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24
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 247 (20 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 γnormalized 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.
An Unbiased Detector of Curvilinear Structures
, 1996
"... The extraction of curvilinear structures is an important lowlevel operation in computer vision that has many applications. Most existing operators use a simple model for the line that is to be extracted, i.e., they do not take into account the surroundings of a line. This leads to the undesired con ..."
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Cited by 148 (11 self)
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The extraction of curvilinear structures is an important lowlevel operation in computer vision that has many applications. Most existing operators use a simple model for the line that is to be extracted, i.e., they do not take into account the surroundings of a line. This leads to the undesired consequence that the line will be extracted in the wrong position whenever a line with different lateral contrast is extracted. In contrast, the algorithm proposed in this paper uses an explicit model for lines and their surroundings. By analyzing the scalespace behaviour of a model line profile, it is shown how the bias that is induced by asymmetrical lines can be removed. Furthermore, the algorithm not only returns the precise subpixel line position, but also the width of the line for each line point, also with subpixel accuracy.
Drainage Queries in TINs: From local to global and back again
 In Proc. 7th Int. Symp. on Spatial Data Handling
, 1996
"... This paper considers the cost of preprocessing a digital terrain model (DTM) represented as a triangulated irregular network (TIN) so that drainage queriese.g., what is the watershed of a query point, or how much water passes through a point given that rain is falling at a known ratecan be ans ..."
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Cited by 27 (6 self)
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This paper considers the cost of preprocessing a digital terrain model (DTM) represented as a triangulated irregular network (TIN) so that drainage queriese.g., what is the watershed of a query point, or how much water passes through a point given that rain is falling at a known ratecan be answered by simply evaluating a summary function. Although the worstcase storage and preprocessing costs are high, the experimentallyobserved costs are reasonable. In order to compute a compact and consistent summary function, the drainage network needs a rigorous definition. This paper, therefore, also surveys some of the previous definitions, extends them, and establishes a number of properties of drainage networks with a focus on TINs. 1 Introduction Terrain drainage characteristics provide important information on water resources, possible flood areas, erosion and other natural processes. In natural resource management, for example, the basic management unit is the watershed, the area a...
Applications of Computational Geometry to Geographic Information Systems
"... Contents 1 Introduction 2 2 Map Data Modeling 4 2.1 TwoDimensional Spatial Entities and Relationships . . . . . . . . . . . . . . . . . . . . . 4 2.2 Raster and Vector Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Subdivisions as Cell Complexes . . . . . . . ..."
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Cited by 22 (1 self)
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Contents 1 Introduction 2 2 Map Data Modeling 4 2.1 TwoDimensional Spatial Entities and Relationships . . . . . . . . . . . . . . . . . . . . . 4 2.2 Raster and Vector Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Subdivisions as Cell Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Topological Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Multiresolution Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Map data processing 8 3.1 Spatial Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Map Overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Geometric Problems in Map Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 Map Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observability of 3D Motion
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2000
"... This paper examines the inherent difficulties in observing 3D rigid motion from image sequences. It does so without considering a particular estimator. Instead, it presents a statistical analysis of all the possible computational models which can be used for estimating 3D motion from an image sequen ..."
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Cited by 21 (13 self)
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This paper examines the inherent difficulties in observing 3D rigid motion from image sequences. It does so without considering a particular estimator. Instead, it presents a statistical analysis of all the possible computational models which can be used for estimating 3D motion from an image sequence. These computational models are classified according to the mathematical constraints that they employ and the characteristics of the imaging sensor (restricted field of view and full field of view). Regarding the mathematical constraints, there exist two principles relating a sequence of images taken by a moving camera. One is the "epipolar constraint," applied to motion fields, and the other the "positive depth" constraint, applied to normal flow fields. 3D motion estimation amounts to optimizing these constraints over the image. A statistical modeling of these constraints leads to functions which are studied with regard to their topographic structure, specifically as regards the errors ...
Aloimonos, Ambiguity in structure from motion: Sphere versus plane
 Internat. J. Comput. Vision
, 1998
"... Abstract. If 3D rigid motion can be correctly estimated from image sequences, the structure of the scene can be correctly derived using the equations for image formation. However, an error in the estimation of 3D motion will result in the computation of a distorted version of the scene structure. Of ..."
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Cited by 19 (6 self)
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Abstract. If 3D rigid motion can be correctly estimated from image sequences, the structure of the scene can be correctly derived using the equations for image formation. However, an error in the estimation of 3D motion will result in the computation of a distorted version of the scene structure. Of computational interest are these regions in space where the distortions are such that the depths become negative, because in order for the scene to be visible it has to lie in front of the image, and thus the corresponding depth estimates have to be positive. The stability analysis for the structure from motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion that results in the estimation of a minimum number of negative depth values. The input used is the value of the flow along some direction, which is more general than optic flow or correspondence. For a planar retina it is shown that the optimal configuration is achieved when the projections of the translational and rotational errors on the image plane are perpendicular. Furthermore, the projection of the actual and the estimated translation lie on a line through the center. For a spherical retina, given a rotational error, the optimal translation is the correct one; given a translational error, the optimal rotational error depends both in direction and value on the actual and estimated translation as well as the scene in view. The proofs, besides illuminating the confounding of translation and rotation in structure from motion, have an important application to ecological optics. The same analysis provides a computational explanation of why it is
SubpixelPrecise Extraction of Watersheds
 ICCV ’99, Proc. 7 th Intl. Conf. Computer Vision
, 1999
"... An approach to extract watersheds and watercourses, as well as their corresponding valleys and hills, from images with subpixel precision is proposed. The critical points of the terrain are essential as the starting points for the construction of these separatrices. They are extracted efficiently wi ..."
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Cited by 14 (0 self)
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An approach to extract watersheds and watercourses, as well as their corresponding valleys and hills, from images with subpixel precision is proposed. The critical points of the terrain are essential as the starting points for the construction of these separatrices. They are extracted efficiently with subpixel precision using an approach based on derivatives of Gaussian filters. The separatrices are extracted by integrating their defining differential equation. Finally, the hills and valleys are constructed by an efficient graph search algorithm. Examples show the quality of the results that can be achieved with the proposed approach. 1 Introduction Watersheds and watercourses are important geomorphological features, which play an important role in hydrological GIS applications. Intuitively, watersheds can be regarded as the lines that separate the area where water drains to different locations. The areas that are enclosed by the watersheds are precisely the regions where water drain...
Visual Space Distortion
 Biological Cybernetics
, 1997
"... We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metr ..."
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Cited by 12 (11 self)
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We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters c...
Ridge's Corner Detection and Correspondence
 In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
, 1997
"... Traditionally, corners are found along step edges. In this paper, we present an alternative approach  corners along ridges/troughs and local minima points. These features seem to be more reliable for tracking. A new approach for subpixel localization of these corners is suggested, using a local ap ..."
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Cited by 12 (0 self)
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Traditionally, corners are found along step edges. In this paper, we present an alternative approach  corners along ridges/troughs and local minima points. These features seem to be more reliable for tracking. A new approach for subpixel localization of these corners is suggested, using a local approximation of the image surface. 1. Introduction Many tracking (or tracking based) methods use a small set of features in order to establish an initial understanding of the scene (e.g. to compute weak calibration). Usually, these methods use features that were obtained by using an existing feature detection program. The resulting features might not suit the tracking needs. In tracking we are interested in matching a set of features from one image to a corresponding set in a second image. Some applications, such as navigation and computation of weak calibration (e.g. fundamental matrix and trifocal tensor), require a small set of features that can be tracked with high reliability along an...
Analysis of tubular structures in threedimensional confocal images
 Network
, 2002
"... Knowledge about the relationship between morphology and the function of neurons is an important instrument in understanding the role that neurons play in information processing in the brain. Inparicular, the diameter and length of segments in dendritic arborization are considered to be crucial morph ..."
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Cited by 10 (0 self)
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Knowledge about the relationship between morphology and the function of neurons is an important instrument in understanding the role that neurons play in information processing in the brain. Inparicular, the diameter and length of segments in dendritic arborization are considered to be crucial morphological features. Consequently, accurate detection of morphological features such as centre line position and diameter is a prerequisite to establish this relationship. Accurate detection of neuron morphology from confocal microscope images is hampered by the low signal to noise ratio of the images and the properties of the microscope point spread function (PSF). The size and the anisotropy of the PSF causes feature detection to be biased and orientation dependent. We deal with these problems by utilizing Gaussian image derivatives for feature detection. Gaussian kernels provide for image derivative estimates with low noise sensitivity. Features of interest such as centre line positions and diameter in a tubular neuronal segment of a dendritic tree can be detected by calculating and subsequently utilizing Gaussian image derivatives. For diameter measurement the microscope PSF is incorporated into the derivative calculation. Results on real and simulated confocal images reveal that centre line position and diameter can be estimated accurately and are bias free even under realistic imaging conditions. 1.