Theodoor Moons

Recognizing color patterns irrespective of viewpoint and illumination

New invariant features are presented that can be used for the recognition of planar color patterns such as labels, logos, pictograms, etc., irrespective of the viewpoint or the illumination conditions, and without the need for error prone contour extraction. The new features are based on moments of powers of the intensities in the individual color bands and combinations thereof. These moments implicitly characterize the shape, the intensity and the color distribution of the pattern in a uniform manner. The paper gives a classification of all functions of such moments which are invariant under both affine deformations of the pattern (thus achieving viewpoint invariance) as well as linear changes of the intensity values of the color bands (hence, coping with changes in the irradiance pattern due to different lighting conditions and/or viewpoints). The discriminant power and classification performance of the new invariants for color pattern recognition is tested on a data set of images of outdoors advertising panels. A comparison to moment invariants presented in literature is included as well.

Foundations of semi-differential invariants

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 semi-differential invariants are implemented in the computer program FORM (Flat Object Recognition Method) for the recognition of planar contours under pseudo-perspective projection.

An extended class of scale-invariant and recursive scale space filters

Explores how the functional form of scale space filters is determined by a number of a priori conditions. In particular, if one assumes scale space filters to be linear, isotropic convolution filters, then two conditions (viz. recursivity and scale-invariance) suffice to narrow down the collection of possible filters to a family that essentially depends on one parameter which determines the qualitative shape of the filter. Gaussian filters correspond to one particular value of this shape-parameter. For other values the filters exhibit a more complicated pattern of excitatory and inhibitory regions. This might well be relevant to the study of the neurophysiology of biological visual systems, for recent research shows the existence of extensive disinhibitory regions outside the periphery of the classical center-surround receptive field of LGN and retinal ganglion cells (in cats). Such regions cannot be accounted for by models based on the second order derivative of the Gaussian. Finally, the authors investigate how this work ties in with another axiomatic approach of scale space operators which focuses on the semigroup properties of the operator family. The authors show that only a discrete subset of filters gives rise to an evolution which can be characterized by means of a partial differential equation. >

Affine reconstruction from perspective image pairs with a relative object-camera translation in between

A method is described to recover the three-dimensional affine structure of a scene consisting of at least five points identified in two perspective views with a relative object-camera translation in between. When compared to the results for arbitrary stereo views, a more detailed reconstruction is possible using less information. The method presented only assumes that the two images are obtained by identical cameras, but no knowledge about the intrinsic parameters of the camera(s) or about the performed translation is assumed. By the same method, affine 3D reconstruction from a single view can be achieved for parallel structures. In that case, four points suffice for affine reconstruction.

Recognition of planar shapes under affine distortion

Methods for the recognition ofplanar shapes from arbitrary viewpoints are described. The adopted model of projection is orthographic. The invariant descriptions derived for this group are one-dimensional shape signatures comparable to the well-known curvature as a function of arc length description of Euclidean geometry. Since the use of such differential invariants in the affine case would lead to unacceptably high orders of derivatives, affine invariant descriptions based onsemi-differential invariants are proposed as an alternative. A systematic discussion of different types of these invariants is given. The usefulness and viability of this methodology is demonstrated on a database containing more than 40 objects.

Invariance from the Euclidean Geometer's Perspective

It is remarkable how well the human visual system can cope with changing viewpoints when it comes to recognising shapes. The state of the art in machine vision is still quite remote from solving such tasks. Nevertheless, a surge in invariance-based research has led to the development of methods for solving recognition problems still considered hard until recently. A nonmathematical account explains the basic philosophy and trade-offs underlying this strand of research. The principles are explained for the relatively simple case of planar-object recognition under arbitrary viewpoints. Well-known Euclidean concepts form the basis of invariance in this case. Introducing constraints in addition to that of planarity may further simplify the invariants. On the other hand, there are problems for which no invariants exist.

Mirror and point symmetry under perspective skewing

Over recent years, symmetry research has shifted from the detection of affinely to perspectively skewed mirror symmetry. Also, links between invariance research and symmetry-specific geometric constraints have been established. The paper aims to contribute to both strands. Several sets of symmetry specific invariants are derived, that can be used in different situations, depending on the a priori assumptions made. It is also argued that all the results directly apply to the case of perspectively skewed point symmetry.

Semi-local projective invariants for the recognition of smooth plane curves

Recently, several methods have been proposed for describing plane, non-algebraic curves in a projectively invariant fashion. These curve representations are invariant under changes in viewpoint and therefore ideally suited for recognition.We report the results of a study where the strengths and weaknesses of a number of semi-local methods are compared on the basis of the same images and edge data. All the methods define a distinguished or canonical projective frame for the curve segment which is used for projective normalisation. In this canonical frame the curve has a viewpoint invariant signature. Measurements on the signature are invariants. All the methods presented are designed to work on real images where extracted data will not be ideal, and parts of curves will be missing because of poor contrast or occlusion.We compare the stability and discrimination of the signatures and invariants over a number of example curves and viewpoints. The paper concludes with a discussion of how the various methods can be integrated within a recognition system.

Automatic modelling and 3D reconstruction of urban buildings from aerial imagery

A method is presented that automatically generates 3D models of generic house roofs from aerial images of residential areas in urban sites. Crucial to the method is the possibility of delineating regions in the images that correspond well to actual roof structures. Restricting the processing to relatively small regions allows at all stages of the algorithm to use constraints that are not very tight, and, at the same time, to keep the combinatorics under control. All modelling is done by reasoning in 3D. By adopting a strategy of hypothesis generation and verification the authors are not only are capable of exploiting all available image data at every step in the algorithm, but also to treat all views equally. Decoupling topology retrieval from metric accuracy makes it possible to generate and test combinations which otherwise would have been ruled out by more tight constraints. The method is implemented and tests on the correctness and completeness of the extracted roof models have been performed.

Model estimation for photometric changes of outdoor planar color surfaces caused by changes in illumination and viewpoint

We compare different ways of representing the global photometric changes in image intensities caused by changes in illumination and viewpoint, aiming at a balance between goodness-of-fit and low complexity. A series of model selection tests are performed for the case of outdoor imagery consisting of several views of several instances of billboards taken under different viewing angles and different illumination (natural light). Possible candidates for a transformation model on (R,G,B) color space are investigated and different approaches for the model selection problem are considered. The results are used within ongoing research into computation of new invariant features for planar color patterns, as the model choice is an important issue to decide on when extracting invariants. These results can be of benefit to other areas of research into color pattern or object recognition.