Generalised color moments combine shape and color information and put them on an equal footing. Rational expressions of such moments can be designed, that are invariant under both geometric deformations and photometric changes. These generalised color moment invariants are effective features for recognition under changing viewpoint and illumination. The paper gives a systematic overview of such moment invariants for several combinations of deformations and photometric changes. Their validity and potential is corroborated through a series of experiments. Both the cases of indoor and outdoor images are considered, as illumination changes tend to differ between these circumstances. Although the generalised color moment invariants are extracted from planar surface patches, it is argued that invariant neighbourhoods offer a concept through which they can also be used to deal with 3D objects and scenes.
The paper contributes to the viewpoint invariant recognition of planar patterns, especially labels and signs under affine deformations. By their nature, the information of such 'eye-catchers' is not contained in the outfine or frame --they often are affinely equivalent like parallelograms and ellipses --but in the intensity content within. Moment invariants are well suited for their recognition. They need a closed bounding contour, but this is comparatively easy to provide for the simple shapes considered. On the other hand, they characterize the intensity patterns without the need for error prone feature extraction. This paper uses lnoments as the basic features, but extends the literature in two respects:(1) deliberate mixes of different types of moments to keep the order of the moments (and hence also the sensitivity to noise) low and yet have a sufficiently large number to safeguard discriminant power; and (2) invariance with respect to photometric changes is incorporated in order to find the simplest moment invariants that can cope with changing lighting conditions which can hardly be avoided when changing viewpoint. The paper gives complete classifications of such affine / photometric moment invariants. Experiments are described that illustrate the use of some of them.
Abstract.This paper elaborates the theoretical foundations of a semi-differential framework for invariance. Semi-differential invariants combine coordinates and their derivatives with respect to some contour parameter at several points of the image contour, thus allowing for an optimal trade-off between identification of points and the calculation of derivatives. A systematic way of generating complete and independent sets of such invariants is presented. It is also shown that invariance under reparametrisation can be cast in the same framework. The theory is illustrated by a complete analysis of 2D affine transformations. In a companion paper (Pauwels et al. 1995) these affine semidifferential invariants are implemented in the computer program F O R M (Flat Object Recognition Method) for the recognition of planar contours under pseudo-perspective projection.
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