This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.

We introduce an extended representation of time series that allows fast, accurate classification and clustering in addition to the ability to explore time series data in a relevance feedback framework. The representation consists of piecewise linear segments to represent shape and a weight vector that contains the relative importance of each individual linear segment. In the classification context, the weights are learned automatically as part of the training cycle. In the relevance feedback context, the weights are determined by an interactive and iterative process in which users rate various choices presented to them. Our representation allows a user to define a variety of similarity measures that can be tailored to specific domains. We demonstrate our approach on space telemetry, medical and synthetic data.

In this paper we present a novel technique for rapidly partitioning surfaces in range images into planar patches. Essential for our segmentation method is the observation that, in a scan line, the points belonging to a planar surface form a straight line segment. On the other hand, all points on a straight line segment surely belong to the same planar surface. Based on this observation, we first divide each scan line into straight line segments and subsequently consider only the set of line segments of all scan lines as segmentation primitives. We have developed a simple link-based data structure to efficiently represent line segments and their neighborhood relationship. The principle of our segmentation method is region growing. Three neighboring line segments satisfying an optimality criterion are selected as a seed region, and then a growing is carried out around the seed region. We use a noise variance estimation to automatically set some thresholds so that the algorithm can adapt ...

There has been much recent interest in adapting data mining algorithms to time series databases. Many of these algorithms need to compare time series. Typically some variation or extension of Euclidean distance is used. However, as we demonstrate in this paper, Euclidean distance can be an extremely brittle distance measure. Dynamic time warping (DTW) has been suggested as a technique to allow more robust distance calculations, however it is computationally expensive. In this paper we introduce a modification of DTW which operates on a higher level abstraction of the data, in particular, a piecewise linear representation. We demonstrate that our approach allows us to outperform DTW by one to three orders of magnitude. We experimentally evaluate our approach on medical, astronomical and sign language data.

In this paper we present a novel edge detection algorithm for range images based on a scan line approximation technique. Compared to the known methods in the literature, our algorithm has a number of advantages. It provides edge strength measures that have a straightforward geometric interpretation and supports a classification of edge points into several subtypes. We give a definition of optimal edge detectors and compare our algorithm to this theoretical model. By simulations we show that our algorithm has a near-optimal performance. We have carried out extensive tests using real range images acquired by three range scanners with quite different characteristics. The good results that were achieved demonstrate the robustness of our edge detection algorithm. CR Categories and Subject Descriptors: I.4.6 [Segmentation]: edge and feature detection, pixel classification; I.4.8 [Scene Analysis]: range data. General Terms: Algorithms. Additional Key Words: edge detection, scan line approxi...

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A central problem in object recognition is to determine the transformation that relates the model to the image, given some partial correspondence between the two. This is useful in determining whether an object is present in an image, and if so, determining where the object is. We present a novel method of solving this problem that uses region information. In our approach the model is divided into volumes, and the image is divided into regions. Given a match between subsets of volumes and regions (without any explicit correspondence between different pieces of the regions) the alignment transformation is computed. The method applies to planar objects under similarity, affine, and projective transformations and to projections of 3-D objects undergoing affine and projective transformations. 1 Introduction A fundamental problem in recognition is pose estimation. Given a correspondence between some portions of an object model and some portions of an image, determine the transformation th...

We show that the set of 2D images produced by the point features of a rigid 3D model can be represented with two lines in two high-dimensional spaces. These lines are the lowest-dimensional representation possible. We use this result to build a system for representing in a hash table at compile time, all the images that groups of model features can produce. Then at run time a group of image features can access the table and find all model groups that could match it. This table is efficient in terms of space, and is built and accessed through analytic methods that account for the effect of sensing error. In real images, it reduces the set of potential matches by a factor of several thousand. We also use this representation of a model's images to analyze two other approaches to recognition: invariants, and non-accidental properties. These are properties of images that some models always produce, and all other models either never produce (invariants) or almost never produce (non-accidental properties). In several domains we determine when invariants exist. In general we show that there are an infinite set of non-accidenta properties that are qualitatively similar.

This paper presents an experimental evaluation of different line extraction algorithms on 2D laser scans for indoor environment. Six popular algorithms in mobile robotics and computer vision are selected and tested. Experiments are performed on 100 real data scans collected in an office environment with a map size of 80m × 50m. Several comparison criteria are proposed and discussed to highlight the advantages and drawbacks of each algorithm, including speed, complexity, correctness and precision. The results of the algorithms are compared with the ground truth using standard statistical methods.

Given an n-vertex polygonal curve P = [p 1, p 2, : ::, pn] in the 2-dimensional space R 2, we consider the problem of approximating P by finding another polygonal curve P 0