Tony Lindeberg

Feature Detection with Automatic Scale Selection

The fact that objects in the world appear in different ways depending on the scale of observation has important implications if one aims at describing them. It shows that the notion of scale is of utmost importance when processing unknown measurement data by automatic methods. In their seminal works, Witkin (1983) and Koenderink (1984) proposed to approach this problem by representing image structures at different scales in a so-called scale-space representation. Traditional scale-space theory building on this work, however, does not address the problem of how to select local appropriate scales for further analysis. This article proposes a systematic methodology for dealing with this problem. A framework is presented for generating hypotheses about interesting scale levels in image data, based on a general principle stating that local extrema over scales of different combinations of γ-normalized derivatives are likely candidates to correspond to interesting structures. Specifically, it is shown how this idea can be used as a major mechanism in algorithms for automatic scale selection, which adapt the local scales of processing to the local image structure.Support for the proposed approach is given in terms of a general theoretical investigation of the behaviour of the scale selection method under rescalings of the input pattern and by integration with different types of early visual modules, including experiments on real-world and synthetic data. Support is also given by a detailed analysis of how different types of feature detectors perform when integrated with a scale selection mechanism and then applied to characteristic model patterns. Specifically, it is described in detail how the proposed methodology applies to the problems of blob detection, junction detection, edge detection, ridge detection and local frequency estimation.In many computer vision applications, the poor performance of the low-level vision modules constitutes a major bottleneck. It is argued that the inclusion of mechanisms for automatic scale selection is essential if we are to construct vision systems to automatically analyse complex unknown environments.

Scale-space theory: a basic tool for analyzing structures at different scales

An inherent property of objects in the world is that they only exist as meaningful entities over certain ranges of scale. If one aims at describing the structure of unknown real-world signals, then ...

Edge Detection and Ridge Detection with Automatic Scale Selection

When computing descriptors of image data, the type of information that can be extracted may be strongly dependent on the scales at which the image operators are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of scale levels when detecting one-dimensional image features, such as edges and ridges.A novel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An important consequence of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analyzed in detail, the gradient magnitude and a differential expression derived from the third-order derivative in the gradient direction. For a certain way of normalizing these differential descriptors, by expressing them in terms of so-called γ-normalized derivatives, an immediate consequence of this definition is that the edge detector will adapt its scale levels to the local image structure. Specifically, sharp edges will be detected at fine scales so as to reduce the shape distortions due to scale-space smoothing, whereas sufficiently coarse scales will be selected at diffuse edges, such that an edge model is a valid abstraction of the intensity profile across the edge.Since the scale-space edge is defined from the intersection of two zero-crossing surfaces in scale-space, the edges will by definition form closed curves. This simplifies selection of salient edges, and a novel significance measure is proposed, by integrating the edge strength along the edge. Moreover, the scale information associated with each edge provides useful clues to the physical nature of the edge.With just slight modifications, similar ideas can be used for formulating ridge detectors with automatic selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge.It is shown how the methodology can be implemented in terms of straightforward visual front-end operations, and the validity of the approach is supported by theoretical analysis as well as experiments on real-world and synthetic data.

Scale-space for discrete signals

A basic and extensive treatment of discrete aspects of the scale-space theory is presented. A genuinely discrete scale-space theory is developed and its connection to the continuous scale-space theory is explained. Special attention is given to discretization effects, which occur when results from the continuous scale-space theory are to be implemented computationally. The 1D problem is solved completely in an axiomatic manner. For the 2D problem, the author discusses how the 2D discrete scale space should be constructed. The main results are as follows: the proper way to apply the scale-space theory to discrete signals and discrete images is by discretization of the diffusion equation, not the convolution integral; the discrete scale space obtained in this way can be described by convolution with the kernel, which is the discrete analog of the Gaussian kernel, a scale-space implementation based on the sampled Gaussian kernel might lead to undesirable effects and computational problems, especially at fine levels of scale; the 1D discrete smoothing transformations can be characterized exactly and a complete catalogue is given; all finite support 1D discrete smoothing transformations arise from repeated averaging over two adjacent elements (the limit case of such an averaging process is described); and the symmetric 1D discrete smoothing kernels are nonnegative and unimodal, in both the spatial and the frequency domain. >

Detecting salient blob-like image structures and their scales with a scale-space primal sketch: a method for focus-of-attention

This article presents: (i) a multiscale 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 representation, 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.

Edge detection and ridge detection with automatic scale selection

When extracting features from image data, the type of information that can be extracted may be strongly dependent on the scales at which the feature detectors are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of scale levels when detecting one-dimensional features, such as edges and ridges. A novel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An important property of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analysed in detail. It is shown that by expressing these in terms of /spl gamma/-normalized derivatives, an immediate consequence of this definition is that fine scales are selected for sharp edges (so as to reduce the shape distortions due to scale-space smoothing), whereas coarse scales are selected for diffuse edges, such that an edge model constitutes a valid abstraction of the intensity profile across the edge. With slight modifications, this idea can be used for formulating a ridge detector with automatic scale selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge.

Hand gesture recognition using multi-scale colour features, hierarchical models and particle filtering

This paper presents algorithms and a prototype system for hand tracking and hand posture recognition. Hand postures are represented in terms of hierarchies of multi-scale colour image features at different scales, with qualitative inter-relations in terms of scale, position and orientation. In each image, detection of multi-scale colour features is performed. Hand states are then simultaneously detected and tracked using particle filtering, with an extension of layered sampling referred to as hierarchical layered sampling. Experiments are presented showing that the performance of the system is substantially improved by performing feature detection in colour space and including a prior with respect to skin colour. These components have been integrated into a real-time prototype system, applied to a test problem of controlling consumer electronics using hand gestures. In a simplified demo scenario, this system has been successfully tested by participants at two fairs during 2001.

Shape-adapted smoothing in estimation of 3-D shape cues from affine deformations of local 2-D brightness structure☆

This article describes a method for reducing the shape distortions due to scale-space smoothing that arise in the computation of 3-D shape cues using operators (derivatives) defined from scale-space representation. More precisely, we are concerned with a general class of methods for deriving 3-D shape cues from a 2-D image data based on the estimation of locally linearized deformations of brightness patterns. This class constitutes a common framework for describing several problems in computer vision (such as shape-from-texture, shape-from disparity-gradients, and motion estimation) and for expressing different algorithms in terms of similar types of visual front-end-operations. It is explained how surface orientation estimates will be biased due to the use of rotationally symmetric smoothing in the image domain. These effects can be reduced by extending the linear scale-space concept into an affine Gaussian scalespace representation and by performing affine shape adaptation of the smoothing kernels. This improves the accuracy of the surface orientation estimates, since the image descriptors, on which the methods are based, will be relative invariant under affine transformations, and the error thus confined to the higher-order terms in the locally linearized perspective transformation. A straightforward algorithm is presented for performing shape adaptation in practice. Experiments on real and synthetic images with known orientation demonstrate that in the presence of moderately high noise levels the accuracy is improved by typically one order of magnitude.

Local descriptors for spatio-temporal recognition

This paper presents and investigates a set of local space-time descriptors for representing and recognizing motion patterns in video. Following the idea of local features in the spatial domain, we use the notion of space-time interest points and represent video data in terms of local space-time events. To describe such events, we define several types of image descriptors over local spatio-temporal neighborhoods and evaluate these descriptors in the context of recognizing human activities. In particular, we compare motion representations in terms of spatio-temporal jets, position dependent histograms, position independent histograms, and principal component analysis computed for either spatio-temporal gradients or optic flow. An experimental evaluation on a video database with human actions shows that high classification performance can be achieved, and that there is a clear advantage of using local position dependent histograms, consistent with previously reported findings regarding spatial recognition.

Fingerprint enhancement by shape adaptation of scale-space operators with automatic scale selection

This work presents two mechanisms for processing fingerprint images; shape-adapted smoothing based on second moment descriptors and automatic scale selection based on normalized derivatives. The shape adaptation procedure adapts the smoothing operation to the local ridge structures, which allows interrupted ridges to be joined without destroying essential singularities such as branching points and enforces continuity of their directional fields. The scale selection procedure estimates local ridge width and adapts the amount of smoothing to the local amount of noise. In addition, a ridgeness measure is defined, which reflects how well the local image structure agrees with a qualitative ridge model, and is used for spreading the results of shape adaptation into noisy areas. The combined approach makes it possible to resolve fine scale structures in clear areas while reducing the risk of enhancing noise in blurred or fragmented areas. The result is a reliable and adaptively detailed estimate of the ridge orientation field and ridge width, as well as a smoothed grey-level version of the input image. We propose that these general techniques should be of interest to developers of automatic fingerprint identification systems as well as in other applications of processing related types of imagery.