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37
Estimating The Tensor Of Curvature Of A Surface From A Polyhedral Approximation
, 1995
"... Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by isosurface construction algorithms, has become a basic step in many computer vision algorithms. Particularly in those targeted at medic ..."
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Cited by 184 (5 self)
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Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by isosurface construction algorithms, has become a basic step in many computer vision algorithms. Particularly in those targeted at medical applications. In this paper we describe a method to estimate the tensor of curvature of a surface at the vertices of a polyhedral approximation. Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain # # # symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature. The resulting algorithm is linear, both in time and in space, as a function of the number of vertices and faces of the polyhedral surface. 1
Matching 3D Anatomical Surfaces with NonRigid Deformations using OctreeSplines
 International Journal of Computer Vision
, 1996
"... Abstract. This paper presents a new method for determining the minimal nonrigid deformation between two 3D surfaces, such as those which describe anatomical structures in 3D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method perform ..."
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Cited by 130 (3 self)
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Abstract. This paper presents a new method for determining the minimal nonrigid deformation between two 3D surfaces, such as those which describe anatomical structures in 3D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3D surfaces. 1.
Illustrating Surface Shape in Volume Data via Principal DirectionDriven 3D Line Integral Convolution
, 1997
"... The threedimensional shape and relative depth of a smoothly curving layered transparent surface may be communicated particularly effectively when the surface is artistically enhanced with sparsely distributed opaque detail. This paper describes how the set of principal directions and principal curv ..."
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Cited by 110 (11 self)
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The threedimensional shape and relative depth of a smoothly curving layered transparent surface may be communicated particularly effectively when the surface is artistically enhanced with sparsely distributed opaque detail. This paper describes how the set of principal directions and principal curvatures specified by local geometric operators can be understood to define a natural "flow " over the surface of an object, and can be used to guide the placement of the lines of a stroke texture that seeks to represent 3D shape information in a perceptually intuitive way. The driving application for this work is the visualization of layered isovalue surfaces in volume data, where the particular identity of an individual surface is not generally known a priori and observers will typically wish to view a variety of different level surfaces from the same distribution, superimposed over underlying opaque structures. By advecting an evenly distributed set of tiny opaque particles, and the empty space between them, via 3D line integral convolution through the vector field defined by the principal directions and principal curvatures of the level surfaces passing through each gridpoint of a 3D volume, it is possible to generate a
Curvaturebased transfer functions for direct volume rendering: Methods and applications
 In Proceedings of IEEE Visualization 2003
, 2003
"... Figure 1: Volume renderings of a 64 3 synthetic volume with four different curvature measures. Left to right: first principal curvature κ ..."
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Cited by 108 (7 self)
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Figure 1: Volume renderings of a 64 3 synthetic volume with four different curvature measures. Left to right: first principal curvature κ
RidgeValley Lines on Meshes via Implicit Surface Fitting
 ACM TRANS. GRAPH
, 2004
"... We propose a simple and effective method for detecting view and scaleindependent ridgevalley lines defined via first and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A highquality estimation of highorder surface derivatives is achieved by combining multil ..."
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Cited by 95 (7 self)
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We propose a simple and effective method for detecting view and scaleindependent ridgevalley lines defined via first and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A highquality estimation of highorder surface derivatives is achieved by combining multilevel implicit surface fitting and finite difference approximations. We demonstrate that the ridges and valleys are geometrically and perceptually salient surface features and, therefore, can be potentially used for shape recognition, coding, and quality evaluation purposes.
Conveying the 3D Shape of Smoothly Curving Transparent Surfaces via Texture
 IEEE Transactions on Visualization and Computer Graphics
, 1997
"... Transparency can be a useful device for depicting multiple overlapping surfaces in a single image. The challenge is to render the transparent surfaces in such a way that their threedimensional shape can be readily understood and their depth distance from underlying structures clearly perceived. ..."
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Cited by 75 (9 self)
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Transparency can be a useful device for depicting multiple overlapping surfaces in a single image. The challenge is to render the transparent surfaces in such a way that their threedimensional shape can be readily understood and their depth distance from underlying structures clearly perceived. This paper describes our investigations into the use of sparselydistributed discrete, opaque texture as an "artistic device" for more explicitly indicating the relative depth of a transparent surface and for communicating the essential features of its 3D shape in an intuitively meaningful and minimally occluding way. The driving application for this work is the visualization of layered surfaces in radiation therapy treatment planning data, and the technique is illustrated on transparent isointensity surfaces of radiation dose. We describe the perceptual motivation and artistic inspiration for defining a stroke texture that is locally oriented in the direction of greatest normal curvatu...
Enhancing Transparent Skin Surfaces with Ridge and Valley Lines
, 1995
"... There are many applications that can benefit from the simultaneous display of multiple layers of data. The objective in these cases is to render the layered surfaces in a such way that the outer structures can be seen and seen through at the same time. This paper focuses on the particular applicatio ..."
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Cited by 68 (8 self)
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There are many applications that can benefit from the simultaneous display of multiple layers of data. The objective in these cases is to render the layered surfaces in a such way that the outer structures can be seen and seen through at the same time. This paper focuses on the particular application of radiation therapy treatment planning, in which physicians need to understand the threedimensional distribution of radiation dose in the context of patient anatomy. We describe a promising technique for communicating the shape and position of the transparent skin surface while at the same time minimally occluding underlying isointensity dose surfaces and anatomical objects: adding a sparse, opaque texture comprised of a small set of carefullychosen lines. We explain the perceptual motivation for explicitly drawing ridge and valley curves on a transparent surface, describe straightforward mathematical techniques for detecting and rendering these lines, and propose a small number of rea...
An Algorithmic Overview of Surface Registration . . .
 MEDICAL IMAGE ANALYSIS
, 2000
"... This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected ..."
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Cited by 58 (1 self)
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This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities and which must be reconciled. Surface registration
3D distance fields: A survey of techniques and applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the ..."
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Cited by 54 (2 self)
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A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?
Apparent ridges for line drawing
 ACM Transactions on Graphics
, 2007
"... Nonphotorealistic line drawing depicts 3D shapes through the rendering of feature lines. A number of characterizations of relevant lines have been proposed but none of these definitions alone seem to capture all visuallyrelevant lines. We introduce a new definition of feature lines based on two pe ..."
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Cited by 39 (1 self)
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Nonphotorealistic line drawing depicts 3D shapes through the rendering of feature lines. A number of characterizations of relevant lines have been proposed but none of these definitions alone seem to capture all visuallyrelevant lines. We introduce a new definition of feature lines based on two perceptual observations. First, human perception is sensitive to the variation of shading, and since shape perception is little affected by lighting and reflectance modification, we should focus on normal variation. Second, viewdependent lines better convey the shape of smooth surfaces better than viewindependent lines. From this we define viewdependent curvature as the variation of the surface normal with respect to a viewing screen plane, and apparent ridges as the locus points of the maximum of the viewdependent curvature. We derive the equation for apparent ridges and present a new algorithm to render line drawings of 3D meshes. We show that our apparent ridges encompass or enhance aspects of several other feature lines.