Learning the Topology of Object Views

Abstract

Abstract.A visual representation of an object must meet at least three basic requirements. First, it must allow identification of the object in the presence of slight but unpredictable changes in its visual appearance. Second, it must account for larger changes in appearance due to variations in the object's fundamental degrees of freedom, such as, e.g., changes in pose. And last, any object representation must be derivable from visual input alone, i.e., it must be learnable. We here construct such a representation by deriving transformations between the different views of a given object, so that they can be parameterized in terms of the object's physical degrees of freedom. Our method allows to automatically derive the appearance representations of an object in conjunction with their linear deformation model from example images. These are subsequently used to provide linear charts to the entire appearance manifold of a three-dimensional object. In contrast to approaches aiming at mere dimensionality reduction the local linear charts to the object's appearance manifold are estimated on a strictly local basis avoiding any reference to a metric embedding space to all views. A real understanding of the object's appearance in terms of its physical degrees of freedom is this way learned from single views alone.

Learning nonlinear image manifolds by global alignment of local linear models

“…In contrast, other approaches for alignment of local models [36], [37], [38] proceed in two steps: first a mixture of local linear models is estimated (typically on the basis of maximum likelihood), and second the local models are aligned on the basis of a second criterion. Such approaches thus do not allow modification of the local models to improve alignment.…”

Reconstruction of images from Gabor graphs with applications in facial image processing

“…1,16,24,25 For object detection and recognition, usually grid graphs are employed, i. e., the landmarks are arranged in a grid structure and the edges link horizontal or vertical neighboring nodes. For frontal faces, a face graph is created.…”

Tracking 3D Object using Flexible Models

“…In [3] a generative model is learned through a PCA analysis of a set of training examples. In [15] elastic graph matching [8] is used to determine the corresponding points of consecutive images. The variations between several views of the same object are expressed in terms of variations in some underlying low-dimensional parameter space using PCA.…”

“…This model describes variations of object appearance in the images due to pose change relatively to the camera point of view. This part of the algorithm is basically derived from [12,15] combined with the use of 2D Thin Plate Spline (TPS) regularization function [17].…”

“…The TPS scheme has been preferred because it can estimate deformations directly from any set of local correspondences [17] while elastic graph matching requires grid node correspondences [12,15]. TPS also takes advantage of a built-in regularization parameter, thus handling erroneous point correspondences, as explained later.…”