=0

fkl fk

r becomes

Fl · Fr =N−1∑

k=0

xkl xk

r + ykl yk

r + zkl zk

r .

(5)

• Means noted

fv =1

N

N−1∑

k=0

fkv become

Fv =1

N( 1 · · · 1︸ ︷︷ ︸

N columns

)T

(N−1∑

k=0

xkv

N−1∑

k=0

ykv

N−1∑

k=0

zkv

)

.

(6)

4.3.2 Color distance

To describe the difference of colors in a space, a distanceis needed. The most common is the L2 norm [7], buthere the LP norm is chosen with P ∈ IN∗:

d(cl, cr) = ((xl − xr)P + (yl − yr)

P + (zl − zr)P )

1P .(7)

This norm is not suitable for HSI space with which

(a)

C

S1

...

SM

scores

3D measure

(see (b))

the

best

score

Compute

using

Select

Fl

Ar

(b)

3D

......

S1

...SM

FMr

3D

measure

measure

Fl

Ar

F1

r

Figure 6. Method corr (S = Score, C = Correspon-dent) – (a) Search the corresponding pixel using thethree components and a 3D measure. (b) Details forcomputing the scores using a 3D measure.

this distance is commonly used [7]:

d(cl, cr) =

√

(Il − Ir)2 + S2l + S2

r − 2SlSrcosθ

θ =

{

|Hl − Hr| if |Hl − Hr| ≤ π

2π − |Hl − Hr| otherwise.

(8)

The vector of distances between colors of the correlationwindows is noted D(Fl,Fr) =

(. . . d(ci

l, cir) . . .

)T

and, if HSI is used, d is defined by equation (8) other-wise, it is defined by equation (7).

4.3.3 Color rank

To sort a color vector, four possibilities are given:• Sort pca: to sort the first principal component of

a PCA, like [16];• Sort bit: to compute the bit mixing code for each

pixel of the correlation window and to sort the pix-els with these codes [17];

• Sort one: to sort only one of the components;• Sort lex: to use the lexicographic order:

if (xkv > xi

v) or (xkv = xi

v and ykv > yi

v)

or (xkv = xi

v and ykv = yi

v and zkv > zi

v)

then ckv > ci

v else ckv ≤ ci

v.

(9)

4

4.3.4 3D measures

In our previous work [4], the commonly used correla-tion measures were classified into five families : cross-correlation-based measures, classical statistics-basedmeasures, derivative-based measures, ordinal measuresand robust measures. The way of adapting every mea-sure into each family is illustrated by an example.

Cross correlation-based measures – The Zeromean Normalized Cross-Correlation noted

ZNCC(fl, fr) =(fl − fl) · (fr − fr)

‖fl − fl‖‖fr − fr‖becomes

ZNCC(Fl,Fr) =(Fl − Fl) · (Fr − Fr)

‖Fl − Fl‖‖Fr − Fr‖.

(10)

Classical statistics-based measures – The Zeromean Normalized Distances given by

ZNDP (fl, fr) =‖(fl − fl) − (fr − fr)‖P

P

√

‖fl − fl‖PP ‖fr − fr‖P

Pbecome

ZNDP (Fl,Fr) =‖D(Fl − Fl,Fr − Fr)‖P

P

√

‖Fl − Fl‖PP ‖Fr − Fr‖P

P.

(11)

Derivative-based measures – These measures [3]use filters to compute the image derivatives. These fil-ters are applied separately to the three channels. Tocompute the norm and the orientation of the gradientvector field, we use [18]. The Pratt measure

PRATT(fl, fr) = ZNCC(Rp(fl),Rp(fr)) becomes

PRATT(Fl,Fr) = ZNCC(Rp(Fl),Rp(Fr)).(12)

The vectors Rp(fv) and the matrices Rp(Fv) are ob-tained after using the Pratt filter [19].

Ordinal measures – The original measures [20, 21,22] use ordered gray levels of the pixels in the correlationwindow. For the color correlation measures, the rank ofthe colors is used (cf. section 4.3.3). The Increment SignCorrelation [21]

ISC(fl, fr) =(al · ar + (1 − al) · (1 − ar))

N − 1becomes

ISC(Fl,Fr) =(bl · br + (1 − bl) · (1 − br))

N − 1.

(13)

The vectors av and bv are obtained respectively afterapplying the Kaneko transform [21] to fv and Fv. Thistransform compares the pixels in the correlation win-dow.

Robust measures – These measures use robuststatistics tools. The Smooth Median Powered Devia-tion [4]

SMPDP (fl, fr) =

h−1∑

i=0

(

|fl − fr − med(fl − fr)|P)

i:N−1

becomes, with D = D(Fl,Fr),

SMPDP (Fl,Fr) =

h−1∑

i=0

(

|D − med(D)|P)

i:N−1.

(14)

5. Evaluation protocol

Ten pairs of color images with ground truth are used: arandom-dot stereogram and nine real images proposedby Scharstein1 [1]. Six of these images are made up ofpiecewise planar objects and three images are complexscenes. Because of the lack of space, the results of onlytwo pairs (fig. 7) are shown.

For the evaluation, ten criteria are chosen:• Percentage of correct and false matches (co, fa).• Percentage of accepted matches (ac): if the dis-

tance between the calculated and the true corre-spondent is one pixel then the calculated correspon-dent is accepted.

• Percentage of false positives and false negatives(FP, FN): the pixel is matched whereas it is notmatched and vice versa.

• Percentage of correct matched pixels in occludedareas: the morphological dilation of the set of pixelswith no corresponding pixels in the other image ofthe pair is considered (di, black and gray pixelsin 7(d) and 7(h)). The results in the set of pixelswithout correspondent (oc, black pixels in 7(d) and7(h)) and in the set of pixels near the pixels withoutcorrespondent (no, gray pixels in 7(d) and 7(h)) aredistinguished.

• Execution time (T) and disparity maps.

The size of the correlation window is 9× 9 (the mostsuitable size for this kind of images found in [4]). Theimages are rectified so the search area is limited to thesize 61×1 (121×1 with “teddy”): 30 (60 with “teddy”)pixels before and after the pixel of interest. Moreover,the symmetry constraint is added in order to try to lo-cate the occluded pixels. The correlation is performedtwice by reversing the roles of the two images. Thematches for which the reverse correlation falls onto theinitial point in the left image are considered as valid,otherwise the pixels are considered as occluded. Thethree methods and the nine color spaces2 are tested andcompared with gray level correlation-based matching.

1http://www.middlebury.edu/stereo/data.html2Here, Xw = 250.155, Yw = 255 and Zw = 301.41.

5

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 7. (a)-(b) “Teddy” images. (c) Disparity map:the clearer the pixel, the larger the disparity and thecloser the 3D point to the image plane. The black pixelsare occluded pixels. (d) Occluded areas, black: pixelswithout correspondent, gray: region around the blackpixels. (e)-(h) Ground truth for “head and lamp” im-ages.

6. Experimental results

In this section, these notations are used: met formethod, mea for measure, fus for fusion, ima for image,var for variant, max for maximum, med for median, Gfor gray level and C for color. The results with “teddy”are shown in tables 2 and 3, for the most representativemeasure of each family. Table 2 gives the parameters toobtain the greatest results for each method – best re-sults are obtained when cor and no are the best. Theresults of the best methods are noted in bold numbers.Table 3 presents the results for the best method for colormatching and the results of gray level matching for eachfamily. The best results are noted in bold numbers and

when the color matching always gives the best results foreach measure, the header of the corresponding columnis written in bold letters.

The results with all the images and particularly with“teddy” permit these remarks:

• method fusion and method corr always havevariants that give better results than the gray levelmethod whereas method pca does not.

• method fusion and method corr always havevariants that improve the percentage of correct pix-els and false negatives.

• method fusion is better than method corr butmethod corr is less time expensive.

• For method fusion:◦ method fusion-score is better than

method fusion-map.◦ Best color space is often a primary system

(60% of the cases).◦ Best fusion operator is often the maximum

(48% of the cases).• For method pca:

◦ Best color space is often H1H2H3 (57% of thecases).

◦ Best method is often pca-ima (65% of thecases).

• For method corr:◦ Best color space is often H1H2H3 (50% of the

cases).◦ Best results are obtained with sort lex.◦ All the LP norms give equivalent results.

The disparity maps obtained with color images arethe clearest because they contain less false negative andthe edges of the objets are more precise than the dispar-ity maps obtained with gray level images (fig. 8 and 9).

Table 2Best results with each method for “teddy”.

Mea Met fusion Met pca Met corr

Space Fus Space Var Space Var

NCC H1H2H3 max H1H2H3 win H1H2H3

D1 XY Z max H1H2H3 win H1H2H3 L∞

PRATT XY Z max RGB ima H1H2H3

ISC XY Z belli H1H2H3 win L∗

u∗

v∗

sort

lex

SMPD2 XY Z med H1H2H3 ima H1H2H3 L2

7. Conclusion

This paper deals with color stereo matching using cor-relation and illustrates how to generalize gray levelcorrelation-based matching to color. Nine color spacesare tested and three different methods are experimented.The results highlight that color always improve match-

6

Table 3Color versus gray level matching for “teddy”.

MeaTy Co Ac Fa FP FN Di Oc no T

NCC G 52.3 23.9 30.6 2.7 14.4 69.9 76.1 65.7 52

C 55.2 24.1 30.4 2.6 11.8 70.6 77.1 66.1 141

D1 G 49.5 22.6 29.8 2.8 17.8 70.9 75.3 67.9 63

C 51.6 21.9 29.3 2.9 16.2 71.9 74.3 70.2 140

PRA G 29.1 8.2 30.7 3.8 36.4 58.5 66.8 52.8 86

TT C 45.2 17.3 28.4 3.5 22.9 65 69.8 61.8 225

ISC G 44.9 19.2 28.2 2.7 24.3 68.9 76.5 63.8 126

C 52.6 22.3 28.6 2.6 16.3 73.1 77.5 70.1 245

SM G 49.9 23.2 30.5 2.4 17.3 74.5 79.7 71 569

PD2 C 56.5 25.3 30.1 2.2 11.2 77.7 80.7 75.6 2109

Gray level color

NCC

SAD

SMPD2

Figure 8. Disparity maps for “teddy”.

ing even if the best color space and the best methodare not easy to distinguished. In fact, the choice of thecolor space and the method depends on the measure.Nevertheless, there is an important result: we can con-clude that method fusion with a primary system ormethod corr with H1H2H3 system are often the best(64% of the cases). An extension of this work wouldbe to consider different areas in order to determine ifcolor can be used, for example, like Koschan [23] whodistinguishes chromatic and achromatic areas.

Gray level color

NCC

SAD

SMPD2

Figure 9. Disparity maps for “head and lamp”.

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[23] A. Koschan. Using perceptual attributes to obtaindense depth maps. In IEEE Southwest Symposium

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Sylvie Chambon is currently a Ph.D.student in IRIT (Institut de Rechercheen Informatique de Toulouse) at PaulSabatier University, in Toulouse. Her re-search interest concern dense correlation-based matching.

Alain Crouzil received the Ph.D.degree in computer sciences at PaulSabatier University, in Toulouse in 1997.He is currently an assistant professor anda member of the TCI group (Traitementet Comprehension d’Images) in IRIT (In-stitut de Recherche en Informatique de

Toulouse). He is interested in stereovision, motion anal-ysis and Shape From Shading.

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