There are currently a number of methods for solving variants of the following problem: Given a tr... more There are currently a number of methods for solving variants of the following problem: Given a triangulated polyhedron P in three-space with or without boundary, construct a smooth surface that interpolates the vertices of P. Problems of this variety arise in numerous areas of application such as medical imaging, scattered data tting, and geometric modeling. In general, while the techniques satisfy the continuity and interpolation requirements of the problem, they often fail to produce pleasing shapes. Our interest in studying this problem has necessitated the construction of a exible software testbed that allows rapid implementation and testing of new surface tting methods and analysis techniques. The testbed is written entirely in the C programming language and is highly portable. Other relevant features of the testbed are discussed, and recommendations for improving the shape characteristics of several interpolation methods are given.
We present a method for constructing tensor product Bezier surfaces from contour (cross-section) ... more We present a method for constructing tensor product Bezier surfaces from contour (cross-section) data. Minimal area triangulations are used to guide the surface construction, and the final surface reflects the optimality of the triangulation. The resulting surface differs from the initial triangulation in two important ways: it is smooth (as opposed to the piecewise planar triangulation), and it is in tensor product form (as opposed to the irregular triangular mesh). The surface reconstruction is efficient because we do not require an exact minimal surface. The triangulations are used as strong hints, but no more than that. The method requires the computation of both open and closed isoparametric curves of the surface, using triangulations as a guide. These isoparametric curves form a tensor product Bezier surface. We show how to control sampling density by filling and pruning isoparametric curves, for accuracy and economy. A rectangular grid of points is produced that is compatible with the expected format for a tensor product surface interpolation, so that a host of well-supported methods are available to generate and manipulate the surface.
Investigative Opthalmology & Visual Science, 2014
PURPOSE. Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test w... more PURPOSE. Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test whether LF contributes to RPE cell loss in aging and to provide a cellular basis for fundus autofluorescence (AF) we created maps of human RPE cell number and histologic AF. METHODS. Retinal pigment epithelium-Bruch's membrane flat mounts were prepared from 20 donor eyes (10 51 and 10 > 80 years; postmortem: 4.2 hours; no retinal pathologies), preserving foveal position. Phalloidin-binding RPE cytoskeleton and LF-AF (488-nm excitation) were imaged at up to 90 predefined positions. Maps were assembled from 83,330 cells in 1470 locations. From Voronoi regions representing each cell, the number of neighbors, cell area, and total AF intensity normalized to an AF standard was determined. RESULTS. Highly variable between individuals, RPE-AF increases significantly with age. A perifoveal ring of high AF mirrors rod photoreceptor topography and fundus-AF. Retinal pigment epithelium cell density peaks at the fovea, independent of age, yet no net RPE cell loss is detectable. The RPE monolayer undergoes considerable lifelong re-modeling. The relationship of cell size and AF, a surrogate for LF concentration, is orderly and linear in both groups. Autofluorescence topography differs distinctly from the topography of age-related rod loss. CONCLUSIONS. Digital maps of quantitative AF, cell density, and packing geometry provide metrics for cellular-resolution clinical imaging and model systems. The uncoupling of RPE LF content, cell number, and photoreceptor topography in aging challenges LF's role in AMD.
There are currently a number of methods for solving variants of the following problem: Given a tr... more There are currently a number of methods for solving variants of the following problem: Given a triangulate dpolyhedroP in three-space with or without boundary, construct a smooth surface that interpolates the vertices of P. Problems of this variety arise in numerous areas of application such as medical imaging,scattered data fitting, and geometric modeling. In general, while the techniques satisfy the
Previous accelerated volume rendering techniques have used auxiliary hierarchicaI datastructures ... more Previous accelerated volume rendering techniques have used auxiliary hierarchicaI datastructures to skip empty and homogeneous regions. Although some recent research has taken advantage of more efficient direct encoding techniques to skip empty regions, no work has been done to directly encode homogeneous but not empty regions. 3-D distance transforms previously used to encode empty space can be extended to preprocess homogeneous regions as well, and these regions can be efficiently encoded and incorporated into volume ray-casting and back projection algorithms with a high degree of ff exibility.
We describe an antialiasing system for ray tracing based on adaptive progressive refinement. The ... more We describe an antialiasing system for ray tracing based on adaptive progressive refinement. The goals of the system are to produce high quality antialiased images at a modest average sample rate, and to refine the image progressively so that the image is available in a usable form early and is refined gradually toward the final result. The method proceeds by adaptive stochastic sampling of the image plane, evaluation of the samples by ray tracing, and image reconstruction from the samples. Adaptive control of the sample generation process is driven by three basic goals: coverage of the image, location of features, and confidence in the values at a distinguished "pixel level" of resolution. A three-stage process of interpolation, filtering, and resampling is used to reconstruct a regular grid of display pixels. This reconstruction can be either batch or incremental.
Human Vision, Visual Processing, and Digital Display, 1989
ABSTRACT The sequential sampling, transmission, and rendering of images has been studied in three... more ABSTRACT The sequential sampling, transmission, and rendering of images has been studied in three related contexts: image transmission, vision, and graphics. The solutions developed in these contexts can be viewed as (different) specializations of a single adaptive sampling scheme. We present an analysis of this general scheme, and show how to specialize it. Our basic assumptions are that we can identify an original image (sometimes a model, sometimes the real world), a transmitter which can directly access the original, and a receiver interested in creating a reconstructed image. Different methods are motivated by different goals and constraints, especially the amount of knowledge that the transmitter is allowed to use (but not communicate). In the image synthesis problem, the process which evaluates the image function at a sample point can be viewed as the transmitter. The process which assembles an image from the individual point samples can be viewed as the receiver. In the progressive transmission problem, the transmitter selects or encodes values from a digital image. The receiver reconstructs increasingly accurate approximations of the image, as the samples arrive. These problems share three subproblems: selection of efficient sampling patterns, methods to adaptively control the sample rate, and filters for image reconstruction. In this paper, we explore several related methods of handling these problems, based on different constraints, and different weighting of the goals.
This paper is concerned with the problem of reconstructing the surfaces of three-dimensional obje... more This paper is concerned with the problem of reconstructing the surfaces of three-dimensional objects, given a collection of planar contours representing cross-sections through the objects. This problem has important aplications in biomedical research and instruction, solid modeling, and industrial inspection. The method we describe produces a triangulated mesh from the data points of the contours which is then used in conjunction with a piecewise parametric surface-fitting algorithm to produce a reconstructed surface. The problem can be broken into four subproblems: the correspondence problem (which contours should be connected by the surface?), the tiling problem (how should the contours be connected?), the branching problem (what do we do when there are branches in the surface?), and the surface-fitting problem (what is the precise geometry of the reconstructed surface?) We describe our system for surface reconstruction from sets of contours with respect to each of these subproble...
There are currently a number of methods for solving variants of the following problem: Given a tr... more There are currently a number of methods for solving variants of the following problem: Given a triangulated polyhedron P in three-space with or without boundary, construct a smooth surface that interpolates the vertices of P. Problems of this variety arise in numerous areas of application such as medical imaging, scattered data tting, and geometric modeling. In general, while the techniques satisfy the continuity and interpolation requirements of the problem, they often fail to produce pleasing shapes. Our interest in studying this problem has necessitated the construction of a exible software testbed that allows rapid implementation and testing of new surface tting methods and analysis techniques. The testbed is written entirely in the C programming language and is highly portable. Other relevant features of the testbed are discussed, and recommendations for improving the shape characteristics of several interpolation methods are given.
Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test whether LF... more Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test whether LF contributes to RPE cell loss in aging and to provide a cellular basis for fundus autofluorescence (AF) we created maps of human RPE cell number and histologic AF. Retinal pigment epithelium-Bruch's membrane flat mounts were prepared from 20 donor eyes (10 ≤ 51 and 10 > 80 years; postmortem: ≤4.2 hours; no retinal pathologies), preserving foveal position. Phalloidin-binding RPE cytoskeleton and LF-AF (488-nm excitation) were imaged at up to 90 predefined positions. Maps were assembled from 83,330 cells in 1470 locations. From Voronoi regions representing each cell, the number of neighbors, cell area, and total AF intensity normalized to an AF standard was determined. Highly variable between individuals, RPE-AF increases significantly with age. A perifoveal ring of high AF mirrors rod photoreceptor topography and fundus-AF. Retinal pigment epithelium cell density peaks at the fovea, independent of age, yet no net RPE cell loss is detectable. The RPE monolayer undergoes considerable lifelong re-modeling. The relationship of cell size and AF, a surrogate for LF concentration, is orderly and linear in both groups. Autofluorescence topography differs distinctly from the topography of age-related rod loss. Digital maps of quantitative AF, cell density, and packing geometry provide metrics for cellular-resolution clinical imaging and model systems. The uncoupling of RPE LF content, cell number, and photoreceptor topography in aging challenges LF's role in AMD.
We have measured the spatial density of cones and rods in eight wholemounted human retinas, obtai... more We have measured the spatial density of cones and rods in eight wholemounted human retinas, obtained from seven individuals between 27 and 44 years of age, and constructed maps of photoreceptor density and betweenindividual variability. The average human retina contains 4.6 million cones (4.08-5.29 million). Peak foveal cone density averages 199,000 cones/mni2 and is highly variable between individuals (100,000-324,000 cones/mm'). The point of highest density may be found in an area as large as 0.032 deg'. Cone density falls steeply with increasing eccentricity and is an order of magnitude lower 1 mm away from the foveal center. Superimposed on this gradient is a streak of high cone density along the horizontal meridian. At equivalent eccentricities, cone density is 40-45'0 higher in nasal compared to temporal retina and slightly higher in midperipheral inferior compared to superior retina. Cone density also increases slightly in far nasal retina. The average human retina contains 92 million rods (77.9-107.3 million). In the fovea, the average horizontal diameter of the rod-free zone is 0.350 mm (1.25"). Foveal rod density increases most rapidly superiorly and least rapidly nasally. The highest rod densities are located along an elliptical ring at the eccentricity of the optic disk and extending into nasal retina with the point of highest density typically in superior retina (5/6 eyes). Rod densities decrease by 15-25r',,1 where the ring crosses the horizontal meridian. Rod density declines slowly from the rod ring to the far periphery and is highest in nasal and superior retina. Individual variability in photoreceptor density differs with retinal region and is similar for both cones and rods. Variability is highest near the fovea, reaches a minimum in the midperiphery. and then increases with eccentricity to the ora serrata. The total number of foveal cones is similar for eyes with widely varying peak cone density, consistent with the idea that the variability reflects differences in the lateral migration of photoreceptors during development. Two fellow eyes had cone and rod numbers within 8"(, and similar but not identical photoreceptor topography.
CHAPTER A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants Stephen Mann,... more CHAPTER A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants Stephen Mann, Charles Loop, Michael Lounsbery, David Meyers, James Painter, Tony DeRose, and Kenneth Sloan 8.1. Introduction The problem of passing a surface through a set of data points ...
There are currently a number of methods for solving variants of the following problem: Given a tr... more There are currently a number of methods for solving variants of the following problem: Given a triangulated polyhedron P in three-space with or without boundary, construct a smooth surface that interpolates the vertices of P. Problems of this variety arise in numerous areas of application such as medical imaging, scattered data tting, and geometric modeling. In general, while the techniques satisfy the continuity and interpolation requirements of the problem, they often fail to produce pleasing shapes. Our interest in studying this problem has necessitated the construction of a exible software testbed that allows rapid implementation and testing of new surface tting methods and analysis techniques. The testbed is written entirely in the C programming language and is highly portable. Other relevant features of the testbed are discussed, and recommendations for improving the shape characteristics of several interpolation methods are given.
We present a method for constructing tensor product Bezier surfaces from contour (cross-section) ... more We present a method for constructing tensor product Bezier surfaces from contour (cross-section) data. Minimal area triangulations are used to guide the surface construction, and the final surface reflects the optimality of the triangulation. The resulting surface differs from the initial triangulation in two important ways: it is smooth (as opposed to the piecewise planar triangulation), and it is in tensor product form (as opposed to the irregular triangular mesh). The surface reconstruction is efficient because we do not require an exact minimal surface. The triangulations are used as strong hints, but no more than that. The method requires the computation of both open and closed isoparametric curves of the surface, using triangulations as a guide. These isoparametric curves form a tensor product Bezier surface. We show how to control sampling density by filling and pruning isoparametric curves, for accuracy and economy. A rectangular grid of points is produced that is compatible with the expected format for a tensor product surface interpolation, so that a host of well-supported methods are available to generate and manipulate the surface.
Investigative Opthalmology & Visual Science, 2014
PURPOSE. Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test w... more PURPOSE. Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test whether LF contributes to RPE cell loss in aging and to provide a cellular basis for fundus autofluorescence (AF) we created maps of human RPE cell number and histologic AF. METHODS. Retinal pigment epithelium-Bruch's membrane flat mounts were prepared from 20 donor eyes (10 51 and 10 > 80 years; postmortem: 4.2 hours; no retinal pathologies), preserving foveal position. Phalloidin-binding RPE cytoskeleton and LF-AF (488-nm excitation) were imaged at up to 90 predefined positions. Maps were assembled from 83,330 cells in 1470 locations. From Voronoi regions representing each cell, the number of neighbors, cell area, and total AF intensity normalized to an AF standard was determined. RESULTS. Highly variable between individuals, RPE-AF increases significantly with age. A perifoveal ring of high AF mirrors rod photoreceptor topography and fundus-AF. Retinal pigment epithelium cell density peaks at the fovea, independent of age, yet no net RPE cell loss is detectable. The RPE monolayer undergoes considerable lifelong re-modeling. The relationship of cell size and AF, a surrogate for LF concentration, is orderly and linear in both groups. Autofluorescence topography differs distinctly from the topography of age-related rod loss. CONCLUSIONS. Digital maps of quantitative AF, cell density, and packing geometry provide metrics for cellular-resolution clinical imaging and model systems. The uncoupling of RPE LF content, cell number, and photoreceptor topography in aging challenges LF's role in AMD.
There are currently a number of methods for solving variants of the following problem: Given a tr... more There are currently a number of methods for solving variants of the following problem: Given a triangulate dpolyhedroP in three-space with or without boundary, construct a smooth surface that interpolates the vertices of P. Problems of this variety arise in numerous areas of application such as medical imaging,scattered data fitting, and geometric modeling. In general, while the techniques satisfy the
Previous accelerated volume rendering techniques have used auxiliary hierarchicaI datastructures ... more Previous accelerated volume rendering techniques have used auxiliary hierarchicaI datastructures to skip empty and homogeneous regions. Although some recent research has taken advantage of more efficient direct encoding techniques to skip empty regions, no work has been done to directly encode homogeneous but not empty regions. 3-D distance transforms previously used to encode empty space can be extended to preprocess homogeneous regions as well, and these regions can be efficiently encoded and incorporated into volume ray-casting and back projection algorithms with a high degree of ff exibility.
We describe an antialiasing system for ray tracing based on adaptive progressive refinement. The ... more We describe an antialiasing system for ray tracing based on adaptive progressive refinement. The goals of the system are to produce high quality antialiased images at a modest average sample rate, and to refine the image progressively so that the image is available in a usable form early and is refined gradually toward the final result. The method proceeds by adaptive stochastic sampling of the image plane, evaluation of the samples by ray tracing, and image reconstruction from the samples. Adaptive control of the sample generation process is driven by three basic goals: coverage of the image, location of features, and confidence in the values at a distinguished "pixel level" of resolution. A three-stage process of interpolation, filtering, and resampling is used to reconstruct a regular grid of display pixels. This reconstruction can be either batch or incremental.
Human Vision, Visual Processing, and Digital Display, 1989
ABSTRACT The sequential sampling, transmission, and rendering of images has been studied in three... more ABSTRACT The sequential sampling, transmission, and rendering of images has been studied in three related contexts: image transmission, vision, and graphics. The solutions developed in these contexts can be viewed as (different) specializations of a single adaptive sampling scheme. We present an analysis of this general scheme, and show how to specialize it. Our basic assumptions are that we can identify an original image (sometimes a model, sometimes the real world), a transmitter which can directly access the original, and a receiver interested in creating a reconstructed image. Different methods are motivated by different goals and constraints, especially the amount of knowledge that the transmitter is allowed to use (but not communicate). In the image synthesis problem, the process which evaluates the image function at a sample point can be viewed as the transmitter. The process which assembles an image from the individual point samples can be viewed as the receiver. In the progressive transmission problem, the transmitter selects or encodes values from a digital image. The receiver reconstructs increasingly accurate approximations of the image, as the samples arrive. These problems share three subproblems: selection of efficient sampling patterns, methods to adaptively control the sample rate, and filters for image reconstruction. In this paper, we explore several related methods of handling these problems, based on different constraints, and different weighting of the goals.
This paper is concerned with the problem of reconstructing the surfaces of three-dimensional obje... more This paper is concerned with the problem of reconstructing the surfaces of three-dimensional objects, given a collection of planar contours representing cross-sections through the objects. This problem has important aplications in biomedical research and instruction, solid modeling, and industrial inspection. The method we describe produces a triangulated mesh from the data points of the contours which is then used in conjunction with a piecewise parametric surface-fitting algorithm to produce a reconstructed surface. The problem can be broken into four subproblems: the correspondence problem (which contours should be connected by the surface?), the tiling problem (how should the contours be connected?), the branching problem (what do we do when there are branches in the surface?), and the surface-fitting problem (what is the precise geometry of the reconstructed surface?) We describe our system for surface reconstruction from sets of contours with respect to each of these subproble...
There are currently a number of methods for solving variants of the following problem: Given a tr... more There are currently a number of methods for solving variants of the following problem: Given a triangulated polyhedron P in three-space with or without boundary, construct a smooth surface that interpolates the vertices of P. Problems of this variety arise in numerous areas of application such as medical imaging, scattered data tting, and geometric modeling. In general, while the techniques satisfy the continuity and interpolation requirements of the problem, they often fail to produce pleasing shapes. Our interest in studying this problem has necessitated the construction of a exible software testbed that allows rapid implementation and testing of new surface tting methods and analysis techniques. The testbed is written entirely in the C programming language and is highly portable. Other relevant features of the testbed are discussed, and recommendations for improving the shape characteristics of several interpolation methods are given.
Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test whether LF... more Lipofuscin (LF) accumulation within RPE cells is considered pathogenic in AMD. To test whether LF contributes to RPE cell loss in aging and to provide a cellular basis for fundus autofluorescence (AF) we created maps of human RPE cell number and histologic AF. Retinal pigment epithelium-Bruch's membrane flat mounts were prepared from 20 donor eyes (10 ≤ 51 and 10 > 80 years; postmortem: ≤4.2 hours; no retinal pathologies), preserving foveal position. Phalloidin-binding RPE cytoskeleton and LF-AF (488-nm excitation) were imaged at up to 90 predefined positions. Maps were assembled from 83,330 cells in 1470 locations. From Voronoi regions representing each cell, the number of neighbors, cell area, and total AF intensity normalized to an AF standard was determined. Highly variable between individuals, RPE-AF increases significantly with age. A perifoveal ring of high AF mirrors rod photoreceptor topography and fundus-AF. Retinal pigment epithelium cell density peaks at the fovea, independent of age, yet no net RPE cell loss is detectable. The RPE monolayer undergoes considerable lifelong re-modeling. The relationship of cell size and AF, a surrogate for LF concentration, is orderly and linear in both groups. Autofluorescence topography differs distinctly from the topography of age-related rod loss. Digital maps of quantitative AF, cell density, and packing geometry provide metrics for cellular-resolution clinical imaging and model systems. The uncoupling of RPE LF content, cell number, and photoreceptor topography in aging challenges LF's role in AMD.
We have measured the spatial density of cones and rods in eight wholemounted human retinas, obtai... more We have measured the spatial density of cones and rods in eight wholemounted human retinas, obtained from seven individuals between 27 and 44 years of age, and constructed maps of photoreceptor density and betweenindividual variability. The average human retina contains 4.6 million cones (4.08-5.29 million). Peak foveal cone density averages 199,000 cones/mni2 and is highly variable between individuals (100,000-324,000 cones/mm'). The point of highest density may be found in an area as large as 0.032 deg'. Cone density falls steeply with increasing eccentricity and is an order of magnitude lower 1 mm away from the foveal center. Superimposed on this gradient is a streak of high cone density along the horizontal meridian. At equivalent eccentricities, cone density is 40-45'0 higher in nasal compared to temporal retina and slightly higher in midperipheral inferior compared to superior retina. Cone density also increases slightly in far nasal retina. The average human retina contains 92 million rods (77.9-107.3 million). In the fovea, the average horizontal diameter of the rod-free zone is 0.350 mm (1.25"). Foveal rod density increases most rapidly superiorly and least rapidly nasally. The highest rod densities are located along an elliptical ring at the eccentricity of the optic disk and extending into nasal retina with the point of highest density typically in superior retina (5/6 eyes). Rod densities decrease by 15-25r',,1 where the ring crosses the horizontal meridian. Rod density declines slowly from the rod ring to the far periphery and is highest in nasal and superior retina. Individual variability in photoreceptor density differs with retinal region and is similar for both cones and rods. Variability is highest near the fovea, reaches a minimum in the midperiphery. and then increases with eccentricity to the ora serrata. The total number of foveal cones is similar for eyes with widely varying peak cone density, consistent with the idea that the variability reflects differences in the lateral migration of photoreceptors during development. Two fellow eyes had cone and rod numbers within 8"(, and similar but not identical photoreceptor topography.
CHAPTER A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants Stephen Mann,... more CHAPTER A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants Stephen Mann, Charles Loop, Michael Lounsbery, David Meyers, James Painter, Tony DeRose, and Kenneth Sloan 8.1. Introduction The problem of passing a surface through a set of data points ...
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