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134
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 723 (34 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
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 654 (15 self)
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In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fairing, to lowpass filtering. We describe a very simple surface signal lowpass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimizationbased fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique.
Edge Detection and Ridge Detection with Automatic Scale Selection
 CVPR'96
, 1996
"... 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 ..."
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Cited by 347 (24 self)
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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 onedimensional features, such as edges and ridges. Anovel concept of a scalespace edge is introduced, defined as a connected set of points in scalespace 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 &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 scalespace 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 scalespace ridge instead reflect the width of the ridge.
Efficient and reliable schemes for nonlinear diffusion filtering
 IEEE Transactions on Image Processing
, 1998
"... AbstractNonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes whi ..."
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Cited by 231 (21 self)
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AbstractNonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS), which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widely used explicit schemes.
Detecting Salient BlobLike Image Structures with a ScaleSpace Primal Sketch: A Method for FocusofAttention
 INT. J. COMP. VISION
, 1993
"... This article presents: (i) a multiscale representation of greylevel shape called the scalespace primal sketch, which makes explicit both features in scalespace and the relations between structures at different scales, (ii) a methodology for extracting significant bloblike image structures from ..."
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Cited by 189 (14 self)
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This article presents: (i) a multiscale representation of greylevel shape called the scalespace primal sketch, which makes explicit both features in scalespace and the relations between structures at different scales, (ii) a methodology for extracting significant bloblike 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 bottomup datadriven 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.
Local scale control for edge detection and blur estimation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... Abstract—The standard approach to edge detection is based on a model of edges as large step changes in intensity. This approach fails to reliably detect and localize edges in natural images where blur scale and contrast can vary over a broad range. The main problem is that the appropriate spatial sc ..."
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Cited by 167 (20 self)
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Abstract—The standard approach to edge detection is based on a model of edges as large step changes in intensity. This approach fails to reliably detect and localize edges in natural images where blur scale and contrast can vary over a broad range. The main problem is that the appropriate spatial scale for local estimation depends upon the local structure of the edge, and thus varies unpredictably over the image. Here we show that knowledge of sensor properties and operator norms can be exploited to define a unique, locally computable minimum reliable scale for local estimation at each point in the image. This method for local scale control is applied to the problem of detecting and localizing edges in images with shallow depth of field and shadows. We show that edges spanning a broad range of blur scales and contrasts can be recovered accurately by a single system with no input parameters other than the second moment of the sensor noise. A natural dividend of this approach is a measure of the thickness of contours which can be used to estimate focal and penumbral blur. Local scale control is shown to be important for the estimation of blur in complex images, where the potential for interference between nearby edges of very different blur scale requires that estimates be made at the minimum reliable scale.
Image alignment and stitching: a tutorial
, 2006
"... This tutorial reviews image alignment and image stitching algorithms. Image alignment algorithms can discover the correspondence relationships among images with varying degrees of overlap. They are ideally suited for applications such as video stabilization, summarization, and the creation of panora ..."
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Cited by 115 (2 self)
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This tutorial reviews image alignment and image stitching algorithms. Image alignment algorithms can discover the correspondence relationships among images with varying degrees of overlap. They are ideally suited for applications such as video stabilization, summarization, and the creation of panoramic mosaics. Image stitching algorithms take the alignment estimates produced by such registration algorithms and blend the images in a seamless manner, taking care to deal with potential problems such as blurring or ghosting caused by parallax and scene movement as well as varying image exposures. This tutorial reviews the basic motion models underlying alignment and stitching algorithms, describes effective direct (pixelbased) and featurebased alignment algorithms, and describes blending algorithms used to produce
Shapeadapted smoothing in estimation of 3D depth cues from affine distortions of local 2D brightness structure
 IN PROC. 3RD EUROPEAN CONF. ON COMPUTER VISION
, 1994
"... Rotationally symmetric operations in the image domain may give rise to shape distortions. This article describes a way of reducing this effect for a general class of methods for deriving 3D shape cues from 2D image data, which are based on the estimation of locally linearized distortion of brightn ..."
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Cited by 82 (18 self)
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Rotationally symmetric operations in the image domain may give rise to shape distortions. This article describes a way of reducing this effect for a general class of methods for deriving 3D shape cues from 2D image data, which are based on the estimation of locally linearized distortion of brightness patterns. By extending the linear scalespace concept into an affine scalespace representation and performing affine shape adaption of the smoothing kernels, the accuracy of surface orientation estimates derived from texture and disparity cues can be improved by typically one order of magnitude. The reason for this is that the image descriptors, on which the methods are based, will be relative invariant under a ne transformations, and the error will thus be confined to the higherorder terms in the locally linearized perspective mapping.
Shapeadapted smoothing in estimation of 3D shape cues from affine distortions of local 2D brightness structure
, 2001
"... This article describes a method for reducing the shape distortions due to scalespace smoothing that arise in the computation of 3D shape cues using operators (derivatives) de ned from scalespace representation. More precisely, we are concerned with a general class of methods for deriving 3D shap ..."
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Cited by 71 (3 self)
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This article describes a method for reducing the shape distortions due to scalespace smoothing that arise in the computation of 3D shape cues using operators (derivatives) de ned from scalespace representation. More precisely, we are concerned with a general class of methods for deriving 3D shape cues from 2D image data based on the estimation of locally linearized deformations of brightness patterns. This class