In this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape. Ve call the representation the curvature primgl ,sketch. We describe an implemented algorithn that computes the curvature primal sketch and illustra. te its performance on a set of tool shapes. The curvature primal sketch derites ils name from the close analogy to the primal sketch representation advocated ty Mart for descri.bi!)g significant intensity changes. We define a set of primitive parameterized curvature discontinuities, and derive expressions for their convolutions vith the first and second derivatives ot' a Gaussian. The convolved primitives, sorted according to the scale at 'which they are detected, provide us with a multi-scaled interpretation of the'contoar of a shape.

Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part of the edge d6tection problem. To characterize the types of intensity changes derivatives of different types, and possibly different scales, are needed. Thus, we consider this part of edge detection as a problem in numerical differentiation.

We prove that the scale map of the zero-crossings of atmost all signals filtered by the second derivative of a gaussian of variable size determines the signal uniquely, up to a constant scaling and a harmonic function. Our proof provides a method for reconstructing almost all signals from knowledge of how the zero-crossing contours of the signal, fitered by a gaussian filter, change with the size of the filter. The proof assumes that the filtered signal can be represented as a polynomial of finite, albeit possibly very high, order. An argument suggests that this restriction is not essential. Stability of the reconstruction scheme is briefly discussed. The result applies to zero- and level-crossings of linear differential operators of gaussian filters. The theorem is extended to two dimensions, that is to images. These results are reminiscent of Logan's theorem. They imply that extrema of derivatives at different scales are a complete representation of a signal.

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—Diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, analyzing images at multiple scales, and enhancing discontinuities. A number of diffusions of image brightness have been defined and studied so far; they may be applied to scalar and vector-valued quantities that are naturally associated with intervals of either the real line, or other flat manifolds. Some quantities of interest in computer vision, and other areas of engineering that deal with images, are defined on curved manifolds; typical examples are orientation and hue that are defined on the circle. Generalizing brightness diffusions to orientation is not straightforward, especially in the case where a discrete implementation is sought. An example of what may go wrong is presented. A method is proposed to define diffusions of orientation-like quantities. First a definition in the continuum is discussed, then a discrete orientation diffusion is proposed. The behavior of such diffusions is explored both analytically and experimentally. It is shown how such orientation diffusions contain a nonlinearity that is reminiscent of edge-process and anisotropic diffusion. A number of open questions are proposed at the end. Index Terms—Orientation analysis, texture analysis, diffusions, scale-space.

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.

Many computer vision problems can be considered to consist of two main tasks: the extraction of image content descriptions and their subsequent matching. The appropriate choice of type and level of description is of course task dependent, yet it is generally accepted that the low-level or so called early vision layers in the Human Visual System are context independent. This paper concentrates on the use of low-level approaches for solving computer vision problems and discusses three inter-related aspects of this: saliency; scale selection and content description. In contrast to many previous approaches which separate these tasks, we argue that these three aspects are intrinsically related. Based on this observation, a multiscale algorithm for the selection of salient regions of an image is introduced and its application to matching type problems such as tracking, object recognition and image retrieval is demonstrated.

We address the formulation of a scale-space theory for discrete signals. In one dimension it is possible to characterize the smoothing transformations completely and an exhaustive treatment is given, answering the following two main questions: 1. Which linear transformations remove structure in the sense that the number of local extrema (or zero-crossings) in the output signal does not exceed the number of local extrema (or zero-crossings) in the original signal? 2. How should one create a multi-resolution family of representations with the property that a signal at a coarser level of scale never contains more structure than a signal at a finer level of scale? We propose that there is only one reasonable way to define a scale-space for 1D discrete signals comprising a continuous scale parameter, namely by (discrete) convolution with the family of kernels T (n; t) = e I n (t), where I n are the modified Bessel functions of integer order. Similar arguments applied in the continuous case uniquely lead to the Gaussian kernel.

This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous B-spline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct B-spline transform). The reverse operation is the signal reconstruction from its spline coefficients with an optional zooming factor rn (indirect B-spline transform) . We derive general expressions for the z transforms and the equivalent continuous impulse responses of B-spline interpolators of order n. We present simple techniques for signal differentiation and filtering in the transformed domain. We then derive recursive filters that efficiently solve the problems of smoothing spline and least squares approximations. The smoothing spline technique approximates a signal with a complete set of coefficients subject to certain regularization or smoothness constraints. The least squares approach, on the other hand, uses a reduced number of B-spline coefficients with equally spaced nodes; this technique is in many ways analogous to the application of antialiasing low-pass filter prior to decimation in order to represent a signal correctly with a reduced number of samples.

An algorithm is presented that scales the pixel intensities of a computer generated greyscale image so that they are all displayable on a standard CRT. This scaling is spatially nonuniform over the image in that different pixels with the same intensity in the original image may have different intensities in the resulting image. The goal of this scaling transformation is to produce an image on the CRT that perceptually mimics the calculated image, while staying within the physical limitations of the CRT. CR Categories and SubjectDescriptors: I.3.0 [Computer Graphics]: