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Using eigencolor normalization for illumination-invariant color object recognition Speaker: 鄭雅勻 Date:2010/12/30 Zhenyong Lin, Junxian Wang, Kai-Kuang Ma Pattern Recognition 35 (2002) 2629 – 2642

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Outline Introduction Related Work Implementation Results Conclusion

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Introduction Color is one of salient features for color object recognition, however, the colors of object images sensitively depend on scene illumination. Color indexing, a histogram intersection algorithm to compare an observed histogram with those established from database. A color histogram is independent of common imaging conditions, such as orientation of a scene, absence or occlusion of colors but not the color of scene illumination changes. To overcome the lighting dependency problem, a color constancy or color normalization method can be used as a pre-processing step.

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Introduction Color constancy process attempts to estimate the illumination, and the image colors are then corrected based on the estimated illumination to remove color bias and only the inherent colors are used for recognition. Calculate color-invariant features from images and use these features for indexing.

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Related Work The failure of the color constancy method implies that the actual illumination of the scene might be different from the measured illumination. ----- B.V. Funt, L. Martin[1998] An approach called color constant color indexing, to demonstrate that the ratio of adjacent colors is relatively insensitive to illumination changes. ----- Funt and Finlayson [1995] Healey and Slater [1994] derived the functions of color distribution moments that are invariant to illumination changes. This approach does not attempt to recover the true colors of objects, but extracts the color-invariant features. To retain the image representation while keeping good indexing, a method called comprehensive color image normalization. ----- G.D. Finlayson, G.Y. Tian[1999]

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Objective We present a new illumination-invariant color normalization algorithm, called eigencolor normalization. △ moments of color distributions [4] G. Healey, D. Slater, △ the normalization algorithm for planar patterns [6,7] J.G. Leu, S.C. Pei, C.N. Lin, The normalized color histograms of an object under different illuminations will become very similar to each other after the normalization process. The color object recognition can be performed more accurately by the color indexing on the normalized histograms.

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Implementation The compact color image It is well-known that the colors of the same object under different illuminations are affine transformations to each other [4,5]. We can establish their affine-transformation relation as follows: Let and denote two n-dimensional histograms that represent the distributions of all color values and respectively.

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Let H(R; G; B) be a color histogram; and the R,G and B values are quantized into 8 bits each (i.e.;0-255 discrete levels) The probability density function h(R; G; B) can be formed as Implementation

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For the color histogram H(R; G; B), the central moment with order of k + r + l is denoted by and defined as Implementation

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If we can find the affine transformation matrices transform Two histogram second-order central moment matrices the same object under two different illuminations direct histogram intersection matching X not good result Then, the affine-transformed Histograms will less correlated and more compact. O improved matching results

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shape compacting technique that has been used for 2-D planar shape object normalization to compact 3-D color image. [6,7] The resulted image is called compact color image. Implementation ‧ it shows that a color image can be compacted by changing its coordinate system. the compact color image is variant to other non-affined transforms ex: skew transformation which is often caused by uneven lighting condition or curved object surface.

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To make the color image more illumination-invariant, we need to further normalize the compact color image. Implementation matrix Q is orthogonal (proof)

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If Q is orthogonal then that is Matrix Q is orthogonal From Eq.(14) From Eq.(9) From Eq.(8) (9)

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Corollary 1. If the affine matrix is orthogonal; then. In this case, the compact color image is the same as the normalized color image. Proof. If the affine matrix is orthogonal Implementation the compact color image is the same as the normalized color image

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Since every 3×3 orthogonal matrix is a rotation matrix in 3-D space [8], the normalized color image can be obtained by rotating the color of the compact color image. Implementation is the norm of the plane containing the main diagonal vector of the 3-D color space and the principal axis of the color distribution of the compact color image.

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‧ Given the rotation axis and the rotation angle (according to the Rodrigues formula [8]), the rigid body rotation matrix can be estimated by : Rodrigues rotation formula Rodrigues’ rotation formula is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix from an axis-angle representation. the Rodrigues formula is: Implementation

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By selecting Q = in our proposed eigencolor normalization algorithm, the new color coordinate system, called

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Result A demonstration of eigencolor normalized histogram Here compare the histograms of a simple color image before and after exploiting the proposed eigencolor normalization processing. Sony DXC-950 3CCD color video camera under a white light source and interfaced to a Matrox Meter frame grabber card. Fig. 2. Color histograms before (from (a) to (c)) and after (from (d) to (f)) applying our eigencolor normalization processing. a,b,c original R,G,B d,e,f normalized R,G,B According to the algorithm, size of 45 × 45 is about 2 seconds on a Pentium III 500 Hz PC.

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Result Color object recognition tests without illumination The color image database contains 66 model images with size of128 × 128 each Fig. 3 the monochrome version of model images The recognition or matching performance of each algorithm is the histogram distance.

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Result All test images except T17 are correctly recognized as the best match. Further note that test image T17 is a much zoom-in and rotation version of model image 40 in Fig. 3.

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Result ‧ Color object recognition tests with illumination changes a color image was captured by the same hardware but under different illuminations, white, red, green and blue.

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Result ‧ Color object recognition performance comparison Sony DXC-930 3-CDD video camera was used with gamma correction of and color temperature being set at 3200 K. region-of-interest image patch 40 × 40 each under four different illuminations Fig. 8. Histograms of two color images (a) and (d) are original histograms (b) and (c) are compact histograms (c) and (f) are eigencolor histograms These color images were taken under four different illuminations (from top to bottom in each sub-figure) Macbeth 5000 tube, Sylvania cool-white fluorescent tube, Phillips ultralume fluorescent tube, Sylvania 75 halogen bulb

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Result two phases, an off-line training phase -> the eigencolor normalized histograms of the database images are generated an on-line matching phase-> the histogram of the eigencolor normalized image of a test object is first obtained ‧ On-line color object recognition under illumination changes syl-cwf -> Sylvania cool-white fluorescent tube ph-ulm -> Philips ultralume fluorescent tube halogen ->Sylvania 75 W halogen tube

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Result

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Conclusions In this paper, we present an effective way to normalize color images for correcting illumination changes, and consequently, improving color object recognition accuracy. The normalized color space, called eigencolor space, is aimed to be more invariant to various illumination changes, which mathematically corresponds to affine transformations as well as non-affine transformation from the original images. Results clearly show that our eigencolor representation approach outperforms in facilitating more accurate recognition of color objects under various illuminations.

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