Edges, interpolation, templates. Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth)
|
|
- Patience Reeves
- 5 years ago
- Views:
Transcription
1 Edges, interpolation, templates Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth)
2 Edge detection edge detection has many applications in image processing an edge detector implements the following steps: compute gradient magnitude f f 0, y0) = ( x0, y0) + ( x0, y0) f ( x x y thin and follow edge points find locations of maximum gradient magnitude follow these maxima to form contours discard points that are not maxima declare maxima as edges
3 Derivatives to compute the derivatives f f f x ( x, y ), f y ( x, y ) = ( x 0, y 0), ( x 0, y 0) x y we rely on a sequence of smoothing with a Gaussian (to eliminate noise) convolution with difference filter f x : f y : ( ) n n n n 3
4 Derivatives accomplished in a single step by convolving image with two derivative of a Gaussian (DoG) filters h x h y where ( n, n) = g ( n +, n) g ( n, n) ( n, n ) = g ( n, n + ) g ( n, n ) g ( n, n ) πσ n + n exp σ = DoG along n DoG along n 4
5 Non-maximum suppression is there a maximum at q? yes, if value at q is larger than those at both p and r p and r are the pixels in the direction of the gradient that are pixel apart from q typically they do not fall in the pixel grid we need to interpolate, e.g. r = α b + ( α) a a α α b 5
6 Predicting the next edge point assume the marked point is an edge point we construct the tangent to the edge curve (which is normal to the gradient at that point) ( f ( x, y), f ( x, y ) T t ( x, y) = ) y use this to predict the next points (here either r or s). x 6
7 Cleaning up even when gradient is ~ zero, there are maxima due to noise check that maximum value of gradient value is large enough (threshold) once we are following an edge we must avoid gaps due to similarity with background use hysteresis use a high threshold to start edge curves and a low threshold to continue them. 7
8 roblem: various parameters, for all values we tried result was not perfect 8
9 Effects of noise Is there an alternative? recall we followed this path to overcome the noise problem are there other alternatives? 9
10 Solution: smooth first this is what we get with st order derivatives 0
11 Derivative theorem of convolution can we extend this idea?
12 Laplacian of Gaussian Consider Laplacian of Gaussian operator where is the edge? zero-crossings of bottom graph
13 The Laplacian of Gaussian another way to detect max of first derivative is to look for a zero second derivative D analogy is the Laplacian f f f ( x, y) = ( x, y) + x y with second-order derivatives, noise is even greater concern smoothing ( x, y) smooth with Gaussian, apply Laplacian this is the same as filtering with a Laplacian of Gaussian filter G σ ( x, y) 3
14 D edge detection filters Laplacian of Gaussian Gaussian derivative of Gaussian is the Laplacian operator: 4
15 The Laplacian of Gaussian this is very close to what the early stages of the brain seem to be doing recordings of retinal ganglion cells called centersurround cells two types: on-center off-center 5
16 Edge detection strategy filter with Laplacian of Gaussian detect zero crossings mark the zero points where: there is a sufficiently large derivative, and enough contrast once again we have parameters scale of Gaussian smoothing thresholds once again no set of universal parameters LoG ZD does not seem to be better than the strategy of looking for maxima of gradient magnitude. 6
17 sigma=4 contrast= LOG zero crossings contrast=4 sigma= 7
18 Non-maximum suppression we have seen that to find if q is a maximum we need to know what is the image value at r but this does not fall on the pixel grid this is called interpolation it is a very frequent operation in image processing a α α b 8
19 Interpolation the most obvious application is to improve the resolution image super-resolved note the increased detail, e.g. the reduced artifacts on the lines 9
20 Interpolation but there are many others e.g. the restoration of degraded movies 0
21 Interpolation image synthesis
22 Interpolation texture mapping
23 Interpolation how does one do this? the simplest method is nearest-neighbor interpolation we simply replicate the image intensity (or color) of the closest pixel e.g. in this case, because the desired location p is closest to (x,y+) we make I( p) = I( x, y + ) this is not very good because it generates artifacts one location replicated from one pixel (x,y+) (x,y) an infinitesimally close neighbor replicated from another p (x+,y+) (x+,y) 3
24 Interpolation much better is bilinear interpolation assume image varies linearly, weight each pixel according to their distance to p let a = p x x, b = p y yand make I( p) = ( a) b I( x, y + ) (x,y+) (x+,y+) + ( + a ( b) I( x + a b I( x a) ( b) I( x, y) +, y) +, y + ) b (x,y) a p (x+,y) works much better than nearest neighbor 4
25 Interpolation note that these can be implemented with filtering for nearest neighbors 5
26 Interpolation for bilinear interpolation 6
27 Interpolation and there are obviously many other filters the best method is frequently bi-cubic interpolation 7
28 Interpolation how do the three methods compare? image interpolated with nearest neighbor 8
29 Interpolation how do the three methods compare? image interpolated with bilinear method 9
30 Interpolation how do the three methods compare? image interpolated with bi-cubic method 30
31 Interpolation so, what method should I use? the higher order the filter, the more computation required the gains are diminishing after some point bilinear usually justified over nearest neighbor bi-cubic sometimes worth it, but judge on a case by case basis higher order than cubic is usually not worth it to play with this: the matlab interp function implements all the methods plus a spline-based method that we will not get into very good applet at rpolation/index.htm 3
32 Filters as templates applying a filter at some point can be seen as taking a dotproduct between the image and some vector filtering the image is a set of dot products insight filters look like the effects they are intended to find filters find effects they look like 3
33 Positive responses 33
34 34
35 The z transform once again, it is a straightforward extension of D Definition: the z-transform of the sequence x[n,n ] is X ( z the region of the (z,z ) plane where this sum is finite is called the Region of Convergence (ROC) it turns out that:, z) x[ n, n] n n = in D the ROC is much more complicated than in D while in D the ROC is bounded by poles (0D subspace of the D complex plane) in D is bounded by pole surfaces (D subspaces of the 4D space of two complex variables) z n z n 35
36 The z-transform computation is also much harder: as you might remember from D most useful tool in computing z-transforms is polynomial factorization z-transform is a ratio of two polynomials Y ( z) = N( z) D( z) we factor in to a sum of low order terms, e.g. Y ( z) = i a and then invert each of the terms to get y[n] iz 36
37 z-transform in D we only have one of two situations ) the sequence is separable, in which case everything reduces to the D case x[ n, n ] = x [ n ] x [ n ] X ( z, z ) = X ( z ) X ( z ) ROC : z ROC of X ( z ) and z ROC of X ( z ) the proof is identical to that of the DSFT ) the signal is not separable here our polynomials are of the form z m z n and, in general, it is not know how to factor them we can solve only if sequence is simple enough that we can do it by inspection (from the definition of the z-transform) 37
38 38 Example consider the sequence the z-transform is ], [ ], [ n n u b a n n x n n = ( ) ( ) ( ) ( ) b z a z bz az az az az az z z X n n n n n n n n > > = = = = = = = ,, ), ( ROC z z a b
39 Sampling in D consider an analog signal x c (t,t ) and let its analog Fourier transform be X c (Ω,Ω ) we use capital Ω to emphasize that this is analog frequency sample with period (T,T ) to obtain a discrete-space signal x [ n, n ] = x c ( t, t ) t t = n T = nt ; 39
40 Sampling in D relationship between the Discrete-Space FT of x[n,n ] and the FT of x c (t,t ) is simple extension of D result X ( ω, ω ) = T T DSFT of x[n,n ] FT of x c (ω,ω ) discrete spectrum analog spectrum Discrete Space spectrum is sum of replicas of analog spectrum in the base replica the analog frequency Ω (Ω ) is mapped into the digital frequency Ω T (Ω T ) discrete spectrum has periodicity (π,π) r = r = ω πr ω πr X, c T T 40
41 For example Ω Ω Ω ω π Ω Ω ω π Ω T Ω T Ω' α = Ω' T Ω'' β = Ω'' T π Ω T π ω no aliasing if π Ω T Ω' T π Ω' T Ω'' T π Ω' T π ω T π / Ω' T π / Ω'' 4
42 Aliasing the frequency (Ω /π,ω /π) is the critical sampling frequency below it we have aliasing ω this is just like the D case, but now there are more possibilities for overlap ω 4
43 Reconstruction if there is no aliasing we can recover the signal in a way similar to the D case y ( t, t ) = c ( t n T ) T T x [ n, n ] π π n = = ( ) n t nt T T note: in D there are many more possibilities than in D sin sin e.g. the sampling grid does not have to be rectangular, e.g. hexagonal sampling when T = T /sqrt(3) and x c ( t, t ) t = ; = [, ] = nt t x n n nt 0 in practice, however, one usually adopts the rectangular grid π π ( t n T ) ( t n T ) n, n both even or odd otherwise 43
44 a sequence of images obtained by downsampling without any filtering aliasing: the lowfrequency parts are replicated throughout the low-res image 44
45 The role of smoothing none some a lot too little leads to aliasing too much leads to loss of information 45
46 Aliasing in video video frames are the result of temporal sampling fast moving objects are above the critical frequency above a certain speed they are aliased and appear to move backwards this was common in old western movies and become known as the wagon wheel effect here is an example: super-resolution increases the frame rate and eliminates aliasing from Space-Time Resolution in Video by E. Shechtman, Y. Caspi and M. Irani (PAMI 005). 46
47 47
Edges, interpolation, templates. Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth)
Edges, interpolation, templates Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth) Gradients and edges edges are points of large gradient magnitude edge detection strategy 1. determine
More informationFiltering, scale, orientation, localization, and texture. Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth)
Filtering, scale, orientation, localization, and texture Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth) Beyond edges we have talked a lot about edges while they are important, it
More informationconvolution shift invariant linear system Fourier Transform Aliasing and sampling scale representation edge detection corner detection
COS 429: COMPUTER VISON Linear Filters and Edge Detection convolution shift invariant linear system Fourier Transform Aliasing and sampling scale representation edge detection corner detection Reading:
More informationEdge Detection (with a sidelight introduction to linear, associative operators). Images
Images (we will, eventually, come back to imaging geometry. But, now that we know how images come from the world, we will examine operations on images). Edge Detection (with a sidelight introduction to
More informationEdge detection. Goal: Identify sudden. an image. Ideal: artist s line drawing. object-level knowledge)
Edge detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded in the edges More compact than pixels Ideal: artist
More informationReview of Filtering. Filtering in frequency domain
Review of Filtering Filtering in frequency domain Can be faster than filtering in spatial domain (for large filters) Can help understand effect of filter Algorithm: 1. Convert image and filter to fft (fft2
More informationCS534: Introduction to Computer Vision Edges and Contours. Ahmed Elgammal Dept. of Computer Science Rutgers University
CS534: Introduction to Computer Vision Edges and Contours Ahmed Elgammal Dept. of Computer Science Rutgers University Outlines What makes an edge? Gradient-based edge detection Edge Operators Laplacian
More informationCS334: Digital Imaging and Multimedia Edges and Contours. Ahmed Elgammal Dept. of Computer Science Rutgers University
CS334: Digital Imaging and Multimedia Edges and Contours Ahmed Elgammal Dept. of Computer Science Rutgers University Outlines What makes an edge? Gradient-based edge detection Edge Operators From Edges
More informationEdge and local feature detection - 2. Importance of edge detection in computer vision
Edge and local feature detection Gradient based edge detection Edge detection by function fitting Second derivative edge detectors Edge linking and the construction of the chain graph Edge and local feature
More informationAnno accademico 2006/2007. Davide Migliore
Robotica Anno accademico 6/7 Davide Migliore migliore@elet.polimi.it Today What is a feature? Some useful information The world of features: Detectors Edges detection Corners/Points detection Descriptors?!?!?
More informationEN1610 Image Understanding Lab # 3: Edges
EN1610 Image Understanding Lab # 3: Edges The goal of this fourth lab is to ˆ Understanding what are edges, and different ways to detect them ˆ Understand different types of edge detectors - intensity,
More informationEdge detection. Gradient-based edge operators
Edge detection Gradient-based edge operators Prewitt Sobel Roberts Laplacian zero-crossings Canny edge detector Hough transform for detection of straight lines Circle Hough Transform Digital Image Processing:
More informationWhat is an edge? Paint. Depth discontinuity. Material change. Texture boundary
EDGES AND TEXTURES The slides are from several sources through James Hays (Brown); Srinivasa Narasimhan (CMU); Silvio Savarese (U. of Michigan); Bill Freeman and Antonio Torralba (MIT), including their
More informationLecture 7: Most Common Edge Detectors
#1 Lecture 7: Most Common Edge Detectors Saad Bedros sbedros@umn.edu Edge Detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the
More informationDIGITAL IMAGE PROCESSING
The image part with relationship ID rid2 was not found in the file. DIGITAL IMAGE PROCESSING Lecture 6 Wavelets (cont), Lines and edges Tammy Riklin Raviv Electrical and Computer Engineering Ben-Gurion
More informationImage Analysis. Edge Detection
Image Analysis Edge Detection Christophoros Nikou cnikou@cs.uoi.gr Images taken from: Computer Vision course by Kristen Grauman, University of Texas at Austin (http://www.cs.utexas.edu/~grauman/courses/spring2011/index.html).
More informationCS 4495 Computer Vision. Linear Filtering 2: Templates, Edges. Aaron Bobick. School of Interactive Computing. Templates/Edges
CS 4495 Computer Vision Linear Filtering 2: Templates, Edges Aaron Bobick School of Interactive Computing Last time: Convolution Convolution: Flip the filter in both dimensions (right to left, bottom to
More informationEdge and Texture. CS 554 Computer Vision Pinar Duygulu Bilkent University
Edge and Texture CS 554 Computer Vision Pinar Duygulu Bilkent University Filters for features Previously, thinking of filtering as a way to remove or reduce noise Now, consider how filters will allow us
More informationEdge Detection. CSE 576 Ali Farhadi. Many slides from Steve Seitz and Larry Zitnick
Edge Detection CSE 576 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick Edge Attneave's Cat (1954) Origin of edges surface normal discontinuity depth discontinuity surface color discontinuity
More informationScaled representations
Scaled representations Big bars (resp. spots, hands, etc.) and little bars are both interesting Stripes and hairs, say Inefficient to detect big bars with big filters And there is superfluous detail in
More informationFiltering Images. Contents
Image Processing and Data Visualization with MATLAB Filtering Images Hansrudi Noser June 8-9, 010 UZH, Multimedia and Robotics Summer School Noise Smoothing Filters Sigmoid Filters Gradient Filters Contents
More informationEdge Detection. Today s reading. Cipolla & Gee on edge detection (available online) From Sandlot Science
Edge Detection From Sandlot Science Today s reading Cipolla & Gee on edge detection (available online) Project 1a assigned last Friday due this Friday Last time: Cross-correlation Let be the image, be
More informationEdge Detection. Announcements. Edge detection. Origin of Edges. Mailing list: you should have received messages
Announcements Mailing list: csep576@cs.washington.edu you should have received messages Project 1 out today (due in two weeks) Carpools Edge Detection From Sandlot Science Today s reading Forsyth, chapters
More informationSegmentation and Grouping
Segmentation and Grouping How and what do we see? Fundamental Problems ' Focus of attention, or grouping ' What subsets of pixels do we consider as possible objects? ' All connected subsets? ' Representation
More informationImage Analysis. Edge Detection
Image Analysis Edge Detection Christophoros Nikou cnikou@cs.uoi.gr Images taken from: Computer Vision course by Kristen Grauman, University of Texas at Austin (http://www.cs.utexas.edu/~grauman/courses/spring2011/index.html).
More informationStraight Lines and Hough
09/30/11 Straight Lines and Hough Computer Vision CS 143, Brown James Hays Many slides from Derek Hoiem, Lana Lazebnik, Steve Seitz, David Forsyth, David Lowe, Fei-Fei Li Project 1 A few project highlights
More informationEdge detection. Winter in Kraków photographed by Marcin Ryczek
Edge detection Winter in Kraków photographed by Marcin Ryczek Edge detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, edges carry most of the semantic and shape information
More informationEdge Detection. CSC320: Introduction to Visual Computing Michael Guerzhoy. René Magritte, Decalcomania. Many slides from Derek Hoiem, Robert Collins
Edge Detection René Magritte, Decalcomania Many slides from Derek Hoiem, Robert Collins CSC320: Introduction to Visual Computing Michael Guerzhoy Discontinuities in Intensity Source: Robert Collins Origin
More informationNeighborhood operations
Neighborhood operations Generate an output pixel on the basis of the pixel and its neighbors Often involve the convolution of an image with a filter kernel or mask g ( i, j) = f h = f ( i m, j n) h( m,
More informationThe SIFT (Scale Invariant Feature
The SIFT (Scale Invariant Feature Transform) Detector and Descriptor developed by David Lowe University of British Columbia Initial paper ICCV 1999 Newer journal paper IJCV 2004 Review: Matt Brown s Canonical
More informationSchool of Computing University of Utah
School of Computing University of Utah Presentation Outline 1 2 3 4 Main paper to be discussed David G. Lowe, Distinctive Image Features from Scale-Invariant Keypoints, IJCV, 2004. How to find useful keypoints?
More informationEdge Detection CSC 767
Edge Detection CSC 767 Edge detection Goal: Identify sudden changes (discontinuities) in an image Most semantic and shape information from the image can be encoded in the edges More compact than pixels
More informationComputer Vision: 4. Filtering. By I-Chen Lin Dept. of CS, National Chiao Tung University
Computer Vision: 4. Filtering By I-Chen Lin Dept. of CS, National Chiao Tung University Outline Impulse response and convolution. Linear filter and image pyramid. Textbook: David A. Forsyth and Jean Ponce,
More informationME/CS 132: Introduction to Vision-based Robot Navigation! Low-level Image Processing" Larry Matthies"
ME/CS 132: Introduction to Vision-based Robot Navigation! Low-level Image Processing" Larry Matthies" lhm@jpl.nasa.gov, 818-354-3722" Announcements" First homework grading is done! Second homework is due
More informationFeature descriptors. Alain Pagani Prof. Didier Stricker. Computer Vision: Object and People Tracking
Feature descriptors Alain Pagani Prof. Didier Stricker Computer Vision: Object and People Tracking 1 Overview Previous lectures: Feature extraction Today: Gradiant/edge Points (Kanade-Tomasi + Harris)
More informationEdge detection. Winter in Kraków photographed by Marcin Ryczek
Edge detection Winter in Kraków photographed by Marcin Ryczek Edge detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image
More informationObtaining Feature Correspondences
Obtaining Feature Correspondences Neill Campbell May 9, 2008 A state-of-the-art system for finding objects in images has recently been developed by David Lowe. The algorithm is termed the Scale-Invariant
More informationBiomedical Image Analysis. Point, Edge and Line Detection
Biomedical Image Analysis Point, Edge and Line Detection Contents: Point and line detection Advanced edge detection: Canny Local/regional edge processing Global processing: Hough transform BMIA 15 V. Roth
More informationEdge Detection Lecture 03 Computer Vision
Edge Detection Lecture 3 Computer Vision Suggested readings Chapter 5 Linda G. Shapiro and George Stockman, Computer Vision, Upper Saddle River, NJ, Prentice Hall,. Chapter David A. Forsyth and Jean Ponce,
More informationEdge Detection. Computer Vision Shiv Ram Dubey, IIIT Sri City
Edge Detection Computer Vision Shiv Ram Dubey, IIIT Sri City Previous two classes: Image Filtering Spatial domain Smoothing, sharpening, measuring texture * = FFT FFT Inverse FFT = Frequency domain Denoising,
More informationAnnouncements. Edge Detection. An Isotropic Gaussian. Filters are templates. Assignment 2 on tracking due this Friday Midterm: Tuesday, May 3.
Announcements Edge Detection Introduction to Computer Vision CSE 152 Lecture 9 Assignment 2 on tracking due this Friday Midterm: Tuesday, May 3. Reading from textbook An Isotropic Gaussian The picture
More information2D Image Processing Feature Descriptors
2D Image Processing Feature Descriptors Prof. Didier Stricker Kaiserlautern University http://ags.cs.uni-kl.de/ DFKI Deutsches Forschungszentrum für Künstliche Intelligenz http://av.dfki.de 1 Overview
More informationFiltering Applications & Edge Detection. GV12/3072 Image Processing.
Filtering Applications & Edge Detection GV12/3072 1 Outline Sampling & Reconstruction Revisited Anti-Aliasing Edges Edge detection Simple edge detector Canny edge detector Performance analysis Hough Transform
More informationSYDE 575: Introduction to Image Processing
SYDE 575: Introduction to Image Processing Image Enhancement and Restoration in Spatial Domain Chapter 3 Spatial Filtering Recall 2D discrete convolution g[m, n] = f [ m, n] h[ m, n] = f [i, j ] h[ m i,
More informationSampling, Aliasing, & Mipmaps
Sampling, Aliasing, & Mipmaps Last Time? Monte-Carlo Integration Importance Sampling Ray Tracing vs. Path Tracing source hemisphere What is a Pixel? Sampling & Reconstruction Filters in Computer Graphics
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 informationMultimedia Computing: Algorithms, Systems, and Applications: Edge Detection
Multimedia Computing: Algorithms, Systems, and Applications: Edge Detection By Dr. Yu Cao Department of Computer Science The University of Massachusetts Lowell Lowell, MA 01854, USA Part of the slides
More informationLecture 6: Edge Detection
#1 Lecture 6: Edge Detection Saad J Bedros sbedros@umn.edu Review From Last Lecture Options for Image Representation Introduced the concept of different representation or transformation Fourier Transform
More informationSegmentation I: Edges and Lines
Segmentation I: Edges and Lines Prof. Eric Miller elmiller@ece.tufts.edu Fall 2007 EN 74-ECE Image Processing Lecture 8-1 Segmentation Problem of breaking an image up into regions are are interesting as
More informationEdges and Binary Images
CS 699: Intro to Computer Vision Edges and Binary Images Prof. Adriana Kovashka University of Pittsburgh September 5, 205 Plan for today Edge detection Binary image analysis Homework Due on 9/22, :59pm
More informationSampling, Aliasing, & Mipmaps
Sampling, Aliasing, & Mipmaps Last Time? Monte-Carlo Integration Importance Sampling Ray Tracing vs. Path Tracing source hemisphere Sampling sensitive to choice of samples less sensitive to choice of samples
More informationDigital Image Processing COSC 6380/4393
Digital Image Processing COSC 6380/4393 Lecture 21 Nov 16 th, 2017 Pranav Mantini Ack: Shah. M Image Processing Geometric Transformation Point Operations Filtering (spatial, Frequency) Input Restoration/
More informationEdge detection. Convert a 2D image into a set of curves. Extracts salient features of the scene More compact than pixels
Edge Detection Edge detection Convert a 2D image into a set of curves Extracts salient features of the scene More compact than pixels Origin of Edges surface normal discontinuity depth discontinuity surface
More informationComputer Vision I. Announcements. Fourier Tansform. Efficient Implementation. Edge and Corner Detection. CSE252A Lecture 13.
Announcements Edge and Corner Detection HW3 assigned CSE252A Lecture 13 Efficient Implementation Both, the Box filter and the Gaussian filter are separable: First convolve each row of input image I with
More informationComputer Vision I. Announcement. Corners. Edges. Numerical Derivatives f(x) Edge and Corner Detection. CSE252A Lecture 11
Announcement Edge and Corner Detection Slides are posted HW due Friday CSE5A Lecture 11 Edges Corners Edge is Where Change Occurs: 1-D Change is measured by derivative in 1D Numerical Derivatives f(x)
More informationUnderstanding Gridfit
Understanding Gridfit John R. D Errico Email: woodchips@rochester.rr.com December 28, 2006 1 Introduction GRIDFIT is a surface modeling tool, fitting a surface of the form z(x, y) to scattered (or regular)
More informationImage features. Image Features
Image features Image features, such as edges and interest points, provide rich information on the image content. They correspond to local regions in the image and are fundamental in many applications in
More informationSIFT: SCALE INVARIANT FEATURE TRANSFORM SURF: SPEEDED UP ROBUST FEATURES BASHAR ALSADIK EOS DEPT. TOPMAP M13 3D GEOINFORMATION FROM IMAGES 2014
SIFT: SCALE INVARIANT FEATURE TRANSFORM SURF: SPEEDED UP ROBUST FEATURES BASHAR ALSADIK EOS DEPT. TOPMAP M13 3D GEOINFORMATION FROM IMAGES 2014 SIFT SIFT: Scale Invariant Feature Transform; transform image
More informationAnnouncements. Image Matching! Source & Destination Images. Image Transformation 2/ 3/ 16. Compare a big image to a small image
2/3/ Announcements PA is due in week Image atching! Leave time to learn OpenCV Think of & implement something creative CS 50 Lecture #5 February 3 rd, 20 2/ 3/ 2 Compare a big image to a small image So
More information2D Image Processing INFORMATIK. Kaiserlautern University. DFKI Deutsches Forschungszentrum für Künstliche Intelligenz
2D Image Processing - Filtering Prof. Didier Stricker Kaiserlautern University http://ags.cs.uni-kl.de/ DFKI Deutsches Forschungszentrum für Künstliche Intelligenz http://av.dfki.de 1 What is image filtering?
More informationEECS 556 Image Processing W 09. Image enhancement. Smoothing and noise removal Sharpening filters
EECS 556 Image Processing W 09 Image enhancement Smoothing and noise removal Sharpening filters What is image processing? Image processing is the application of 2D signal processing methods to images Image
More informationLocal Features: Detection, Description & Matching
Local Features: Detection, Description & Matching Lecture 08 Computer Vision Material Citations Dr George Stockman Professor Emeritus, Michigan State University Dr David Lowe Professor, University of British
More information[ ] Review. Edges and Binary Images. Edge detection. Derivative of Gaussian filter. Image gradient. Tuesday, Sept 16
Review Edges and Binary Images Tuesday, Sept 6 Thought question: how could we compute a temporal gradient from video data? What filter is likely to have produced this image output? original filtered output
More informationOperators-Based on Second Derivative double derivative Laplacian operator Laplacian Operator Laplacian Of Gaussian (LOG) Operator LOG
Operators-Based on Second Derivative The principle of edge detection based on double derivative is to detect only those points as edge points which possess local maxima in the gradient values. Laplacian
More informationImage gradients and edges April 11 th, 2017
4//27 Image gradients and edges April th, 27 Yong Jae Lee UC Davis PS due this Friday Announcements Questions? 2 Last time Image formation Linear filters and convolution useful for Image smoothing, removing
More informationImage gradients and edges April 10 th, 2018
Image gradients and edges April th, 28 Yong Jae Lee UC Davis PS due this Friday Announcements Questions? 2 Last time Image formation Linear filters and convolution useful for Image smoothing, removing
More informationLocal Image preprocessing (cont d)
Local Image preprocessing (cont d) 1 Outline - Edge detectors - Corner detectors - Reading: textbook 5.3.1-5.3.5 and 5.3.10 2 What are edges? Edges correspond to relevant features in the image. An edge
More informationSampling, Aliasing, & Mipmaps
Last Time? Sampling, Aliasing, & Mipmaps 2D Texture Mapping Perspective Correct Interpolation Common Texture Coordinate Projections Bump Mapping Displacement Mapping Environment Mapping Texture Maps for
More informationDigital Signal Processing Lecture Notes 22 November 2010
Digital Signal Processing Lecture otes 22 ovember 2 Topics: Discrete Cosine Transform FFT Linear and Circular Convolution Rate Conversion Includes review of Fourier transforms, properties of Fourier transforms,
More informationTheoretically Perfect Sensor
Sampling 1/67 Sampling The ray tracer samples the geometry, only gathering information from the parts of the world that interact with a finite number of rays In contrast, a scanline renderer can push all
More informationTo Do. Advanced Computer Graphics. Discrete Convolution. Outline. Outline. Implementing Discrete Convolution
Advanced Computer Graphics CSE 163 [Spring 2018], Lecture 4 Ravi Ramamoorthi http://www.cs.ucsd.edu/~ravir To Do Assignment 1, Due Apr 27. Please START EARLY This lecture completes all the material you
More informationEdge and corner detection
Edge and corner detection Prof. Stricker Doz. G. Bleser Computer Vision: Object and People Tracking Goals Where is the information in an image? How is an object characterized? How can I find measurements
More informationCAP 5415 Computer Vision Fall 2012
CAP 5415 Computer Vision Fall 01 Dr. Mubarak Shah Univ. of Central Florida Office 47-F HEC Lecture-5 SIFT: David Lowe, UBC SIFT - Key Point Extraction Stands for scale invariant feature transform Patented
More informationOutline. Sampling and Reconstruction. Sampling and Reconstruction. Foundations of Computer Graphics (Fall 2012)
Foundations of Computer Graphics (Fall 2012) CS 184, Lectures 19: Sampling and Reconstruction http://inst.eecs.berkeley.edu/~cs184 Outline Basic ideas of sampling, reconstruction, aliasing Signal processing
More informationDigital Image Processing. Image Enhancement - Filtering
Digital Image Processing Image Enhancement - Filtering Derivative Derivative is defined as a rate of change. Discrete Derivative Finite Distance Example Derivatives in 2-dimension Derivatives of Images
More informationBiomedical Image Analysis. Spatial Filtering
Biomedical Image Analysis Contents: Spatial Filtering The mechanics of Spatial Filtering Smoothing and sharpening filters BMIA 15 V. Roth & P. Cattin 1 The Mechanics of Spatial Filtering Spatial filter:
More informationTheoretically Perfect Sensor
Sampling 1/60 Sampling The ray tracer samples the geometry, only gathering information from the parts of the world that interact with a finite number of rays In contrast, a scanline renderer can push all
More informationThe main goal of Computer Graphics is to generate 2D images 2D images are continuous 2D functions (or signals)
Motivation The main goal of Computer Graphics is to generate 2D images 2D images are continuous 2D functions (or signals) monochrome f(x,y) or color r(x,y), g(x,y), b(x,y) These functions are represented
More informationEE795: Computer Vision and Intelligent Systems
EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 10 130221 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Canny Edge Detector Hough Transform Feature-Based
More informationImage gradients and edges
Image gradients and edges Thurs Sept 3 Prof. Kristen Grauman UT-Austin Last time Various models for image noise Linear filters and convolution useful for Image smoothing, remov ing noise Box filter Gaussian
More informationLocal Features Tutorial: Nov. 8, 04
Local Features Tutorial: Nov. 8, 04 Local Features Tutorial References: Matlab SIFT tutorial (from course webpage) Lowe, David G. Distinctive Image Features from Scale Invariant Features, International
More informationComputer Vision for HCI. Topics of This Lecture
Computer Vision for HCI Interest Points Topics of This Lecture Local Invariant Features Motivation Requirements, Invariances Keypoint Localization Features from Accelerated Segment Test (FAST) Harris Shi-Tomasi
More informationSampling and Reconstruction
Sampling and Reconstruction Sampling and Reconstruction Sampling and Spatial Resolution Spatial Aliasing Problem: Spatial aliasing is insufficient sampling of data along the space axis, which occurs because
More informationSampling and Monte-Carlo Integration
Sampling and Monte-Carlo Integration Sampling and Monte-Carlo Integration Last Time Pixels are samples Sampling theorem Convolution & multiplication Aliasing: spectrum replication Ideal filter And its
More informationEECS490: Digital Image Processing. Lecture #20
Lecture #20 Edge operators: LoG, DoG, Canny Edge linking Polygonal line fitting, polygon boundaries Edge relaxation Hough transform Image Segmentation Thresholded gradient image w/o smoothing Thresholded
More informationAnalysis and Synthesis of Texture
Analysis and Synthesis of Texture CMPE 264: Image Analysis and Computer Vision Spring 02, Hai Tao 31/5/02 Extracting image structure by filter banks Q Represent image textures using the responses of a
More informationSolution: filter the image, then subsample F 1 F 2. subsample blur subsample. blur
Pyramids Gaussian pre-filtering Solution: filter the image, then subsample blur F 0 subsample blur subsample * F 0 H F 1 F 1 * H F 2 { Gaussian pyramid blur F 0 subsample blur subsample * F 0 H F 1 F 1
More informationEE368 Project Report CD Cover Recognition Using Modified SIFT Algorithm
EE368 Project Report CD Cover Recognition Using Modified SIFT Algorithm Group 1: Mina A. Makar Stanford University mamakar@stanford.edu Abstract In this report, we investigate the application of the Scale-Invariant
More informationOutline. Foundations of Computer Graphics (Spring 2012)
Foundations of Computer Graphics (Spring 2012) CS 184, Lectures 19: Sampling and Reconstruction http://inst.eecs.berkeley.edu/~cs184 Basic ideas of sampling, reconstruction, aliasing Signal processing
More informationMotivation. The main goal of Computer Graphics is to generate 2D images. 2D images are continuous 2D functions (or signals)
Motivation The main goal of Computer Graphics is to generate 2D images 2D images are continuous 2D functions (or signals) monochrome f(x,y) or color r(x,y), g(x,y), b(x,y) These functions are represented
More informationEdge Detection. CMPUT 206: Introduction to Digital Image Processing. Nilanjan Ray. Source:
Edge Detection CMPUT 206: Introduction to Digital Image Processing Nilanjan Ray Source: www.imagingbook.com What are edges? Are image positions where local image intensity changes significantly along a
More informationCS5670: Computer Vision
CS5670: Computer Vision Noah Snavely Lecture 2: Edge detection From Sandlot Science Announcements Project 1 (Hybrid Images) is now on the course webpage (see Projects link) Due Wednesday, Feb 15, by 11:59pm
More informationImage Processing. Traitement d images. Yuliya Tarabalka Tel.
Traitement d images Yuliya Tarabalka yuliya.tarabalka@hyperinet.eu yuliya.tarabalka@gipsa-lab.grenoble-inp.fr Tel. 04 76 82 62 68 Noise reduction Image restoration Restoration attempts to reconstruct an
More informationImage Processing and Analysis
Image Processing and Analysis 3 stages: Image Restoration - correcting errors and distortion. Warping and correcting systematic distortion related to viewing geometry Correcting "drop outs", striping and
More informationPERFORMANCE ANALYSIS OF CANNY AND OTHER COMMONLY USED EDGE DETECTORS Sandeep Dhawan Director of Technology, OTTE, NEW YORK
International Journal of Science, Environment and Technology, Vol. 3, No 5, 2014, 1759 1766 ISSN 2278-3687 (O) PERFORMANCE ANALYSIS OF CANNY AND OTHER COMMONLY USED EDGE DETECTORS Sandeep Dhawan Director
More informationProf. Feng Liu. Winter /15/2019
Prof. Feng Liu Winter 2019 http://www.cs.pdx.edu/~fliu/courses/cs410/ 01/15/2019 Last Time Filter 2 Today More on Filter Feature Detection 3 Filter Re-cap noisy image naïve denoising Gaussian blur better
More informationIntroduction. Introduction. Related Research. SIFT method. SIFT method. Distinctive Image Features from Scale-Invariant. Scale.
Distinctive Image Features from Scale-Invariant Keypoints David G. Lowe presented by, Sudheendra Invariance Intensity Scale Rotation Affine View point Introduction Introduction SIFT (Scale Invariant Feature
More informationComputer Vision. Recap: Smoothing with a Gaussian. Recap: Effect of σ on derivatives. Computer Science Tripos Part II. Dr Christopher Town
Recap: Smoothing with a Gaussian Computer Vision Computer Science Tripos Part II Dr Christopher Town Recall: parameter σ is the scale / width / spread of the Gaussian kernel, and controls the amount of
More informationPerception. Autonomous Mobile Robots. Sensors Vision Uncertainties, Line extraction from laser scans. Autonomous Systems Lab. Zürich.
Autonomous Mobile Robots Localization "Position" Global Map Cognition Environment Model Local Map Path Perception Real World Environment Motion Control Perception Sensors Vision Uncertainties, Line extraction
More informationFourier analysis and sampling theory
Reading Required: Shirley, Ch. 9 Recommended: Fourier analysis and sampling theory Ron Bracewell, The Fourier Transform and Its Applications, McGraw-Hill. Don P. Mitchell and Arun N. Netravali, Reconstruction
More information