Abstract. In this paper we address one of the standard problems of image processing and computer vision: The detection of points of interest (POI). We propose two new approaches for improving the detection results. First, we define an energy tensor which can be considered as a phase invariant extension of the structure tensor. Second, we use the channel representation for robustly clustering the POI information from the first step resulting in sub-pixel accuracy for the localisation of POI. We compare our method to several related approaches on a theoretical level and show a brief experimental comparison to the Harris detector. 1

A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor control. Previous approaches based on first-order Taylor series expansions of images can be regarded as special cases of the Lie group approach, which utilizes a matrix-exponential-based generative model of images and can handle arbitrarily large transformations. We present an unsupervised expectation-maximization algorithm for learning Lie transformation operators directly from image data containing examples of transformations. Our experimental results show that the Lie operators learned by the algorithm from an artificial data set containing six types of affine transformations closely match the analytically predicted affine operators. We then demonstrate that the algorithm can also recover novel transformation operators from natural image sequences. We conclude by showing that the learned operators can be used to both generate and estimate transformations in images, thereby providing a basis for achieving visual invariance.

Abstract. In this paper we propose a new operator which combines advantages of monogenic scale-space and Gaussian scale-space, of the monogenic signal and the structure tensor. The gradient energy tensor (GET) defined in this paper is based on Gaussian derivatives up to third order using different scales. These filters are commonly available, separable, and have an optimal uncertainty. The response of this new operator can be used like the monogenic signal to estimate the local amplitude, the local phase, and the local orientation of an image, but it also allows to measure the coherence of image regions as in the case of the structure tensor. Both theoretically and in experiments the new approach compares favourably with existing methods. 1

The paper makes a short presentation of three existing methods for estimation of orientation tensors, the so-called structure tensor, quadrature filter based techniques, and techniques based on approximating a local polynomial model. All three methods can be used for estimating an orientation tensor which in the 3D case can be used for motion estimation. The methods are based on rather different approaches in terms of the underlying signal models. However, they produce more or less similar results which indicates that there should be a common framework for estimation of the tensors. Such a framework is proposed, in terms of a second order mapping from signal to tensor with additional conditions on the mapping. It it also shown that the three methods in principle fall into this framework. The optic-flow equation

This paper presents an algorithm for estimation of local curvature from gradients of a tensor field that represents local orientation. The algorithm is based on an operator representation of the orientation tensor, which means that change of local orientation corresponds to a rotation of the eigenvectors of the tensor. The resulting curvature descriptor is a vector that points in the direction of the image in which the local orientation rotates anti-clockwise and the norm of the vector is the inverse of the radius of curvature. Two coefficients are defined that relate the change of local orientation with either curves or radial patterns. 1 Introduction Two-dimensional curvature can be defined in different ways. For example, curvature can be defined as the rate of change of the tangent angle with respect to the curve length. An other way is to first estimate local orientation, resulting in a field of orientation descriptors, and then consider its variation with respect to the image coo...

Nyckelord Keywords Rapporttyp Report: category Licentiatavhandling C-uppsats D-uppsats vrig rapport Sprk Language Svenska/Swedish Engelska/English ISBN Serietitel och serienummer Title of series, numbering URL fr elektronisk version Titel Title Frfattare Author Datum Date Avdelning, Institution Division, department ISRN Examensarbete ISSN LiTH-ISY-R-2300 95-11-01/lli To find a shape in an image, a technique called snakes or active contours can be used. An active contour is a curve that moves towards the sought-for shape in a way controlled by internal forces (elasticity and rigidity) and an image derived force, the latter attracting the contour to certain features, such as edges, in the image. We will here discuss contours (surfaces) in 3D image volumes. A new, noise-resistant, way of creating the image force, attracting the contour to planar structure in 3-D images, is discussed. Also, a method to increase stability and control of the contour is described. The experime...