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Derivation of optical flow using a spatiotemporal-frequency approach
COMPUTERVISION, 6RAPmCS, AND iMAGEPROCESSING36, 133-135 (1986)
Abstracts of Papers Accepted for Publication PAPERS Analyzing Oriented Patterns. MICHAEL KASS A N D ANDREW WITKIN. Schlumberger Palo Alto Research, 3340 HiUview Avenue, Palo Alto, California 94304. Received September 3, 1985; accepted November 4, 1985. Oriented patterns, such as those produced by propagation, accretion, or deformation, are common in nature and therefore an important class for visual analysis. Our approach to understanding such patterns is to decompose them into two parts: the flow field, describing the direction of anisotropy; and the residual pattern obtained by describing the image in a coordinate system built from the flow field. We develop a method for the local estimation of anisotropy and a method for combining the estimates to construct a flow coordinate system. Several examples of the use of these methods are presented. These include the use of the flow coordinates to provide preferred directions for edge detection, detection of anomalies, fitting simple models to the straightened pattern, and detecting singularities in the flow field. Fast Binary-Image Boundary Extraction. W. H. H. J. LUNSC~R. Develcon Electronics, Saskatoon, Saskatchewan, Canada S7K 5C7. M. P. B~DDO~S. Department of Electrical Engineering, The University of British Columbia, Vancouver, British Columbia, Canada V6T lW5. Received November 11, 1984; accepted March 14, 1986.
A scheme for obtaining boundaries of binary images is presented. It was inspired by Zahn. In 1969 he showed how to obtain outlines from a raster scanned binary image using a 3 • 2 pixel operator. The present proposal uses a slightly larger operator; it will produce complete descriptions of all closed borders (borders which encounter the outer edges of image space are not included): A nice feature is that only two of the most recently scanned lines of picture must be stored at any one time. Boundaries are continuously calculated during the scan; lookup tables and lists log and link the border points. It is important to signal when a closed contour has been detected. A very fast new, but not infallible, technique based on Euler numbers is proposed. Indication of closure is not guaranteed but it can be used to trigger slow-acting closure verification resulting in reduced processing overhead. Implementation design topics are illustrated in a number of simulations involving segmentation of 50 random-noise images. The results show that the real-time constraint can be satisfied with current technology when the natural parallelism within the system is exploited.
Data Dependent Filters for Edge Enhancement of Landsat Images. KNUT CONRADSENAND GERT NILSSON. IMSOR, The Technical University of Denmark, DK-2800 Lyngby, Denmark. Received May 22, 1985; revised March 10, 1986. In the paper some 2D filters are presented that are very efficient in edge enhancement of Landsat imagery. The filtered images are obtained as differences between the original images and some minimum mean-squared error predictions based on suitably chosen "predictor sets." The filters are compared to other high-pass filters such as the Laplacian and Gaussian filters, and they compare very favorably.
Derivation of Optical Flow Using a Spatiotemporal-FrequencyApproach. LOWELLJACOBSONAND HARRY WECHSI~R. Department of Electrical Engineering, University of Minnesota, Minneapolis, Minnesota 55455. Received May 7, 1986. We advance in this paper the spatiotemporal-frequency (STF) approach for computing the optical flow of a time-varying image. STF flow derivation provides an attractive alternative to earlier approaches 0734-189X/86 $3.00 Copyright 9 1986 by Academic Press, Inc. All fights of reproduction in any form reserved.
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.
Abstracts of Papers Accepted for Publication PAPERS Analyzing Oriented Patterns. MICHAEL KASS A N D ANDREW WITKIN. Schlumberger Palo Alto Research, 3340 HiUview Avenue, Palo Alto, California 94304. Received September 3, 1985; accepted November 4, 1985. Oriented patterns, such as those produced by propagation, accretion, or deformation, are common in nature and therefore an important class for visual analysis. Our approach to understanding such patterns is to decompose them into two parts: the flow field, describing the direction of anisotropy; and the residual pattern obtained by describing the image in a coordinate system built from the flow field. We develop a method for the local estimation of anisotropy and a method for combining the estimates to construct a flow coordinate system. Several examples of the use of these methods are presented. These include the use of the flow coordinates to provide preferred directions for edge detection, detection of anomalies, fitting simple models to the straightened pattern, and detecting singularities in the flow field. Fast Binary-Image Boundary Extraction. W. H. H. J. LUNSC~R. Develcon Electronics, Saskatoon, Saskatchewan, Canada S7K 5C7. M. P. B~DDO~S. Department of Electrical Engineering, The University of British Columbia, Vancouver, British Columbia, Canada V6T lW5. Received November 11, 1984; accepted March 14, 1986.
A scheme for obtaining boundaries of binary images is presented. It was inspired by Zahn. In 1969 he showed how to obtain outlines from a raster scanned binary image using a 3 • 2 pixel operator. The present proposal uses a slightly larger operator; it will produce complete descriptions of all closed borders (borders which encounter the outer edges of image space are not included): A nice feature is that only two of the most recently scanned lines of picture must be stored at any one time. Boundaries are continuously calculated during the scan; lookup tables and lists log and link the border points. It is important to signal when a closed contour has been detected. A very fast new, but not infallible, technique based on Euler numbers is proposed. Indication of closure is not guaranteed but it can be used to trigger slow-acting closure verification resulting in reduced processing overhead. Implementation design topics are illustrated in a number of simulations involving segmentation of 50 random-noise images. The results show that the real-time constraint can be satisfied with current technology when the natural parallelism within the system is exploited.
Data Dependent Filters for Edge Enhancement of Landsat Images. KNUT CONRADSENAND GERT NILSSON. IMSOR, The Technical University of Denmark, DK-2800 Lyngby, Denmark. Received May 22, 1985; revised March 10, 1986. In the paper some 2D filters are presented that are very efficient in edge enhancement of Landsat imagery. The filtered images are obtained as differences between the original images and some minimum mean-squared error predictions based on suitably chosen "predictor sets." The filters are compared to other high-pass filters such as the Laplacian and Gaussian filters, and they compare very favorably.
Derivation of Optical Flow Using a Spatiotemporal-FrequencyApproach. LOWELLJACOBSONAND HARRY WECHSI~R. Department of Electrical Engineering, University of Minnesota, Minneapolis, Minnesota 55455. Received May 7, 1986. We advance in this paper the spatiotemporal-frequency (STF) approach for computing the optical flow of a time-varying image. STF flow derivation provides an attractive alternative to earlier approaches 0734-189X/86 $3.00 Copyright 9 1986 by Academic Press, Inc. All fights of reproduction in any form reserved.
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.