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44
Feature detection with automatic scale selection
 International Journal of Computer Vision
, 1998
"... 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 ..."
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Cited by 488 (26 self)
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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 socalled scalespace representation. Traditional scalespace 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 proposed 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 γnormalized 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
Face Recognition: the Problem of Compensating for Changes in Illumination Direction
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... A face recognition system must recognize a face from a novel image despite the variations between images of the same face. A common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these varia ..."
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Cited by 269 (3 self)
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A face recognition system must recognize a face from a novel image despite the variations between images of the same face. A common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations. Examples of such representations are edge maps, image intensity derivatives, and images convolved with 2D Gaborlike filters. Here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination, as well as viewpoint and facial expression. Our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination. Similar results were obtained for changes due to viewpoint and expression. Image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination. However, systems...
Measurement of Color Invariants
, 2000
"... This paper presents the measurement of object reflectance from color images. We exploit the Gaussian scalespace paradigm to de£ne a framework for the robust measurement of object reflectance from color images. Illumination and geometrical invariant properties are derived from a physical reflectance ..."
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Cited by 105 (34 self)
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This paper presents the measurement of object reflectance from color images. We exploit the Gaussian scalespace paradigm to de£ne a framework for the robust measurement of object reflectance from color images. Illumination and geometrical invariant properties are derived from a physical reflectance model based on the KubelkaMunk theory. Imaging conditions are assumed to be white illumination and matte, dull object or general object, respectively, summarized by: shadow highlights illumination illumination intensity color
On scale selection for differential operators
 8TH SCIA
, 1993
"... Although traditional scalespace theory provides a wellfounded 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 heur ..."
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Cited by 49 (11 self)
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Although traditional scalespace theory provides a wellfounded 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 twostage 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.
Logical/Linear Operators for Image Curves
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify aspects of linear operator theory and boolean logic. A family of these operators appropriate for measuring the loworder differential struct ..."
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Cited by 46 (7 self)
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We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify aspects of linear operator theory and boolean logic. A family of these operators appropriate for measuring the loworder differential structure of image curves is developed. These L/L operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld. Tangential conditions guarantee continuity, while normal conditions select and categorize contrast profiles. The resulting operators allow for coarse measurement of curvilinear differential structure (orientation and curvature) while successfully segregating edge and linelike features. By thus reducing the incidence of falsepositive responses, these operators are a substantial improvement over (thresholded) linear operators which attempt to resolve the same class of features. ...
Shape from Texture from a MultiScale Perspective
 Proc. 4th Int. Conf. on Computer Vision
, 1993
"... : The problem of scale in shape from texture is addressed. The need for (at least) two scale parameters is emphasized; a local scale describing the amount of smoothing used for suppressing noise and irrelevant details when computing primitive texture descriptors from image data, and an integration s ..."
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Cited by 38 (14 self)
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: The problem of scale in shape from texture is addressed. The need for (at least) two scale parameters is emphasized; a local scale describing the amount of smoothing used for suppressing noise and irrelevant details when computing primitive texture descriptors from image data, and an integration scale describing the size of the region in space over which the statistics of the local descriptors is accumulated. A novel mechanism for automatic scale selection is proposed, based on normalized derivatives. It is used for adaptive determination of the two scale parameters in a multiscale texture descriptor, the windowed second moment matrix, which is defined in terms of Gaussian smoothing, first order derivatives, and nonlinear pointwise combinations of these. The same scaleselection method can be used for multiscale blob detection without any tuning parameters or thresholding. The resulting texture description can be combined with various assumptions about surface texture in order to ...
The Topological Structure of ScaleSpace Images
, 1998
"... We investigate the "deep structure" of a scalespace image. The emphasis is on topology, i.e. we concentrate on critical pointspoints with vanishing gradientand toppointscritical points with degenerate Hessianand monitor their displacements, respectively generic morsifications in scales ..."
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Cited by 37 (19 self)
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We investigate the "deep structure" of a scalespace image. The emphasis is on topology, i.e. we concentrate on critical pointspoints with vanishing gradientand toppointscritical points with degenerate Hessianand monitor their displacements, respectively generic morsifications in scalespace. Relevant parts of catastrophe theory in the context of the scalespace paradigm are briefly reviewed, and subsequently rewritten into coordinate independent form. This enables one to implement topological descriptors using a conveniently defined, global coordinate system. 1 Introduction 1.1 Historical Background A fairly well understood way to endow an image with a topology is to embed it into a oneparameter family of images known as a "scalespace image". The parameter encodes "scale" or "resolution" (coarse/fine scale means low/high resolution, respectively). Among the simplest is the linear or Gaussian scalespace model. Proposed by Iijima [13] in the context of pattern recogniti...
Discrete derivative approximations with scalespace properties: A basis for lowlevel feature extraction
 J. Math. Imaging Vision
, 1993
"... It is developed how discrete derivative approximations can be de ned so that scalespace 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 amu ..."
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Cited by 28 (12 self)
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It is developed how discrete derivative approximations can be de ned so that scalespace 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 amultiscale 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 scalespace 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 multiscale lowlevel 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.
General Intensity Transformations and Differential Invariants
, 1994
"... We consider the group of invertible image grayvalue transformations and propose a generating equation for a complete set of differential grayvalue invariants up to any order. Such invariants describe the image’s geometrical structure independent of how its grayvalues are mapped (contrast or brig ..."
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Cited by 28 (3 self)
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We consider the group of invertible image grayvalue transformations and propose a generating equation for a complete set of differential grayvalue invariants up to any order. Such invariants describe the image’s geometrical structure independent of how its grayvalues are mapped (contrast or brightness adjustments).
Recognition by Symmetry Derivatives and the Generalized Structure Tensor
 IEEEPAMI
, 2004
"... We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show t ..."
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Cited by 24 (15 self)
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We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: They are obtained by replacing the original differential polynomial with the same polynomial, but using ordinary coordinates x and y corresponding to partial derivatives. Moreover, the symmetry derivatives of Gaussians are closed under the convolution operator and they are invariant to the Fourier transform. The equivalent of the structure tensor, representing and extracting orientations of curve patterns, had previously been shown to hold in harmonic coordinates in a nearly identical manner. As a result, positions, orientations, and certainties of intricate patterns, e.g., spirals, crosses, parabolic shapes, can be modeled by use of symmetry derivatives of Gaussians with greater analytical precision as well as computational efficiency. Since Gaussians and their derivatives are utilized extensively in image processing, the revealed properties have practical consequences for local orientation based feature extraction. The usefulness of these results is demonstrated by two applications: 1) tracking cross markers in long image sequences from vehicle crash tests and 2) alignment of noisy fingerprints.