Catálogo de publicaciones - libros

We derive a probabilistic multi-scale model for contour completion based on image statistics. The boundaries of human segmented images are used as “ground truth”. A probabilistic formulation of contours demands a prior model and a measurement model. From the image statistics of boundary contours, we derive both the prior model of contour shape and the local likelihood model of image measurements. We observe multi-scale phenomena in the data, and accordingly propose a higher-order Markov model over scales for the contour continuity prior. Various image cues derived from orientation energy are evaluated and incorporated into the measurement model. Based on these models, we have designed a multi-scale algorithm for contour completion, which exploits both contour continuity and texture. Experimental results are shown on a wide range of images.

We investigate the statistics of local geometric structures in natural images. Previous studies [,] of high-contrast 3×3 natural image patches have shown that, in the state space of these patches, we have a concentration of data points along a low-dimensional non-linear manifold that corresponds to edge structures. In this paper we extend our analysis to a filter-based multiscale image representation, namely the local 3-jet of Gaussian scale-space representations. A new picture of natural image statistics seems to emerge, where primitives (such as edges, blobs, and bars) generate low-dimensional structures in the state space of image data.

The Beltrami flow [,] is one of the most effective denoising algorithms in image processing. For gray-level images, we show that the Beltrami flow equation can be arranged in a reaction-diffusion form. This reveals the edge-enhancing properties of the equation and suggests the application of additive operator split (AOS) methods [,] for faster convergence. As we show with numerical simulations, the AOS method results in an unconditionally stable semi-implicit linearized difference scheme in 2 and 3. The values of the edge indicator function are used from the previous step in scale, while the pixel values of the next step are used to approximate the flow. The optimum ratio between the reaction and diffusion counterparts of the governing PDE is studied, in order to achieve a better quality of segmentation. The computational time decreases by a factor of ten, as compared to the explicit scheme. For 2D color images, the Beltrami flow equations are coupled, and do not yield readily to the AOS technique. However, in the proximity of an edge, the cross-products of color gradients nearly vanish, and the coupling becomes weak. The principal directions of the edge indicator matrix are normal and tangent to the edge. Replacing the action of the matrix on the gradient vector by an action of its eigenvalue, we reduce the color problem to the gray level case with a reasonable accuracy. The scalar edge indicator function for the color case becomes essentially the same as that for the gray level image, and the fast implicit technique is implemented.

A new feature detection technique is presented that utilises local radial symmetry to identify regions of interest within a scene. This transform is significantly faster than existing techniques using radial symmetry and offers the possibility of real-time implementation on a standard processor. The new transform is shown to perform well on a wide variety of images and its performance is tested against leading techniques from the literature. Both as a facial feature detector and as a generic region of interest detector the new transform is seen to offer equal or superior performance to contemporary techniques whilst requiring drastically less computational effort.

Quadrature filters are a well known method of low-level computer vision for estimating certain properties of the signal, as there are local amplitude and local phase. However, 2D quadrature filters suffer from being not rotation invariant. Furthermore, they do not allow to detect truly 2D features as corners and junctions unless they are combined to form the structure tensor. The present paper deals with a new 2D generalization of quadrature filters which is rotation invariant and allows to analyze intrinsically 2D signals. Hence, the new approach can be considered as the union of properties of quadrature filters and of the structure tensor. The proposed method first estimates the local orientation of the signal which is then used for steering some basis filter responses. Certain linear combination of these filter responses are derived which allow to estimate the local isotropy and two perpendicular phases of the signal. The phase model is based on the assumption of an angular band-limitation in the signal. As an application, a simple and efficient point-of-interest operator is presented and it is compared to the Plessey detector.

Edge detection depends not only upon the assumed model of what an edge is, but also on how this model is represented. The problem of how to represent the edge model is typically neglected, despite the fact that the representation is a bottleneck for both computational cost and accuracy. We propose to represent edge models by a partition of the edge manifold corresponding to the edge model, where each local element of the partition is described by its principal components. We describe the construction of this representation and demonstrate its benefits for various edge models.

We address the issue of regularizing Osher and Rudin’s shock filter, used for image deblurring, in order to allow processes that are more robust against noise. Previous solutions to the problem suggested adding some sort of diffusion term to the shock equation. We analyze and prove some properties of coupled shock and diffusion processes. Finally we propose an original solution of adding a complex diffusion term to the shock equation. This new term is used to smooth out noise and indicate inflection points simultaneously. The imaginary value, which is an approximated smoothed second derivative scaled by time, is used to control the process. This results in a robust deblurring process that performs well also on noisy signals.

There has been considerable success in automated reconstruction for image sequences where small baseline algorithms can be used to establish matches across a number of images. In contrast in the case of widely separated views, methods have generally been restricted to two or three views.

In this paper we investigate the problem of establishing relative viewpoints given a large number of images where no ordering information is provided. A typical application would be where images are obtained from different sources or at different times: both the viewpoint (position, orientation, scale) and lighting conditions may vary significantly over the data set.

Such a problem is not fundamentally amenable to exhaustive pair wise and triplet wide baseline matching because this would be prohibitively expensive as the number of views increases. Instead, we investiate how a combination of image invariants, covariants, and multiple view relations can be used in concord to enable efficient multiple view matching. The result is a matching algorithm which is linear in the number of views.

The methods are illustrated on several real image data sets. The output enables an image based technique for navigating in a 3D scene, moving from one image to whichever image is the next most appropriate.

Estimating the parameters of a pencil of lines is addressed. A statistical model for the measurements is developed, from which the Cramer Rao lower bound is determined. An estimator is derived, and its performance is simulated and compared to the bound. The estimator is shown to be asymptotically efficient, and superior to the classical least squares algorithm.

Natural images are the composite consequence of multiple factors related to scene structure, illumination, and imaging. Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing the multifactor structure of image ensembles and for addressing the difficult problem of disentangling the constituent factors or modes. Our multilinear modeling technique employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the -mode SVD. As a concrete example, we consider the multilinear analysis of ensembles of facial images that combine several modes, including different facial geometries (people), expressions, head poses, and lighting conditions. Our resulting “TensorFaces” representation has several advantages over conventional eigenfaces. More generally, multilinear analysis shows promise as a unifying framework for a variety of computer vision problems.