jzujovic's image [8 articles]

Abstract

Isometric surfaces share the same geometric structure also known as the first fundamental form. For example, bending of a given surface, that includes length preserving deformations without tearing or stretching the surface, are considered to be isometric. We present a method to construct a bending invariant canonical form for such surfaces. This invariant representation is an embedding of the intrinsic geodesic structure of the surface in a finite dimensional Euclidean space, in which geodesic distances are approximated by Euclidean ones. The ...

Abstract

The images generated by varying the underlying articulation parameters of an object (pose, attitude, light source position, and so on) can be viewed as points on a low-dimensional image parameter articulation manifold (IPAM) in a high-dimensional ambient space. In this paper, we develop theory and methods for the inverse problem of estimating, from a given image on or near an IPAM, the underlying parameters that produced it. Our approach is centered on the observation that, while typical image manifolds are not ...

Abstract

In this paper, we study families of images generated by varying aparameter that controls the appearance of the object/scene in each image. Each image is viewed as a point in high-dimensional space; the family of images forms a low-dimensional submanifold that we call an image appearance manifold (IAM). We conduct a detailed study of some representative IAMs generated by translations/rotations of simple objects in the plane and by rotations of objects in 3-D space. Our central, somewhat surprising, finding is that ...

Abstract

Abstract  Can we detect low dimensional structure in high dimensional data sets of images? In this paper, we propose an algorithm for unsupervised learning of image manifolds by semidefinite programming. Given a data set of images, our algorithm computes a low dimensional representation of each image with the property that distances between nearby images are preserved. More generally, it can be used to analyze high dimensional data that lies on or near a low dimensional manifold. We illustrate the algorithm on easily ...

Abstract

Many low-level vision algorithms assume a prior probability over images, and there has been great interest in trying to learn this prior from examples. Since images are very non Gaussian, high dimensional, continuous signals, learning their distribution presents a tremendous computational challenge. Perhaps the most successful recent algorithm is the Fields of Experts (FOE) [20] model which has shown impressive performance by modeling image statistics with a product of potentials defined on filter outputs. However, as in previous models of images ...

Abstract

Image matching is a fundamental computer vision problem that includes many scenarios, such as varying the view scene matching, feature selection and registration, object recognition, and general object class matching. This article presents a unified framework and working algorithm for these different matching scenarios. The proposed feature-based image matching method demonstrates excellent robustness to significant geometrical transformation, intra-class variation and background clutter which are usually presented in different matching scenarios. ...

Abstract

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness ...