Catálogo de publicaciones - libros

A large part of “image processing” involves the computation of significant points, curves and areas (“features”). These can be defined as loci where absolute differential invariants of the image assume fiducial values, taking spatial scale and intensity (in a generic sense) scale into account. “Differential invariance” implies a group of “similarities” or “congruences”. These “motions” define the geometrical structure of image space. Classical Euclidian invariants don’t apply to images because image space is non-Euclidian. We analyze image structure from first principles and construct the fundamental group of image space motions. Image space is a Cayley-Klein geometry with one isotropic dimension. The analysis leads to a principled definition of “features” and the operators that define them.

In many vision problems, the observed data lies in a nonlinear manifold in a high-dimensional space. This paper presents a generic modelling scheme to characterize the nonlinear structure of the manifold and to learn its multimodal distribution. Our approach represents the data as a linear combination of parameterized local components, where the statistics of the component parameterization describe the nonlinear structure of the manifold. The components are adaptively selected from the training data through a progressive density approximation procedure, which leads to the maximum likelihood estimate of the underlying density. We show results on both synthetic and real training sets, and demonstrate that the proposed scheme has the ability to reveal important structures of the data.

In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of spatial critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the behaviour of critical point trajectories when various different types of generic events, . annihilations and creations of pairs of spatial critical points, (almost) coincide. Although such events are non-generic in mathematical sense, they are not unlikely to be encountered in practice. Furthermore the behaviour leads to the observation that fine-to-coarse tracking of critical points doesn’t suffice. We apply the theory to an artificial image and a simulated MR image and show the occurrence of the described behaviour.

This paper proposes an image matching method that is robust to illumination variation and affine distortion. Our idea is to do image matching through establishing an imaging function that describes the functional relationship relating intensity values between two images. Similar methodology has been proposed by Viola [] and Lai & Fang []. Viola proposed to do image matching through establishment of an imaging function based on a consistency principle. Lai & Fang proposed a parametric form of the imaging function. In cases where the illumination variation is not globally uniform and the parametric form of imaging function is not obvious, one needs to have a more robust method. Our method aims to take care of spatially non-uniform illumination variation and affine distortion. Central to our method is the proposal of a localized consistency principle, implemented through a non-parametric way of estimating the imaging function. The estimation is effected through optimizing a similarity measure that is robust under spatially non-uniform illumination variation and affine distortion. Experimental results are presented from both synthetic and real data. Encouraging results were obtained.

The performances of many image analysis tasks depend on the image resolution at which they are applied. Traditionally, resolution selection methods rely on spatial derivatives of image intensities. Differential measurements, however, are sensitive to noise and are local. They cannot characterize patterns, such as textures, which are defined over extensive image regions. In this work, we present a novel tool for resolution selection that considers sufficiently large image regions and is robust to noise. It is based on the generalized entropies of the histograms of an image at multiple resolutions. We first examine, in general, the variation of histogram entropies with image resolution. Then, we examine the sensitivity of this variation for shapes and textures in an image. Finally, we discuss the significance of resolutions of maximum histogram entropy. It is shown that computing features at these resolutions increases the discriminability between images. It is also shown that maximum histogram entropy values can be used to improve optical flow estimates for block based algorithms in image sequences with a changing zoom factor.

Two new techniques based on nonparametric estimation of probability densities are introduced which improve on the performance of equivalent robust methods currently employed in computer vision. The first technique draws from the projection pursuit paradigm in statistics, and carries out regression M-estimation with a weak dependence on the accuracy of the scale estimate. The second technique exploits the properties of the multivariate adaptive mean shift, and accomplishes the fusion of uncertain measurements arising from an unknown number of sources. As an example, the two techniques are extensively used in an algorithm for the recovery of multiple structures from heavily corrupted data.

Nonlinear partial differential equations (PDE) are now widely used to regularize images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a geometric framework to design PDE flows acting on constrained datasets. We focus our interest on flows of matrix-valued functions undergoing orthogonal and spectral constraints. The corresponding evolution PDE’s are found by minimization of cost functionals, and depend on the natural metrics of the underlying constrained manifolds (viewed as Lie groups or homogeneous spaces). Suitable numerical schemes that fit the constraints are also presented. We illustrate this theoretical framework through a recent and challenging problem in medical imaging: the regularization of diffusion tensor volumes (DTMRI).

The modal correspondence method of Shapiro and Brady aims to match point-sets by comparing the eigenvectors of a pairwise point proximity matrix. Although elegant by means of its matrix representation, the method is notoriously susceptible to differences in the relational structure of the point-sets under consideration. In this paper we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. We place the modal matching problem in a probabilistic setting in which the correspondences between pairwise clusters can be used to constrain the individual point correspondences. To meet this goal we commence by describing an iterative method which can be applied to the point proximity matrix to identify the locations of pairwise modal clusters. Once we have assigned points to clusters, we compute within-cluster and between-cluster proximity matrices. The modal co-efficients for these two sets of proximity matrices are used to compute cluster correspondence and cluster-conditional point correspondence probabilities. A sensitivity study on synthetic point-sets reveals that the method is considerably more robust than the conventional method to clutter or point-set contamination.

We introduce a new type of local feature based on the phase and amplitude responses of complex-valued steerable filters. The design of this local feature is motivated by a desire to obtain feature vectors which are semi-invariant under common image deformations, yet distinctive enough to provide useful identity information. A recent proposal for such local features involves combining differential invariants to particular image deformations, such as rotation. Our approach differs in that we consider a wider class of image deformations, including the addition of noise, along with both global and local brightness variations. We use steerable filters to make the feature robust to rotation. And we exploit the fact that phase data is often locally stable with respect to scale changes, noise, and common brightness changes. We provide empirical results comparing our local feature with one based on differential invariants. The results show that our phase-based local feature leads to better performance when dealing with common illumination changes and 2-D rotation, while giving comparable effects in terms of scale changes.

Independent representations have recently attracted significant attention from the biological vision and cognitive science communities. It has been 1) argued that properties such as sparseness and independence play a major role in visual perception, and 2) shown that imposing such properties on visual representations originates receptive fields similar to those found in human vision. We present a study of the impact of feature independence in the performance of visual recognition architectures. The contributions of this study are of both theoretical and empirical natures, and support two main conclusions. The first is that the intrinsic complexity of the recognition problem (Bayes error) is higher for independent representations. The increase can be significant, close to 10% in the databases we considered. The second is that criteria commonly used in independent component analysis are not sufficient to eliminate all the dependencies that impact recognition. In fact, “independent components” can be less independent than previous representations, such as principal components or wavelet bases.