A performance study of the tangent distance method in transformation-invariant image classification

A common problem in image analysis is the transformation-invariant estimation of the similarity between a query image and a set of reference images representing different classes. This typically requires the comparison of the distance between the query image and the transformation manifolds of the reference images. The tangent distance algorithm is a popular method that estimates the manifold distance by employing a linear approximation of the transformation manifolds. In this paper, we present a performance analysis of the tangent distance method in image classification applications for general transformation models. In particular, we characterize the misclassification error in terms of the geometric properties of the individual manifolds such as their curvature, as well as their relative properties such as the separation between them. We then extend our results to a multi-scale analysis where the images are smoothed with a low-pass filter and study the effect of smoothing on the misclassification error. Our theoretical results are confirmed by experiments and may find use in the selection of algorithm parameters in multiscale transformation-invariant image analysis methods.


Analysis of Image Registration with Tangent Distance
Vural, Elif (2014-01-01)
The computation of the geometric transformation between a reference and a target image, known as registration or alignment, corresponds to the projection of the target image onto the transformation manifold of the reference image (the set of images generated by its geometric transformations). However, it often takes a nontrivial form such that the exact computation of projections on the manifold is difficult. The tangent distance method is an effective algorithm for solving this problem by exploiting a line...
A comparative study on pose estimation algorithms using visual data
Çetinkaya, Güven; Alatan, Abdullah Aydın; Department of Electrical and Electronics Engineering (2012)
Computation of the position and orientation of an object with respect to a camera from its images is called pose estimation problem. Pose estimation is one of the major problems in computer vision, robotics and photogrammetry. Object tracking, object recognition, self-localization of robots are typical examples for the use of pose estimation. Determining the pose of an object from its projections requires 3D model of an object in its own reference system, the camera parameters and 2D image of the object. Mo...
A Study of the Classification of Low-Dimensional Data with Supervised Manifold Learning
Vural, Elif (2018-01-01)
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalizat...
Alignment of uncalibrated images for multi-view classification
Arık, Sercan Ömer; Vural, Elif; Frossard, Pascal (2011-12-29)
Efficient solutions for the classification of multi-view images can be built on graph-based algorithms when little information is known about the scene or cameras. Such methods typically require a pairwise similarity measure between images, where a common choice is the Euclidean distance. However, the accuracy of the Euclidean distance as a similarity measure is restricted to cases where images are captured from nearby viewpoints. In settings with large transformations and viewpoint changes, alignment of im...
Analysis of Descent-Based Image Registration
Vural, Elif (2013-01-01)
We present a performance analysis for image registration with gradient descent. We consider a typical multiscale registration setting where the global two-dimensional translation between a pair of images is estimated by smoothing the images and minimizing the distance between them with gradient descent. Our study particularly concentrates on the effect of noise and low-pass filtering on the alignment accuracy. We analyze the well-behavedness of the image distance function by estimating the neighborhood of t...
Citation Formats
E. Vural, “A performance study of the tangent distance method in transformation-invariant image classification,” 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41683.