About: Affine transformation is a(n) research topic. Over the lifetime, 23531 publication(s) have been published within this topic receiving 434668 citation(s). The topic is also known as: Affine map.
Papers published on a yearly basis
••21 Jun 1994
TL;DR: A feature selection criterion that is optimal by construction because it is based on how the tracker works, and a feature monitoring method that can detect occlusions, disocclusions, and features that do not correspond to points in the world are proposed.
Abstract: No feature-based vision system can work unless good features can be identified and tracked from frame to frame. Although tracking itself is by and large a solved problem, selecting features that can be tracked well and correspond to physical points in the world is still hard. We propose a feature selection criterion that is optimal by construction because it is based on how the tracker works, and a feature monitoring method that can detect occlusions, disocclusions, and features that do not correspond to points in the world. These methods are based on a new tracking algorithm that extends previous Newton-Raphson style search methods to work under affine image transformations. We test performance with several simulations and experiments. >
TL;DR: The results clearly indicate that the proposed nonrigid registration algorithm is much better able to recover the motion and deformation of the breast than rigid or affine registration algorithms.
Abstract: In this paper the authors present a new approach for the nonrigid registration of contrast-enhanced breast MRI. A hierarchical transformation model of the motion of the breast has been developed. The global motion of the breast is modeled by an affine transformation while the local breast motion is described by a free-form deformation (FFD) based on B-splines. Normalized mutual information is used as a voxel-based similarity measure which is insensitive to intensity changes as a result of the contrast enhancement. Registration is achieved by minimizing a cost function, which represents a combination of the cost associated with the smoothness of the transformation and the cost associated with the image similarity. The algorithm has been applied to the fully automated registration of three-dimensional (3-D) breast MRI in volunteers and patients. In particular, the authors have compared the results of the proposed nonrigid registration algorithm to those obtained using rigid and affine registration techniques. The results clearly indicate that the nonrigid registration algorithm is much better able to recover the motion and deformation of the breast than rigid or affine registration algorithms.
01 Nov 1993
TL;DR: A modification to the matching pursuit algorithm of Mallat and Zhang (1992) that maintains full backward orthogonality of the residual at every step and thereby leads to improved convergence is proposed.
Abstract: We describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. affine (wavelet) frames. We propose a modification to the matching pursuit algorithm of Mallat and Zhang (1992) that maintains full backward orthogonality of the residual (error) at every step and thereby leads to improved convergence. We refer to this modified algorithm as orthogonal matching pursuit (OMP). It is shown that all additional computation required for the OMP algorithm may be performed recursively. >
TL;DR: A comparative evaluation of different detectors is presented and it is shown that the proposed approach for detecting interest points invariant to scale and affine transformations provides better results than existing methods.
Abstract: In this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations. Our scale and affine invariant detectors are based on the following recent results: (1) Interest points extracted with the Harris detector can be adapted to affine transformations and give repeatable results (geometrically stable). (2) The characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives (the Laplacian). (3) The affine shape of a point neighborhood is estimated based on the second moment matrix. Our scale invariant detector computes a multi-scale representation for the Harris interest point detector and then selects points at which a local measure (the Laplacian) is maximal over scales. This provides a set of distinctive points which are invariant to scale, rotation and translation as well as robust to illumination changes and limited changes of viewpoint. The characteristic scale determines a scale invariant region for each point. We extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood. An iterative algorithm modifies location, scale and neighborhood of each point and converges to affine invariant points. This method can deal with significant affine transformations including large scale changes. The characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point. We present a comparative evaluation of different detectors and show that our approach provides better results than existing methods. The performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale/affine invariant descriptors computed on the regions associated with our points.
TL;DR: A general technique that facilitates nonlinear spatial (stereotactic) normalization and image realignment is presented that minimizes the sum of squares between two images following non linear spatial deformations and transformations of the voxel (intensity) values.
Abstract: This paper concerns the spatial and intensity transformations that map one image onto another. We present a general technique that facilitates nonlinear spatial (stereotactic) normalization and image realignment. This technique minimizes the sum of squares between two images following nonlinear spatial deformations and transformations of the voxel (intensity) values. The spatial and intensity transformations are obtained simultaneously, and explicitly, using a least squares solution and a series of linearising devices. The approach is completely noninteractive (automatic), nonlinear, and noniterative. It can be applied in any number of dimensions. Various applications are considered, including the realignment of functional magnetic resonance imaging (MRI) time-series, the linear (affine) and nonlinear spatial normalization of positron emission tomography (PET) and structural MRI images, the coregistration of PET to structural MRI, and, implicitly, the conjoining of PET and MRI to obtain high resolution functional images. © 1995 Wiley-Liss, Inc.