- Email: [email protected]
An object centered hierarchical representation for 3D objects: The prism tree
ABSTRACTS OF PAPERS ACCEPTED FOR PUBLICATION based on (1) feature correspondence, (2) spatiotemporal gradients, and (3) Fourier-phase changes. After briefly surveying these three earlier approaches to flow computation, we provide an historical overview of the development of the STF approach. Then an improved STF method for flow derivation that has recently been developed by the authors is presented along with experimental results that demonstrate its use. We conclude by showing that STF derivation (a) promises substantially improved performance over other flow computation methods, and (b) provides a partial explanation of motion coherence as observed in human vision.
An Object Centered Hierarchical Representation for 3D Objects: The Prism Tree. JEANPONCE. Cedar Hall, Robotics Laboratory, Computer Science Department, Stanford University, Stanford, California 94305. OLIVlER FAUGERAS. INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay C~dex, France. Received September 11, 1985; accepted June 26, 1986. Efficient computation of surfaces and/or solids intersections is a cornerstone of many algorithms in geometric modelling and computer graphics, for example, set operations between solids, or ray casting display of surfaces. We present an object centered, information preserving, hierarchical representation for polyhedra called prism tree, establish its fundamental properties, and give a neighbor-finding algorithm. The representation is then used to decompose the intersection algorithms in two steps: the localization of intersections, and their processing. When dealing with polyhedra with many faces (typically more than 1000), the first step is by far the most expensive. The prism tree structure is used to compute efficiently this localization step. A preliminary implementation of the set operations and ray casting algorithms has been constructed.
Deblurring Gaussion Blur. ROBERTA. HUMMEL,B. KIMIA, AND STEVENW. ZUCKER. Department of Computer Science, New York University, New York 10012. Received December 6, 1984; revised December 23, 1986. Gaussian blur, or convolution against a Gaussian kernel, is a common model for image and signal degradation. In general, the process of reversing Gaussian blur is unstable, and cannot be represented as a convolution filter in the spatial domain. If we restrict the space of allowable functions to polynomials of fixed finite degree, then a convolution inverse does exist. We give constructive formulas for the deblurring kernels in terms of Hermite polynomials, and observe that their use yields optimal approximate deblurring solutions among the space of bounded degree polynomials. The more common methods of achieving stable approximate deblurring include restrictions to band-limited functions or functions of bounded norm.
A Dynamic Screen Techniquefor Shaded Graphics Display of Slice-Represented Objects. R. ANTHONY REYNOLDS. General Robotics and Active Sensory Processing Group, Department of Computer and Information Science, Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104. DAN GORDON. Department of Computer Science, University of Cincinnati, Cincinnati, Ohio 45221. LIH-SHYANGCHEN. Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, Pennsylvania 19104. Received March 21, 1985; accepted June 19, 1986. We present a very rapid method of constructing realistic images of 3-dimensional (3D) objects on a 2-dimensional (2D) display screen. Our technique is well suited to objects represented by slices, since it traverses the slices in a front-to-back sequence relative to the observer, accessing each slice just once. A dynamic data structure--the dynamic screen--is used to represent the unlit screen pixels. When each slice is accessed, only unlit pixels are processed and newly lit pixels are efficiently removed from the data structure. Implementation of the method for large medical objects results in display times significantly faster than previous software methods.
Planar Decomposition for Quadtree Data Structure. PINAI~ MAZb'MDER. Computer Systems Group, Coordinated Science Laboratory, 1101 West Springfield Avenue, University of Illinois, Urbana, Illinois 61801. Received April 23, 1985; accepted June 2, 1986.
An Object Centered Hierarchical Representation for 3D Objects: The Prism Tree. JEANPONCE. Cedar Hall, Robotics Laboratory, Computer Science Department, Stanford University, Stanford, California 94305. OLIVlER FAUGERAS. INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay C~dex, France. Received September 11, 1985; accepted June 26, 1986. Efficient computation of surfaces and/or solids intersections is a cornerstone of many algorithms in geometric modelling and computer graphics, for example, set operations between solids, or ray casting display of surfaces. We present an object centered, information preserving, hierarchical representation for polyhedra called prism tree, establish its fundamental properties, and give a neighbor-finding algorithm. The representation is then used to decompose the intersection algorithms in two steps: the localization of intersections, and their processing. When dealing with polyhedra with many faces (typically more than 1000), the first step is by far the most expensive. The prism tree structure is used to compute efficiently this localization step. A preliminary implementation of the set operations and ray casting algorithms has been constructed.
Deblurring Gaussion Blur. ROBERTA. HUMMEL,B. KIMIA, AND STEVENW. ZUCKER. Department of Computer Science, New York University, New York 10012. Received December 6, 1984; revised December 23, 1986. Gaussian blur, or convolution against a Gaussian kernel, is a common model for image and signal degradation. In general, the process of reversing Gaussian blur is unstable, and cannot be represented as a convolution filter in the spatial domain. If we restrict the space of allowable functions to polynomials of fixed finite degree, then a convolution inverse does exist. We give constructive formulas for the deblurring kernels in terms of Hermite polynomials, and observe that their use yields optimal approximate deblurring solutions among the space of bounded degree polynomials. The more common methods of achieving stable approximate deblurring include restrictions to band-limited functions or functions of bounded norm.
A Dynamic Screen Techniquefor Shaded Graphics Display of Slice-Represented Objects. R. ANTHONY REYNOLDS. General Robotics and Active Sensory Processing Group, Department of Computer and Information Science, Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104. DAN GORDON. Department of Computer Science, University of Cincinnati, Cincinnati, Ohio 45221. LIH-SHYANGCHEN. Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, Pennsylvania 19104. Received March 21, 1985; accepted June 19, 1986. We present a very rapid method of constructing realistic images of 3-dimensional (3D) objects on a 2-dimensional (2D) display screen. Our technique is well suited to objects represented by slices, since it traverses the slices in a front-to-back sequence relative to the observer, accessing each slice just once. A dynamic data structure--the dynamic screen--is used to represent the unlit screen pixels. When each slice is accessed, only unlit pixels are processed and newly lit pixels are efficiently removed from the data structure. Implementation of the method for large medical objects results in display times significantly faster than previous software methods.
Planar Decomposition for Quadtree Data Structure. PINAI~ MAZb'MDER. Computer Systems Group, Coordinated Science Laboratory, 1101 West Springfield Avenue, University of Illinois, Urbana, Illinois 61801. Received April 23, 1985; accepted June 2, 1986.