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.

Although traditional scale-space theory provides a well-founded framework for dealing with image structures at different scales, it does not directly address the problem of how to select appropriate scales for further analysis. This paper introduces a new tool for dealing with this problem. A heuristic principle is proposed stating that local extrema over scales of different combinations of normalized scale invariant derivatives are likely candidates to correspond to interesting structures. Support is given by theoretical considerations and experiments on real and synthetic data. The resulting methodology lends itself naturally to two-stage algorithms; feature detection at coarse scales followed by feature localization at ner scales. Experiments on blob detection, junction detection and edge detection demonstrate that the proposed method gives intuitively reasonable results.

Multiscale image analysis has been used successfully in a number of applications to classify image features according to their relative scales. As a consequence, much has been learned about the scale-space behavior of intensity extrema, edges, intensity ridges, and grey-level blobs. In this paper, we investigate the multiscale behavior of gradient watershed regions. These regions are defined in terms of the gradient properties of the gradient magnitude of the original image. Boundaries of gradient watershed regions correspond to the edges of objects in an image. Multiscale analysis of intensity minima in the gradient magnitude image provides a mechanism for imposing a scale-based hierarchy on the watersheds associated with these minima. This hierarchy can be used to label watershed boundaries according to their scale. This provides valuable insight into the multiscale properties of edges in an image without following these curves through scale-space. In addition, the gradient watershed region hierarchy can be used for automatic or interactive image segmentation. By selecting subtrees of the region hierarchy, visually sensible objects in an image can be easily constructed.

It is developed how discrete derivative approximations can be de ned so that scale-space properties hold exactly also in the discrete domain. Starting from a set of natural requirements on the rst processing stages of a visual system, the visual front end, an axiomatic derivation is given of how amulti-scale representation of derivative approximations can be constructed from a discrete signal, so that it possesses an algebraic structure similar to that possessed by the derivatives of the traditional scale-space representation in the continuous domain. A family of kernels is derived which constitute discrete analogues to the continuous Gaussian derivatives. The representation has theoretical advantages to other discretizations of the scalespace theory in the sense that operators which commute before discretization commute after discretization. Some computational implications of this are that derivativeapproximations can be computed directly from smoothed data, and that this will give exactly the same result as convolution with the corresponding derivative approximation kernel. Moreover, a number of normalization conditions are automatically satis ed. The proposed methodology leads to a conceptually very simple scheme of computations for multi-scale low-level feature extraction, consisting of four basic steps � (i) large support convolution smoothing, (ii) small support di erence computations, (iii) point operations for computing di erential geometric entities, and (iv) nearest neighbour operations for feature detection. Applications are given demonstrating how the proposed scheme can be used for edge detection and junction detection based on derivatives up to order three.

We consider the group of invertible image gray-value transformations and propose a generating equation for a complete set of differential gray-value invariants up to any order. Such invariants describe the image’s geometrical structure independent of how its gray-values are mapped (contrast or brightness adjustments).

When observing a dynamic world, the size of image structures may vary over time.

Corresponding image points of a rigid object in a discrete sequence of images fulfil the so called multilinear constraint. In this paper the continuous time analogue of this constraint, for a continuous stream of images, is introduced and studied. The constraint link the Taylor expansion of the motion of the image points with the Taylor expansion of the relative motion and orientation between the object and the camera. The analysis is done both for calibrated and uncalibrated cameras. Two simplifications are also presented for the uncalibrated camera case. One simplification is made using an affine reduction and the so called kinetic depths. The second simplification is based upon a projective reduction with respect to the image of a planar configuration. The analysis shows that the constraint involving second order derivatives are needed to determine camera motion. Experiments with real and simulated data are also presented.

We investigate the deep structure of a scale space image. We concentrate on scale space critical points -- points with vanishing gradient with respect to both spatial and scale direction. We show that these points are always saddle points. They turn

This article presents a method for segmenting and classifying edges using minimum description length (MDL) approximation with automatically generated break points. A scheme is proposed where junction candidates are first detected in a multi-scale preprocessing step, which generates junction candidates with associated regions of interest. These junction features are matched to edges based on spatial coincidence. For each matched pair, a tentative break point is introduced at the edge point closest to the junction. Finally, these feature combinations serve as input for an MDL approximation method which tests the validity of the break point hypotheses and classifies the resulting edge segments as either "straight " or "curved". Experiments on real world image data demonstrate the viability of the approach.

A major problem in computer vision for decades concerned the representation of the differential structure of the jet bundle of an input image in a way robust to noise and consistent with the input data. Consequently the description of local and global image properties remained unfeasible for quite a long time. We show that on the basis of physical assumptions it is necessary to describe the differential structure of an input image in terms of one-parameter families of images that are similarity solutions of the spatially isotropic diffusion equation underlying the observation process. These images represent the differential structure of the input image at a continuous range of resolutions or scales. Knowing these scaled versions of the differential structure we give a coordinate independent multi-scale description of an input image: by means of implicit differentiation, dioeerential geometry and homology we may compute local and global invariants of manifolds implicitly de...