In this paper we compare the performance of descriptors computed for local interest regions, as for example extracted by the Harris-Affine detector [32]. Many different descriptors have been proposed in the literature. However, it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector. The descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector. Our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations. We compare shape context [3], steerable filters [12], PCA-SIFT [19], differential invariants [20], spin images [21], SIFT [26], complex filters [37], moment invariants [43], and cross-correlation for different types of interest regions. We also propose an extension of the SIFT descriptor, and show that it outperforms the original method. Furthermore, we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the SIFT based descriptors perform best. Moments and steerable filters show the best performance among the low dimensional descriptors.

this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting

Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. We show how to obtain a voxel grid from arbitrary 3D shapes and, using Fourier methods, we present an algorithm that computes the symmetry descriptor in O(N 4 log N) time for an N × N × N voxel grid and computes a multiresolution approximation in O(N 3 log N) time. In our initial experiments, we have found that the symmetry descriptor is insensitive to noise and stable under point sampling. We have also found that it performs well in shape matching tasks, providing a measure of shape similarity that is orthogonal to existing methods.

Introduction Many of the vision algorithms described in the literature are tested on a very small number of images. It is generally agreed that algorithms need to be tested on much larger numbers if any statistically meaningful measure of performance is to be obtained. However, these tests are rarely performed; in our opinion this is normally due to two reasons. Firstly, the scale of the testing problem when high levels of reliability are sought, since it is the proportion of failure cases that allows the reliability to be assessed and a large number of failure cases are needed to form an accurate estimation of reliability. For reliable and robust algorithms, this requires an inordinate number of test cases. Secondly, the difficulty of selecting test images to ensure that they are representative. This is aggravated by fact that assumptions made may be valid in one application domain but not in another. This makes it very difficult to relate the results of one evaluation to othe

We consider the relationship between the performance characteristics of vision algorithms and algorithm design. In the first part we discuss the issues involved in testing. A description of good practice is given covering test objectives, test data, test metrics and the test protocol. In the second part we discuss aspects of good algorithmic design including understanding of the statistical properties of data and common algorithmic operations, and suggest how some common problems may be overcome. 1

In this paper we propose to transform an image descriptor so that nearest neighbor (NN) search for correspondences becomes the optimal matching strategy under the assumption that inter-image deviations of corresponding descriptors have Gaussian distribution. The Euclidean NN in the transformed domain corresponds to the NN according to a truncated Mahalanobis metric in the original descriptor space. We provide theoretical justification for the proposed approach and show experimentally that the transformation allows a significant dimensionality reduction and improves matching performance of a state-of-the art SIFT descriptor. We observe consistent improvement in precision-recall and speed of fast matching in tree structures at the expense of little overhead for projecting the descriptors into transformed space. In the context of SIFT vs. transformed M-SIFT comparison, tree search structures are evaluated according to different criteria and query types. All search tree experiments confirm that transformed M-SIFT performs better than the original SIFT. 1.

Abstract. If a physical object has a smooth or piecewise smooth boundary, its images obtained by cameras in varying positions undergo smooth apparent deformations. These deformations are locally well approximated by affine transforms of the image plane. In consequence the solid object recognition problem has often been led back to the computation of affine invariant image local features. Such invariant features could be obtained by normalization methods, but no fully affine normalization method exists for the time being. Even scale invariance is only dealt with rigorously by the SIFT method. By simulating zooms out and normalizing translation and rotation, SIFT is invariant to four out of the six parameters of an affine transform. The method proposed in this paper, Affine-SIFT (ASIFT), simulates all image views obtainable by varying the two camera axis orientation parameters, namely the latitude and the longitude angles, left over by the SIFT method. Then it covers the other four parameters by using the SIFT method itself. The resulting method will be mathematically proved to be fully affine invariant. Against any prognosis, simulating all views depending on the two camera orientation parameters is feasible with no dramatic computational load. A two-resolution scheme further reduces the ASIFT complexity to about twice that of SIFT. A new notion, the transition tilt, measuring the amount of distortion from one view to another is introduced. While an absolute tilt from a frontal to a slanted view exceeding 6 is rare, much higher transition tilts are common when two slanted views of an object are compared (see Fig. 1.1). The attainable transition tilt is measured for each affine image comparison method. The new method permits to reliably identify features that have undergone transition tilts of large magnitude, up to 36 and higher. This fact is substantiated by many experiments which show that ASIFT outperforms significantly the state-of-the-art methods SIFT, MSER, Harris-Affine, and Hessian-Affine.

Abstract—Isometric surfaces share the same geometric structure, also known as the “first fundamental form. ” For example, all possible bendings of a given surface that includes all length preserving deformations without tearing or stretching the surface are considered to be isometric. We present a method to construct a bending invariant signature for such surfaces. This invariant representation is an embedding of the geometric structure of the surface in a small dimensional Euclidean space in which geodesic distances are approximated by Euclidean ones. The bending invariant representation is constructed by first measuring the intergeodesic distances between uniformly distributed points on the surface. Next, a multidimensional scaling (MDS) technique is applied to extract coordinates in a finite dimensional Euclidean space in which geodesic distances are replaced by Euclidean ones. Applying this transform to various surfaces with similar geodesic structures (first fundamental form) maps them into similar signature surfaces. We thereby translate the problem of matching nonrigid objects in various postures into a simpler problem of matching rigid objects. As an example, we show a simple surface classification method that uses our bending invariant signatures. Index Terms—MDS (Multi-Dimensional Scaling), FMTD (Fast Marching Method on Triangulate Domains), isometric signature, classification, geodesic distance.

In this paper we compare the performance of descriptors computed for local interest regions, as for example extracted by the Harris-Affine detector [32]. Many different descriptors have been proposed in the literature. However, it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector. The descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector. Our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations. We compare shape context [3], steerable filters [12], PCA-SIFT [19], differential invariants [20], spin images [21], SIFT [26], complex filters [37], moment invariants [43], and cross-correlation for different types of interest regions. We also propose an extension of the SIFT descriptor, and show that it outperforms the original method. Furthermore, we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the SIFT based descriptors perform best. Moments and steerable filters show the best performance among the low dimensional descriptors.

It is frequently remarked that designers of computer vision algorithms and systems cannot reliably predict how algorithms will respond to new problems. A variety of reasons have been given for this situation and a variety of remedies prescribed in literature. Most of these involve, in some way, paying greater attention to the domain of the problem and to performing detailed empirical analysis. The goal of this paper is to review what we see as current best practices in these areas and also suggest refinements that may benefit the field of computer vision. A distinction is made between the historical emphasis on algorithmic novelty and the increasing importance of validation on particular data sets and problems.