Class-Based Feature Matching Across Unrestricted Transformations

We develop a novel method for class-based feature matching across large changes in viewing conditions. The method is based on the property that when objects share a similar part, the similarity is preserved across viewing conditions. Given a feature and a training set of object images, we first identify the subset of objects that share this feature. The transformation of the feature's appearance across viewing conditions is determined mainly by properties of the feature, rather than of the object in which it is embedded. Therefore, the transformed feature will be shared by approximately the same set of objects. Based on this consistency requirement, corresponding features can be reliably identified from a set of candidate matches. Unlike previous approaches, the proposed scheme compares feature appearances only in similar viewing conditions, rather than across different viewing conditions. As a result, the scheme is not restricted to locally planar objects or affine transformations. The approach also does not require examples of correct matches. We show that by using the proposed method, a dense set of accurate correspondences can be obtained. Experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes. Finally, we show that the scheme can be successfully used for invariant object recognition

M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

Affine Invariant Contour Descriptors Using Independent Component Analysis and Dyadic Wavelet Transform

The paper presents a novel technique for affine invariant feature extraction with the view of object recognition based on parameterized contour. The proposed technique first normalizes an input image by removing the affine deformations using independent component analysis which also reduces the noise introduced during contour parameterization. Then four invariant functionals are constructed using the restored object contour, dyadic wavelet transform and conics in the context of wavelets. Experimental results are conducted using three different standard datasets to confirm the validity of the proposed technique. Beside this the error rates obtained in terms of invariant stability are significantly lower when compared to other wavelet based invariants. Also the proposed invariants exhibit higher feature disparity than the method of Fourier descriptors

Children, Humanoid Robots and Caregivers

This paper presents developmental learning on a humanoid robot from human-robot interactions. We consider in particular teaching humanoids as children during the child's Separation and Individuation developmental phase (Mahler, 1979). Cognitive development during this phase is characterized both by the child's dependence on her mother for learning while becoming awareness of her own individuality, and by self-exploration of her physical surroundings. We propose a learning framework for a humanoid robot inspired on such cognitive development

Universal tools for analysing structures and interactions in geometry

This study examined symmetry and perspective in modern geometric transformations, treating them as functions that preserve specific properties while mapping one geometric figure to another. The purpose of this study was to investigate geometric transformations as a tool for analysis, to consider invariants as universal tools for studying geometry. Materials and Methods: The Erlangen ideas of F. I. Klein were used, which consider geometry as a theory of group invariants with respect to the transformation of the plane and space. Results and Discussion: Projective transformations and their extension to two-dimensional primitives were investigated. Two types of geometric correspondences, collinearity and correlation, and their properties were studied. The group of homotheties, including translations and parallel translations, and their role in the affine group were investigated. Homology with ideal line axes, such as stretching and centre stretching, was considered. Involutional homology and harmonic homology with the centre, axis, and homologous pairs of points were investigated. In this study unified geometry concepts, exploring how different geometric transformations relate and maintain properties across diverse geometric systems. Conclusions: It specifically examined Möbius transforms, including their matrix representation, trace, fixed points, and categorized them into identical transforms, nonlinear transforms, shifts, dilations, and inversions