Results 1  10
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13
On Edge Detection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1984
"... Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses th ..."
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Cited by 176 (6 self)
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Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part of the edge d6tection problem. To characterize the types of intensity changes derivatives of different types, and possibly different scales, are needed. Thus, we consider this part of edge detection as a problem in numerical differentiation.
A Theory of Refractive and Specular 3D Shape by Lightpath Triangulation
"... We investigate the feasibility of reconstructing an arbitrarilyshaped specular scene (refractive or mirrorlike) from one or more viewpoints. By reducing shape recovery to the problem of reconstructing individual 3D light paths that cross the image plane, we obtain three key results. First, we show ..."
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Cited by 52 (5 self)
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We investigate the feasibility of reconstructing an arbitrarilyshaped specular scene (refractive or mirrorlike) from one or more viewpoints. By reducing shape recovery to the problem of reconstructing individual 3D light paths that cross the image plane, we obtain three key results. First, we show how to compute the depth map of a specular scene from a single viewpoint, when the scene redirects incoming light just once. Second, for scenes where incoming light undergoes two refractions or reflections, we show that three viewpoints are sufficient to enable reconstruction in the general case. Third, we show that it is impossible to reconstruct individual light paths when light is redirected more than twice. Our analysis assumes that, for every point on the image plane, we know at least one 3D point on its light path. This leads to reconstruction algorithms that rely on an “environment matting” procedure to establish pixeltopoint correspondences along a light path. Preliminary results for a variety of scenes (mirror, glass, etc) are also presented.
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...
Dynamic Refraction Stereo
, 2005
"... In this paper we consider the problem of reconstructing the 3D position and surface normal of points on an unknown, arbitrarilyshaped refractive surface. We show that two viewpoints are sufficient to solve this problem in the general case, even if the refractive index is unknown. The key requiremen ..."
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Cited by 36 (6 self)
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In this paper we consider the problem of reconstructing the 3D position and surface normal of points on an unknown, arbitrarilyshaped refractive surface. We show that two viewpoints are sufficient to solve this problem in the general case, even if the refractive index is unknown. The key requirements are (1) knowledge of a function that maps each point on the two image planes to a known 3D point that refracts to it, and (2) light is refracted only once. We apply this result to the problem of reconstructing the timevarying surface of a liquid from patterns placed below it. To do this, we introduce a novel "stereo matching" criterion called refractive disparity, appropriate for refractive scenes, and develop an optimizationbased algorithm for individually reconstructing the position and normal of each point projecting to a pixel in the input views. Results on reconstructing a variety of complex, deforming liquid surfaces suggest that our technique can yield detailed reconstructions that capture the dynamic behavior of freeflowing liquids.
Scale Space Hierarchy
 JOURNAL OF MATHEMATICAL IMAGING AND VISION
, 2001
"... 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 ..."
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Cited by 10 (7 self)
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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
Calculations on critical points under gaussian blurring
 In Nielsen et al
, 1999
"... Abstract. The behaviour of critical points of Gaussian scalespace images is mainly described by their creation and annihilation. In existing literature these events are determined in socalled canonical coordinates. A description in a userdefined Cartesian coordinate system is stated, as well as t ..."
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Cited by 10 (8 self)
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Abstract. The behaviour of critical points of Gaussian scalespace images is mainly described by their creation and annihilation. In existing literature these events are determined in socalled canonical coordinates. A description in a userdefined Cartesian coordinate system is stated, as well as the results of a straightforward implementation. The location of a catastrophe can be predicted with subpixel accuracy. An example of an annihilation is given. Also an upper bound is derived for the area where critical points can be created. Experimental data of an MR, a CT, and an artificial noise image satisfy this result. 1
Surface Networks
, 2002
"... © Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, phys ..."
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Cited by 2 (0 self)
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© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physicochemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2dimensional surfaces by storing only the most important (also called fundamental, critical or surfacespecific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has four
On the Behaviour of Critical Points under Gaussian Blurring
, 1999
"... The level of detail of an image can be expressed in terms of its topology, i.e. the distribution of Morse critical points and their types, which in turn is governed by resolution. We study the behaviour of critical points as a function of resolution for Gaussian scalespace images using catastrophe ..."
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Cited by 1 (1 self)
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The level of detail of an image can be expressed in terms of its topology, i.e. the distribution of Morse critical points and their types, which in turn is governed by resolution. We study the behaviour of critical points as a function of resolution for Gaussian scalespace images using catastrophe theory. Unlike existing literature, in which one employs local, socalled canonical coordinates for theoretical convenience, we state results in terms of a global, userdefined Cartesian coordinate system. This enables a fairly straightforward implementation of these results in practice. 1 Introduction 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 [10] in the context of pattern recognition it went largel...
Topological Analysis of Scalar Functions for Scientific Data Visualization
, 2004
"... Scientists attempt to understand physical phenomena by studying various quantities measured over the region of interest. A majority of these quantities are scalar (realvalued) functions. These functions are typically studied using traditional visualization techniques like isosurface extraction, ..."
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Cited by 1 (0 self)
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Scientists attempt to understand physical phenomena by studying various quantities measured over the region of interest. A majority of these quantities are scalar (realvalued) functions. These functions are typically studied using traditional visualization techniques like isosurface extraction, volume rendering etc. As the data grows in size and becomes increasingly complex, these techniques are no longer e#ective. State of the art visualization methods attempt to automatically extract features and annotate a display of the data with a visualization of its features. In this thesis, we study and extract the topological features of the data and use them for visualization. We have three results: .