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.

This paper describes a new approach to low level image processing; in particular, edge and corner detection and structure preserving noise reduction.

This article presents: (i) a multi-scale representation of grey-level shape called the scale-space primal sketch, which makes explicit both features in scale-space and the relations between structures at different scales, (ii) a methodology for extracting significant blob-like image structures from this representations, and (iii) applications to edge detection, histogram analysis, and junction classification demonstrating how the proposed method can be used for guiding later stage visual processes. The representation gives a qualitative description of image structure, which allows for detection of stable scales and associated regions of interest in a solely bottom-up data-driven way. In other words, it generates coarse segmentation cues, and can hence be seen as preceding further processing, which can then be properly tuned. It is argued that once such information is available, many other processing tasks can become much simpler. Experiments on real imagery demonstrate that the proposed theory gives intuitive results.

Abstract | This paper addresses the problem of retrieving images from large image databases. The method is based on local greyvalue invariants which are computed at automatically detected interest points. Avoting algorithm and semi-local constraints make retrieval possible. Indexing allows for e cient retrieval from a database of more than 1000 images. Experimental results show correct retrieval in the case of partial visibility, similarity transformations, extraneous features, and small perspective deformations.

this paper, the boxes H i #!# indicate circular convolution of a #nite input image of size N with a #lter with impulse response h i #n# and Fourier transform

We discuss the physical generation process of images as a combination of occlusions, transparencies and contrast changes. This description #ts to the phenomenological description of Gaetano Kanizsa, according to which visual perception tends to remain stable with respect to these basic operations by detecting several kinds of essential singularities which we call junctions. The most frequent junctions are T-junctions and X-junctions, generated respectively by occlusion and transparency. We deduce a mathematical and computational model for image analysis according to which the "atoms", that is, the starting elements of every image analysis process must be "pieces of level lines joining T-or X-junctions". A junction detection algorithm, parameter-free except for two #xed thresholds eliminating quantization e#ects in space and grey level, is proposed for the computation of the "atoms of perception" thus de#ned. We then propose the adequate modi#cation of morphological #ltering algorithms so that they smooth the "atoms" without altering the junctions. This permits to display easy-to-read topographic maps for images, where the subjacent #and mostly hidden to the human awareness# occlusion-transparency structure is put into evidence by the interplay of level lines. 1

The purpose of this report 1 is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scale-space paradigm. It is argued that the design of optic flow based applications may benefit from a manifest separation between factual image structure on the one hand, and goal-specific details and hypotheses about image flow formation on the other. The approach is based on a physical symmetry principle known as gauge invariance. Data-independent models can be incorporated by means of admissible gauge conditions, each of which may single out a distinct solution, but all of which must be compatible with the evidence supported by the image data. The theory is illustrated by examples and verified by simulations, and performance is compared to several techniques reported in the literature. 1 Introduction The conventional "spacetime" representation of a movie as...

Abstract. We propose a simple approach to evolution of polygonal curves that is specially designed to t discrete nature of curves in digital images. It leads to simpli cation of shape complexity withnoblurring (i.e., shape rounding) e ects and no dislocation of relevant features. Moreover, in our approach the problem to determine the size of discrete steps for numerical implementations does not occur, since our evolution method leads in a natural way to a nite number of discrete evolution steps which are just the iterations of a basic procedure of vertex deletion.

This article presents a theory for multi-scale representation of temporal data. Assuming that a real-time vision system should represent the incoming data at di erent time scales, an additional causality constraint arises compared to traditional scale-space theory|we can only use what has occurred in the past for computing representations at coarser time scales. Based on a previously developed scale-space theory in terms of noncreation of local maxima with increasing scale, a complete classi cation is given of the scale-space kernels that satisfy this property of non-creation of structure and respect the time direction as causal. It is shown that the cases of continuous and discrete time are inherently di erent. For continuous time, there is no non-trivial time-causal semi-group structure. Hence, the time-scale parameter must be discretized, and the only way to construct a linear multi-time-scale representation is by (cascade) convolution with truncated exponential functions having (possibly) di erent time constants. For discrete time, there is a canonical semi-group structure allowing for a continuous temporal scale parameter. It gives rise to a Poisson-type temporal scale-space. In addition, geometric moving average kernels and time-delayed generalized binomial kernels satisfy temporal causality and allow for highly e cient implementations. It is shown that temporal derivatives and derivative approximations can be obtained directly as linear combinations of the temporal channels in the multi-time-scale representation. Hence, to maintain a representation of temporal derivatives at multiple time scales, there is no need for other time bu ers than the temporal channels in the multi-time-scale representation. The framework presented constitutes a useful basis for expressing a large class of algorithms for computer vision, image processing and coding. 1

The subject of scale selection is essential to many aspects of multi-scale and multi-resolution processing of image data. This article shows how a general heuristic principle for scale selection can be appliedtotheproblem of detecting and localizing junctions. In a rst uncommitted processing step initial hypotheses about interesting scale levels (and regions of interest) are generated from scales where normalized di erential invariants assume maxima over scales (and space). Then, based on this scale (and region) information, a more re ned processing stage is invoked tuned to the task at hand. The resulting method is the rst junction detector with automatic scale selection. Whereas this article deals with the speci c problem of junction detection, the underlying ideas apply also to other types of di erential feature detectors, such as blob detectors, edge detectors, and ridge detectors. 1.