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.

Stable local feature detection and representation is a fundamental component of many image registration and object recognition algorithms. Mikolajczyk and Schmid [14] recently evaluated a variety of approaches and identified the SIFT [11] algorithm as being the most resistant to common image deformations. This paper examines (and improves upon) the local image descriptor used by SIFT. Like SIFT, our descriptors encode the salient aspects of the image gradient in the feature point's neighborhood; however, instead of using SIFT's smoothed weighted histograms, we apply Principal Components Analysis (PCA) to the normalized gradient patch. Our experiments demonstrate that the PCAbased local descriptors are more distinctive, more robust to image deformations, and more compact than the standard SIFT representation. We also present results showing that using these descriptors in an image retrieval application results in increased accuracy and faster matching.

This paper presents a powerful framework for generic object recognition. Boosting is used as an underlying learning technique. For the first time a combination of various weak classifiers of different types of descriptors is used, which slightly increases the classification result but dramatically improves the stability of a classifier. Besides applying well known techniques to extract salient regions we also present a new segmentation method-“Similarity-Measure-Segmentation”. This approach delivers segments, which can consist of several disconnected parts. This turns out to be a mighty description of local similarity. With regard to the task of object categorization, Similarity-Measure-Segmentation performs equal or better than current state-of-the-art segmentation techniques. In contrast to previous solutions we aim at handling of complex objects appearing in highly cluttered images. Therefore we have set up a database containing images with the required complexity. On these images we obtain very good classification results of up to 87 % ROC-equal error rate. Focusing the performance on common databases for object recognition our approach outperforms all comparable solutions.

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The problem of the independence and completeness of rotation moment invariants is addressed in this paper. First, a general method for constructing invariants of arbitrary orders by means of complex moments is described. As a major contribution of the paper, it is shown that for any set of invariants there exists a relatively small basis by means of which all other invariants can be generated. The method how to construct such a basis and how to prove its independence and completeness is presented. Some practical impacts of the new results are mentioned at the end of the paper.

We present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions. Moment invariants to convolution with an arbitrary centrosymmetric filter are derived first, and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance. Several examples of the invariants are calculated explicitly to illustrate the proposed procedure. Their invariance, robustness, and capability of using in template matching and in image registration are demonstrated on 3D MRI data and 2D indoor images.

Our goal is an automated 2D-image-pair registration algorithm capable of aligning images taken of a wide variety of natural and man-made scenes as well as many medical images. The algorithm should handle low overlap, substantial orientation and scale differences, large illumination variations, and physical changes in the scene. An important component of this is the ability to automatically reject pairs that have no overlap or have too many differences to be aligned well. We propose a complete algorithm including techniques for initialization, for estimating transformation parameters, and for automatically deciding if an estimate is correct. Keypoints extracted and matched between images are used to generate initial similarity transform estimates, each accurate over a small region. These initial estimates are rank-ordered and tested individually in succession. Each estimate is refined using the Dual-Bootstrap ICP algorithm, driven by matching of multiscale features. A three-part decision criteria, combining measurements of alignment accuracy, stability in the estimate, and consistency in the constraints, determines whether the refined transformation estimate is accepted as correct. Experimental results on a data set of 22 challenging image pairs show that the algorithm effectively aligns 19 of the 22 pairs and rejects 99.8 percent of the misalignments that occur when all possible pairs are tried. The algorithm substantially out-performs algorithms based on keypoint matching alone.

A new method is presented to learn object categories from unlabeled and unsegmented images for generic object recognition. We assume that each object can be characterized by a set of typical regions, and use a new segmentation method- “Similarity-Measure Segmentation ”- to split the im-ages into regions of interest. This approach may also deliver segments, which are split into several disconnected parts, which turns out to be a powerful description of local similarities. Several textu-ral features are calculated for each region, which are used to learn object categories with Boosting. We demonstrate the flexibility and power of our method by excellent results on various datasets. In comparison, our recognition results are significantly higher than results published in related work. 1

Abstract—For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database. Index Terms—Integral invariants, shape, shape matching, shape distance, shape retrieval. 1

In this paper we undertake a systematic investigation of affine invariant object detection and image denoising. Edge detection is first presented from the point of view of the affine invariant scale-space obtained by curvature based motion of the image level-sets. In this case, affine invariant maps are derived as a weighted difference of images at different scales. We then introduce the affine gradient as an affine invariant differential function of lowest possible order with qualitative behavior similar to the Euclidean gradient magnitude. These edge detectors are the basis for the extension of the affine invariant scale-space to a complete affine flow for image denoising and simplification, and to define affine invariant active contours for object detection and edge integration. The active contours are obtained as a gradient flow in a conformally Euclidean space defined by the image on which the object is to be detected. That is, we show that objects can be segmented in an affine invariant manner by computing a path of minimal weighted affine distance, the weight being given by functions of the affine edge detectors. The gradient path is computed via an algorithm which allows to simultaneously detect any number of objects independently of the initial curve topology. Based on the same theory of affine invariant gradient flows we show that the affine geometric heat flow is minimizing, in an affine invariant form, the area enclosed by the curve.