Convolution. 1D Formula: 2D Formula: Example on the web:


 Lucinda Oliver
 1 years ago
 Views:
Transcription
1 Basic Filters (7) Convolution/correlation/Linear filtering Gaussian filters Smoothing and noise reduction First derivatives of Gaussian Second derivative of Gaussian: Laplacian Oriented Gaussian filters Steerability
2 Convolution 1D Formula: 2D Formula: Example on the web:
3
4 Kernel: 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
5 Kernel:
6 Kernel: 15 x 15 matrix of value 1/225
7 Basic Properties Commutes: f * g = g * f Associative: (f * g) * h = f * (g * h) Linear: (af + bg) * h = a f * h + b g * h Shift invariant: f t * h = (f * h) t Only operator both linear and shift invariant Differentiation:
8 Practicalities (discrete convolution/correlation) MATLAB: conv (1D) or conv2 (2D), corr Border issues: When applying convolution with a KxK kernel, the result is undefined for pixels closer than K pixels from the border of the image Options: Warp around Expand/Pad Crop K
9 1D: 2D: Slight abuse of notations: We ignore the normalization constant such that
10 ,! = 5 Kernel:
11 Simple Averaging Gaussian Smoothing
12 Image Noise
13 Gaussian Smoothing to Remove Noise No smoothing! = 2! =
14 Shape of Gaussian filter as function of!"! = 1! = 3! = 5
15 Note about Finite Kernel Support Gaussian function has infinite support In discrete filtering, we have finite kernel size
16 Increasing!"
17 Basic Properties Gaussian removes highfrequency components from the image! low pass filter Larger! remove more details Combination of 2 Gaussian filters is a Gaussian filter: Separable filter: Critical implication: Filtering with a NxN Gaussian kernel can be implemented as two convolutions of size N! reduction quadratic to linear! must be implemented that way
18 Oriented Gaussian Filters G! smoothes the image by the same amount in all directions If we have some information about preferred directions, we might want to smooth with some value! 1 in the direction defined by the unit vector [a b] and by! 2 in the direction defined by [c d] We can write this in a more compact form by using the standard multivariate Gaussian notation: The two (orthogonal) directions of filtering are given by the eigenvectors of #, the amount of smoothing is given by the square root of the corresponding eigenvalues of #.
19
20
21
22 Image Derivatives Image Derivatives Derivatives increase noise Derivative of Gaussian Laplacian of Gaussian (LOG)
23 Image Derivatives We want to compute, at each pixel (x,y) the derivatives: In the discrete case we could take the difference between the left and right pixels: Convolution of the image by Problem: Increases noise Difference between Actual image values True difference (derivative) Twice the amount of noise as in the original image
24 Original Image Noise Added Derivative in the horizontal direction
25 Smooth Derivatives Solution: First smooth the image by a Gaussian G! and then take derivatives: Applying the differentiation property of the convolution: Therefore, taking the derivative in x of the image can be done by convolution with the derivative of a Gaussian: Crucial property: The Gaussian derivative is also separable:
26 G G x
27 Derivative + Smoothing Without smoothing With smoothing Better but still blurs away edge information
28 I Applying the first derivative of Gaussian
29 Input Difference operator Derivative from difference operator Gaussian derivative operator Derivative from Gaussian derivative
30 There is ALWAYS a tradeoff between smoothing and good edge localization! Image with Edge Edge Location Image + Noise Derivatives detect edge and noise Smoothed derivative removes noise, but blurs edge
31 g Second derivatives: Laplacian g xx
32 DOG Approximation to LOG
33 Gaussian Separable, lowpass filter Derivatives of Gaussian Separable, output of convolution is gradient at scale!: Laplacian Directional Derivatives Notseparable, approximated by A difference of Gaussians. Output of convolution is Laplacian of image: Zerocrossings correspond to edges Output of convolution is magnitude of derivative in direction $. Filter is linear combination of derivatives in x and y Oriented Gaussian Smooth with different scales in orthogonal directions
34 Edge Detection Edge Detection Gradient operators Canny edge detectors Laplacian detectors
35 Edge = discontinuity of intensity in some direction. Could be detected by looking for places where the derivatives of the image have large values. What is an edge?
36 $ Edge pixels are at local maxima of gradient magnitude Gradient computed by convolution with Gaussian derivatives Gradient direction is always perpendicular to edge direction
37 Small sigma Large sigma
38 != 10!= 1 Large!! Good detection (high SNR) Poor localization Small!! Poor detection (low SNR) Good localization
39 Canny s Result Given a filter f, define the two objective functions: %(f) large if f produces good localization #(f) large if f produces good detection (high SNR) Problem: Find a family of filters f that maximizes the compromise criterion %(f)#(f) under the constraint that a single peak is generated by a step edge Solution: Unique solution, a close approximation is the Gaussian derivative filter! Canny Derivative of Gaussian
40 Next Steps The gradient magnitude enhances the edges but 2 problems remain: What threshold should we use to retain only the real edges? Even if we had a perfect threshold, we would still have poorly localized edges. How to extract optimally localize contours? Solution: Two standard tools: Nonlocal maxima suppression Hysteresis thresholding
41 Different thresholds applied to gradient magnitude
42 Input image
43 Different thresholds applied to gradient magnitude
44 NonLocal Maxima Suppression Gradient magnitude at center pixel is lower than the gradient magnitude of a neighbor in the direction of the gradient! Discard center pixel (set magnitude to 0) Gradient magnitude at center pixel is greater than gradient magnitude of all the neighbors in the direction of the gradient! Keep center pixel unchanged
45 T = 15 T = 5 Two thresholds applied to gradient magnitude
46 Hysteresis Thresholding Weak pixels but connected Weak pixels but isolated Very strong edge response. Let s start here Weaker response but it is connected to a confirmed edge point. Let s keep it. Continue. Note: Darker squares illustrate stronger edge response (larger M)
47 T=15 T=5 Hysteresis T h =15 T l = 5 Hysteresis thresholding
48
49 Summary Edges are discontinuities of intensity in images Correspond to local maxima of image gradient Gradient computed by convolution with derivatives of Gaussian General principle applies: Large!: Poor localization, good detection Small!: Good localization, poor detection Canny showed that Gaussian derivatives yield good compromise between localization and detection Edges correspond to zerocrossings of the second derivative (Laplacian in 2D)
Computer Vision: Filtering
Computer Vision: Filtering Raquel Urtasun TTI Chicago Jan 10, 2013 Raquel Urtasun (TTIC) Computer Vision Jan 10, 2013 1 / 82 Today s lecture... Image formation Image Filtering Raquel Urtasun (TTIC) Computer
More informationEdge detection. (Trucco, Chapt 4 AND Jain et al., Chapt 5) Edges are significant local changes of intensity in an image.
Edge detection (Trucco, Chapt 4 AND Jain et al., Chapt 5) Definition of edges Edges are significant local changes of intensity in an image. Edges typically occur on the boundary between two different
More informationDigital Imaging and Multimedia. Filters. Ahmed Elgammal Dept. of Computer Science Rutgers University
Digital Imaging and Multimedia Filters Ahmed Elgammal Dept. of Computer Science Rutgers University Outlines What are Filters Linear Filters Convolution operation Properties of Linear Filters Application
More information What is a feature?  Image processing essentials  Edge detection (Sobel & Canny)  Hough transform  Some images
Seminar: Feature extraction by André Aichert I Feature detection  What is a feature?  Image processing essentials  Edge detection (Sobel & Canny)  Hough transform  Some images II An Entropybased
More informationComputational Foundations of Cognitive Science
Computational Foundations of Cognitive Science Lecture 15: Convolutions and Kernels Frank Keller School of Informatics University of Edinburgh keller@inf.ed.ac.uk February 23, 2010 Frank Keller Computational
More informationWhat is an Edge? Computer Vision Week 4. How to detect edges? What is an Edge? Edge Detection techniques. Edge Detection techniques.
What is an Edge? Computer Vision Week 4 Edge Detection Linear filtering; pyramids, wavelets Interest Operators surface normal discontinuity depth discontinuity surface color discontinuity illumination
More informationCanny Edge Detection
Canny Edge Detection 09gr820 March 23, 2009 1 Introduction The purpose of edge detection in general is to significantly reduce the amount of data in an image, while preserving the structural properties
More informationBildverarbeitung und Mustererkennung Image Processing and Pattern Recognition
Bildverarbeitung und Mustererkennung Image Processing and Pattern Recognition 1. Image PreProcessing  Pixel Brightness Transformation  Geometric Transformation  Image Denoising 1 1. Image PreProcessing
More informationjorge s. marques image processing
image processing images images: what are they? what is shown in this image? What is this? what is an image images describe the evolution of physical variables (intensity, color, reflectance, condutivity)
More informationMVA ENS Cachan. Lecture 2: Logistic regression & intro to MIL Iasonas Kokkinos Iasonas.kokkinos@ecp.fr
Machine Learning for Computer Vision 1 MVA ENS Cachan Lecture 2: Logistic regression & intro to MIL Iasonas Kokkinos Iasonas.kokkinos@ecp.fr Department of Applied Mathematics Ecole Centrale Paris Galen
More informationToday s Topics. Lecture 11: LoG and DoG Filters. Recall: First Derivative Filters. SecondDerivative Filters
Today s Topics Lecture : LoG and DoG Filters Laplacian of Gaussian (LoG) Filter  useful for finding edges  also useful for finding blobs! approimation using Difference of Gaussian (DoG) Recall: First
More informationImage Gradients. Given a discrete image Á Òµ, consider the smoothed continuous image Üµ defined by
Image Gradients Given a discrete image Á Òµ, consider the smoothed continuous image Üµ defined by Üµ Ü ¾ Ö µ Á Òµ Ü ¾ Ö µá µ (1) where Ü ¾ Ö Ô µ Ü ¾ Ý ¾. ½ ¾ ¾ Ö ¾ Ü ¾ ¾ Ö. Here Ü is the 2norm for the
More information2D Image Processing. Edge and Corner Detection. Prof. Didier Stricker Dr. Alain Pagani
2D Image Processing Edge and Corner Detection Prof. Didier Stricker Dr. Alain Pagani Kaiserlautern University http://ags.cs.unikl.de/ DFKI Deutsches Forschungszentrum für Künstliche Intelligenz http://av.dfki.de
More informationOneDimensional Processing for Edge Detection using Hilbert Transform P. Kiran Kumar, Sukhendu Das and B. Yegnanarayana Department of Computer Science and Engineering Indian Institute of Technology, Madras
More informationCorrelation and Convolution Class Notes for CMSC 426, Fall 2005 David Jacobs
Correlation and Convolution Class otes for CMSC 46, Fall 5 David Jacobs Introduction Correlation and Convolution are basic operations that we will perform to extract information from images. They are in
More informationImage Filtering & Edge Detection
What is imae filterin? Imae Filterin & Ede Detection Modify the pixels in an imae based on some function of a local neihborhood of the pixels. Some function Readin: Chapter 7 and 8, F&P Linear Functions
More information2.2 Creaseness operator
2.2. Creaseness operator 31 2.2 Creaseness operator Antonio López, a member of our group, has studied for his PhD dissertation the differential operators described in this section [72]. He has compared
More informationImage Segmentation and Registration
Image Segmentation and Registration Dr. Christine Tanner (tanner@vision.ee.ethz.ch) Computer Vision Laboratory, ETH Zürich Dr. Verena Kaynig, Machine Learning Laboratory, ETH Zürich Outline Segmentation
More informationCOMPUTATIONAL INTELLIGENCE (INTRODUCTION TO MACHINE LEARNING) SS16. Lecture 2: Linear Regression Gradient Descent Nonlinear basis functions
COMPUTATIONAL INTELLIGENCE (INTRODUCTION TO MACHINE LEARNING) SS16 Lecture 2: Linear Regression Gradient Descent Nonlinear basis functions LINEAR REGRESSION MOTIVATION Why Linear Regression? Regression
More informationColorCrack: Identifying Cracks in Glass
ColorCrack: Identifying Cracks in Glass James Max Kanter Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge, MA 02139 kanter@mit.edu Figure 1: ColorCrack automatically identifies cracks
More informationImplementation of Image Processing Algorithms on the Graphics Processing Units
Implementation of Image Processing Algorithms on the Graphics Processing Units Natalia Papulovskaya, Kirill Breslavskiy, and Valentin Kashitsin Department of Information Technologies of the Ural Federal
More informationAdmin stuff. 4 Image Pyramids. Spatial Domain. Projects. Fourier domain 2/26/2008. Fourier as a change of basis
Admin stuff 4 Image Pyramids Change of office hours on Wed 4 th April Mon 3 st March 9.3.3pm (right after class) Change of time/date t of last class Currently Mon 5 th May What about Thursday 8 th May?
More information521466S Machine Vision Assignment #7 Hough transform
521466S Machine Vision Assignment #7 Hough transform Spring 2014 In this assignment we use the hough transform to extract lines from images. We use the standard (r, θ) parametrization of lines, lter the
More informationImplementation of Canny Edge Detector of color images on CELL/B.E. Architecture.
Implementation of Canny Edge Detector of color images on CELL/B.E. Architecture. Chirag Gupta,Sumod Mohan K cgupta@clemson.edu, sumodm@clemson.edu Abstract In this project we propose a method to improve
More informationProblem definition: optical flow
Motion Estimation http://www.sandlotscience.com/distortions/breathing_objects.htm http://www.sandlotscience.com/ambiguous/barberpole.htm Why estimate motion? Lots of uses Track object behavior Correct
More informationEECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines
EECS 556 Image Processing W 09 Interpolation Interpolation techniques B splines What is image processing? Image processing is the application of 2D signal processing methods to images Image representation
More informationSpatial filtering. Computer Vision & Digital Image Processing. Spatial filter masks. Spatial filters (examples) Smoothing filters
Spatial filtering Computer Vision & Digital Image Processing Spatial Filtering Use of spatial masks for filtering is called spatial filtering May be linear or nonlinear Linear filters Lowpass: attenuate
More informationADVANCED LINEAR ALGEBRA FOR ENGINEERS WITH MATLAB. Sohail A. Dianat. Rochester Institute of Technology, New York, U.S.A. Eli S.
ADVANCED LINEAR ALGEBRA FOR ENGINEERS WITH MATLAB Sohail A. Dianat Rochester Institute of Technology, New York, U.S.A. Eli S. Saber Rochester Institute of Technology, New York, U.S.A. (g) CRC Press Taylor
More informationComputational Optical Imaging  Optique Numerique.  Deconvolution 
Computational Optical Imaging  Optique Numerique  Deconvolution  Winter 2014 Ivo Ihrke Deconvolution Ivo Ihrke Outline Deconvolution Theory example 1D deconvolution Fourier method Algebraic method
More informationBIL Computer Vision Mar 5, 2014
BIL 719  Computer Vision Mar 5, 2014 Image pyramids Aykut Erdem Dept. of Computer Engineering Hacettepe University Image Scaling This image is too big to fit on the screen. How can we reduce it? How to
More informationImage Segmentation Preview Segmentation subdivides an image to regions or objects Two basic properties of intensity values Discontinuity Edge detection Similarity Thresholding Region growing/splitting/merging
More informationImage Processing with. ImageJ. Biology. Imaging
Image Processing with ImageJ 1. Spatial filters Outlines background correction image denoising edges detection 2. Fourier domain filtering correction of periodic artefacts 3. Binary operations masks morphological
More informationImage Enhancement in the Frequency Domain
Image Enhancement in the Frequency Domain Jesus J. Caban Outline! Assignment #! Paper Presentation & Schedule! Frequency Domain! Mathematical Morphology %& Assignment #! Questions?! How s OpenCV?! You
More informationJ. P. Oakley and R. T. Shann. Department of Electrical Engineering University of Manchester Manchester M13 9PL U.K. Abstract
A CURVATURE SENSITIVE FILTER AND ITS APPLICATION IN MICROFOSSIL IMAGE CHARACTERISATION J. P. Oakley and R. T. Shann Department of Electrical Engineering University of Manchester Manchester M13 9PL U.K.
More informationIMPACT OF POSE AND GLASSES ON FACE DETECTION USING THE RED EYE EFFECT
IMPACT OF POSE AND GLASSES ON FACE DETECTION USING THE RED EYE EFFECT Yednekachew Asfaw, Bryan Chen and Andy Adler University Of Ottawa March 2003 Face Detection Applications for face detection Surveillance
More informationFeature Tracking and Optical Flow
02/09/12 Feature Tracking and Optical Flow Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem Many slides adapted from Lana Lazebnik, Silvio Saverse, who in turn adapted slides from Steve
More informationAnalysis of Face Recognition Based On Edge Detection Algorithm with Hardware Interfacing
Analysis of Face Recognition Based On Edge Detection Algorithm with Hardware Interfacing Pankaj Bhandari 1, Pankaj K Gupta 2, Karthik U.S Goutham Reddy 3,Jeeva.B 4 UG Students, Department of ECE, N.I.T
More informationSharpening through spatial filtering
Sharpening through spatial filtering Stefano Ferrari Università degli Studi di Milano stefano.ferrari@unimi.it Elaborazione delle immagini (Image processing I) academic year 2011 2012 Sharpening The term
More informationConvolution, Noise and Filters
T H E U N I V E R S I T Y of T E X A S Convolution, Noise and Filters Philip Baldwin, Ph.D. Department of Biochemistry Response to an Entire Signal The response of a system with impulse response h(t) to
More informationPATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION Introduction In the previous chapter, we explored a class of regression models having particularly simple analytical
More informationTABLE OF CONTENTS CHAPTER TITLE PAGE
vii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS LIST OF APPENDICES ii iii iv v vi
More informationSign Language Recognition System
International Journal of Computational Engineering Research Vol, 03 Issue, 6 Sign Language Recognition System Er. Aditi Kalsh 1, Dr. N.S. Garewal 2 1 Assistant Professor, Department of Electronics & Communication,
More informationImage Enhancement: Frequency domain methods
Image Enhancement: Frequency domain methods The concept of filtering is easier to visualize in the frequency domain. Therefore, enhancement of image f ( m, n) can be done in the frequency domain, based
More informationIntroduction to Computer Vision. Week 11, Fall 2010 Instructor: Prof. Ko Nishino
Introduction to Computer Vision Week 11, Fall 2010 Instructor: Prof. Ko Nishino The Projective Plane Why do we need homogeneous coordinates? represent points at infinity, homographies, perspective projection,
More informationEdge Detection Techniques: Evaluations and Comparisons
Applied Mathematical Sciences, Vol. 2, 2008, no. 31, 15071520 Edge Detection Techniques: Evaluations and Comparisons Ehsan Nadernejad Department of Computer Engineering, Faculty of Engineering Mazandaran
More informationCHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES. From Exploratory Factor Analysis Ledyard R Tucker and Robert C.
CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES From Exploratory Factor Analysis Ledyard R Tucker and Robert C MacCallum 1997 180 CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES In
More informationMarkov chains and Markov Random Fields (MRFs)
Markov chains and Markov Random Fields (MRFs) 1 Why Markov Models We discuss Markov models now. This is the simplest statistical model in which we don t assume that all variables are independent; we assume
More informationMotivation. Lecture 31: Object Recognition: SIFT Keys. Simple Example. Simple Example. Simple Example
Lecture 31: Object Recognition: SIFT Keys Motivation Want to recognize a known objects from unknown viewpoints. find them in an image database of models Local Feature based Approaches Represent appearance
More informationIncreasing for all. Convex for all. ( ) Increasing for all (remember that the log function is only defined for ). ( ) Concave for all.
1. Differentiation The first derivative of a function measures by how much changes in reaction to an infinitesimal shift in its argument. The largest the derivative (in absolute value), the faster is evolving.
More informationFace Recognition using SIFT Features
Face Recognition using SIFT Features Mohamed Aly CNS186 Term Project Winter 2006 Abstract Face recognition has many important practical applications, like surveillance and access control.
More informationNumerical Methods For Image Restoration
Numerical Methods For Image Restoration CIRAM Alessandro Lanza University of Bologna, Italy Faculty of Engineering CIRAM Outline 1. Image Restoration as an inverse problem 2. Image degradation models:
More informationLecture 2: 2D Fourier transforms and applications
Lecture 2: 2D Fourier transforms and applications B14 Image Analysis Michaelmas 2014 A. Zisserman Fourier transforms and spatial frequencies in 2D Definition and meaning The Convolution Theorem Applications
More informationIntroduction to Inverse Problems (2 lectures)
Introduction to Inverse Problems (2 lectures) Summary Direct and inverse problems Examples of direct (forward) problems Deterministic and statistical points of view Illposed and illconditioned problems
More informationVisualization and Feature Extraction, FLOW Spring School 2016 Prof. Dr. Tino Weinkauf. Flow Visualization. ImageBased Methods (integrationbased)
Visualization and Feature Extraction, FLOW Spring School 2016 Prof. Dr. Tino Weinkauf Flow Visualization ImageBased Methods (integrationbased) Spot Noise (Jarke van Wijk, Siggraph 1991) Flow Visualization:
More informationIEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER A Performance Evaluation of Local Descriptors
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER 2005 1615 A Performance Evaluation of Local Descriptors Krystian Mikolajczyk and Cordelia Schmid Abstract In this
More informationModel Based Detection of Tubular Structures in 3D Images
Model ased Detection of Tubular Structures in 3D Images Karl Krissian Grégoire Malandain Nicholas Ayache Epidaure project INRIA 2004 route des Lucioles 06902 Sophia Antipolis France; and Régis Vaillant
More informationBlind Deconvolution of Barcodes via Dictionary Analysis and Wiener Filter of Barcode Subsections
Blind Deconvolution of Barcodes via Dictionary Analysis and Wiener Filter of Barcode Subsections Maximilian Hung, Bohyun B. Kim, Xiling Zhang August 17, 2013 Abstract While current systems already provide
More informationThe Image Deblurring Problem
page 1 Chapter 1 The Image Deblurring Problem You cannot depend on your eyes when your imagination is out of focus. Mark Twain When we use a camera, we want the recorded image to be a faithful representation
More informationLeastSquares Intersection of Lines
LeastSquares Intersection of Lines Johannes Traa  UIUC 2013 This writeup derives the leastsquares solution for the intersection of lines. In the general case, a set of lines will not intersect at a
More informationELECE8104 Stochastics models and estimation, Lecture 3b: Linear Estimation in Static Systems
Stochastics models and estimation, Lecture 3b: Linear Estimation in Static Systems Minimum Mean Square Error (MMSE) MMSE estimation of Gaussian random vectors Linear MMSE estimator for arbitrarily distributed
More informationQUALITY TESTING OF WATER PUMP PULLEY USING IMAGE PROCESSING
QUALITY TESTING OF WATER PUMP PULLEY USING IMAGE PROCESSING MRS. A H. TIRMARE 1, MS.R.N.KULKARNI 2, MR. A R. BHOSALE 3 MR. C.S. MORE 4 MR.A.G.NIMBALKAR 5 1, 2 Assistant professor Bharati Vidyapeeth s college
More informationStatistical Machine Learning
Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classes
More informationCHAPTER 7. E IGENVALUE ANALYSIS
1 CHAPTER 7. E IGENVALUE ANALYSIS Written by: Sophia Hassiotis, January, 2003 Last revision: March, 2015 7.1 Stress TensorMohr s Circle for 2D Stress Let s review the use of the Mohr s Circle in finding
More informationPerformance of Dynamic Load Balancing Algorithms for Unstructured Mesh Calculations
Performance of Dynamic Load Balancing Algorithms for Unstructured Mesh Calculations Roy D. Williams, 1990 Presented by Chris Eldred Outline Summary Finite Element Solver Load Balancing Results Types Conclusions
More informationColor to Grayscale Conversion with Chrominance Contrast
Color to Grayscale Conversion with Chrominance Contrast Yuting Ye University of Virginia Figure 1: The sun in Monet s Impression Sunrise has similar luminance as the sky. It can hardly be seen when the
More informationModified Hybrid Median Filter for Effective Speckle Reduction in Ultrasound Images
Modified Hybrid Median Filter for Effective Speckle Reduction in Ultrasound Images R.VANITHAMANI 1, G.UMAMAHESWARI, M.EZHILARASI 3 1 Lecturer, Department of Biomedical Instrumentation Engineering, Avinashilingam
More informationRemoval of Noise from MRI using Spectral Subtraction
International Journal of Electronic and Electrical Engineering. ISSN 09742174, Volume 7, Number 3 (2014), pp. 293298 International Research Publication House http://www.irphouse.com Removal of Noise
More informationNeural Networks. CAP5610 Machine Learning Instructor: GuoJun Qi
Neural Networks CAP5610 Machine Learning Instructor: GuoJun Qi Recap: linear classifier Logistic regression Maximizing the posterior distribution of class Y conditional on the input vector X Support vector
More informationAN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS
AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS Revised Edition James Epperson Mathematical Reviews BICENTENNIAL 0, 1 8 0 7 z ewiley wu 2007 r71 BICENTENNIAL WILEYINTERSCIENCE A John Wiley & Sons, Inc.,
More informationA New Robust Algorithm for Video Text Extraction
A New Robust Algorithm for Video Text Extraction Pattern Recognition, vol. 36, no. 6, June 2003 Edward K. Wong and Minya Chen School of Electrical Engineering and Computer Science Kyungpook National Univ.
More informationTwo Topics in Parametric Integration Applied to Stochastic Simulation in Industrial Engineering
Two Topics in Parametric Integration Applied to Stochastic Simulation in Industrial Engineering Department of Industrial Engineering and Management Sciences Northwestern University September 15th, 2014
More informationImage Processing Techniques applied to Liquid Argon Time Projection Chamber(LArTPC) Data
Image Processing Techniques applied to Liquid Argon Time Projection Chamber(LArTPC) Data Jessica Esquivel On Behalf of the MicroBooNE Collaboration Syracuse University Advisor: Mitch Soderberg Outline
More informationGaussian Processes in Machine Learning
Gaussian Processes in Machine Learning Carl Edward Rasmussen Max Planck Institute for Biological Cybernetics, 72076 Tübingen, Germany carl@tuebingen.mpg.de WWW home page: http://www.tuebingen.mpg.de/ carl
More informationAn Iterative Image Registration Technique with an Application to Stereo Vision
An Iterative Image Registration Technique with an Application to Stereo Vision Bruce D. Lucas Takeo Kanade Computer Science Department CarnegieMellon University Pittsburgh, Pennsylvania 15213 Abstract
More informationThis is a square root. The number under the radical is 9. (An asterisk * means multiply.)
Page of Review of Radical Expressions and Equations Skills involving radicals can be divided into the following groups: Evaluate square roots or higher order roots. Simplify radical expressions. Rationalize
More informationG E N E R A L A P P R O A CH: LO O K I N G F O R D O M I N A N T O R I E N T A T I O N I N I M A G E P A T C H E S
G E N E R A L A P P R O A CH: LO O K I N G F O R D O M I N A N T O R I E N T A T I O N I N I M A G E P A T C H E S In object categorization applications one of the main problems is that objects can appear
More informationComponent Ordering in Independent Component Analysis Based on Data Power
Component Ordering in Independent Component Analysis Based on Data Power Anne Hendrikse Raymond Veldhuis University of Twente University of Twente Fac. EEMCS, Signals and Systems Group Fac. EEMCS, Signals
More informationEvaluation of Interest Point Detectors
International Journal of Computer Vision 37(2), 151 172, 2000 c 2000 Kluwer Academic Publishers. Manufactured in The Netherlands. Evaluation of Interest Point Detectors CORDELIA SCHMID, ROGER MOHR AND
More informationModified Sift Algorithm for Appearance Based Recognition of American Sign Language
Modified Sift Algorithm for Appearance Based Recognition of American Sign Language Jaspreet Kaur,Navjot Kaur Electronics and Communication Engineering Department I.E.T. Bhaddal, Ropar, Punjab,India. Abstract:
More informationPoker Vision: Playing Cards and Chips Identification based on Image Processing
Poker Vision: Playing Cards and Chips Identification based on Image Processing Paulo Martins 1, Luís Paulo Reis 2, and Luís Teófilo 2 1 DEEC Electrical Engineering Department 2 LIACC Artificial Intelligence
More informationPCA to Eigenfaces. CS 510 Lecture #16 March 23 th A 9 dimensional PCA example
PCA to Eigenfaces CS 510 Lecture #16 March 23 th 2015 A 9 dimensional PCA example is dark around the edges and bright in the middle. is light with dark vertical bars. is light with dark horizontal bars.
More informationIMAGE MODIFICATION DEVELOPMENT AND IMPLEMENTATION: A SOFTWARE MODELING USING MATLAB
Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology IJCSMC, Vol. 4, Issue. 8, August 2015,
More informationIOSR Journal of Computer Engineering (IOSRJCE) eissn: , pissn: PP
Computer Aided Fracture Detection Of XRay Images R.Aishwariya 1, M.Kalaiselvi Geetha 2, M.Archana 3 1, 2, 3 (Department of Computer Science, Annamalai University, India) ABSTRACT:The usage of medical
More informationState of Stress at Point
State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,
More informationLecture 3: Linear methods for classification
Lecture 3: Linear methods for classification Rafael A. Irizarry and Hector Corrada Bravo February, 2010 Today we describe four specific algorithms useful for classification problems: linear regression,
More informationEnhancement of scanned documents in Besov spaces using wavelet domain representations
Enhancement of scanned documents in Besov spaces using wavelet domain representations Kathrin Berkner 1 Ricoh Innovations, Inc., 2882 Sand Hill Road, Suite 115, Menlo Park, CA 94025 ABSTRACT After scanning,
More informationQuadratic Equations and Inequalities
MA 134 Lecture Notes August 20, 2012 Introduction The purpose of this lecture is to... Introduction The purpose of this lecture is to... Learn about different types of equations Introduction The purpose
More informationPicture Perfect: The Mathematics of JPEG Compression
Picture Perfect: The Mathematics of JPEG Compression May 19, 2011 1 2 3 in 2D Sampling and the DCT in 2D 2D Compression Images Outline A typical color image might be 600 by 800 pixels. Images Outline A
More informationNonlinear Iterative Partial Least Squares Method
Numerical Methods for Determining Principal Component Analysis Abstract Factors Béchu, S., RichardPlouet, M., Fernandez, V., Walton, J., and Fairley, N. (2016) Developments in numerical treatments for
More informationLABEL PROPAGATION ON GRAPHS. SEMISUPERVISED LEARNING. Changsheng Liu 10302014
LABEL PROPAGATION ON GRAPHS. SEMISUPERVISED LEARNING Changsheng Liu 10302014 Agenda Semi Supervised Learning Topics in Semi Supervised Learning Label Propagation Local and global consistency Graph
More informationDATA ANALYSIS II. Matrix Algorithms
DATA ANALYSIS II Matrix Algorithms Similarity Matrix Given a dataset D = {x i }, i=1,..,n consisting of n points in R d, let A denote the n n symmetric similarity matrix between the points, given as where
More informationDigital Image Processing Using Matlab. Haris PapasaikaHanusch Institute of Geodesy and Photogrammetry, ETH Zurich
Haris PapasaikaHanusch Institute of Geodesy and Photogrammetry, ETH Zurich haris@geod.baug.ethz.ch Images and Digital Images A digital image differs from a photo in that the values are all discrete. Usually
More informationSTA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.cs.toronto.edu/~rsalakhu/ Lecture 6 Three Approaches to Classification Construct
More informationComputer Vision  part II
Computer Vision  part II Review of main parts of Section B of the course School of Computer Science & Statistics Trinity College Dublin Dublin 2 Ireland www.scss.tcd.ie Lecture Name Course Name 1 1 2
More informationStitching of Xray Images
IT 12 057 Examensarbete 30 hp November 2012 Stitching of Xray Images Krishna Paudel Institutionen för informationsteknologi Department of Information Technology Abstract Stitching of Xray Images Krishna
More informationMaximum and Minimum Values
Jim Lambers MAT 280 Spring Semester 200910 Lecture 8 Notes These notes correspond to Section 11.7 in Stewart and Section 3.3 in Marsden and Tromba. Maximum and Minimum Values In singlevariable calculus,
More informationBindel, Fall 2012 Matrix Computations (CS 6210) Week 8: Friday, Oct 12
Why eigenvalues? Week 8: Friday, Oct 12 I spend a lot of time thinking about eigenvalue problems. In part, this is because I look for problems that can be solved via eigenvalues. But I might have fewer
More informationBrightness and geometric transformations
Brightness and geometric transformations Václav Hlaváč Czech Technical University in Prague Center for Machine Perception (bridging groups of the) Czech Institute of Informatics, Robotics and Cybernetics
More informationDistinctive Image Features from ScaleInvariant Keypoints
Distinctive Image Features from ScaleInvariant Keypoints David G. Lowe Computer Science Department University of British Columbia Vancouver, B.C., Canada lowe@cs.ubc.ca January 5, 2004 Abstract This paper
More informationNoise Reduction in Video Images Using Coring on QMF Pyramids by. Arthur J. Kalb
Noise Reduction in Video Images Using Coring on QMF Pyramids by Arthur J. Kalb Submitted to the Department of Electrical Engineering and Computer Science on May 20, 1991, in partial fulfillment of the
More information