Image Filtering. Slides, adapted from. Steve Seitz and Rick Szeliski, U.Washington

Size: px
Start display at page:

Download "Image Filtering. Slides, adapted from. Steve Seitz and Rick Szeliski, U.Washington"

Transcription

1 Image Filtering Slides, adapted from Steve Seitz and Rick Szeliski, U.Washington

2 The power of blur All is Vanity by Charles Allen Gillbert ( ) Harmon LD & JuleszB (1973) The recognition of faces. Scientific American 229(5):71 82

3 The power of blur All is Vanity by Charles Allen Gillbert ( ) Harmon LD & JuleszB (1973) The recognition of faces. Scientific American 229(5):71 82

4 Image filtering applications Today: 1. Noise removal 2. Blur 3. Image gradient 4. Edge detection 5. Image pyramids

5 Images as functions We can think of an image as a function, f: R 2 -> R f( x, y ) = intensity at position/pixel ( x, y ) Realistically, we expect the image only to be defined over a rectangle, with a finite range: f: [a,b]x[c,d] -> [,1] A color image is just three functions pasted together. We will focus mostly on intensity images.

6 Images as functions

7 What is a digital image We usually work with digital (discrete) images: Sample the 2D space on a regular grid Quantize each sample (round to nearest integer)

8 What is a digital image We usually work with digital (discrete) images: Sample the 2D space on a regular grid Quantize each sample (round to nearest integer) The image can now be represented as a matrix of integer values

9 Filtering noise Image

10 Filtering noise Image

11 Filtering noise Mean image Image

12 Filtering noise Mean image Image What happens at boundaries?

13 Cross-correlation filtering Let s write this down as an equation. Assume the averaging window is (2k+1)x(2k+1): We can generalize this idea by allowing different weights for different neighboring pixels:

14 Cross-correlation filtering This is called a cross-correlation operation H is called the filter, kernel, or mask. Note: The above allows negative filter indices. When you implement need to use: H[u+k,v+k] instead of H[u,v]

15 Mean kernel What s the kernel for a 3x3 mean filter?

16 Mean kernel What s the kernel for a 3x3 mean filter?

17 Mean vs. Gaussian filtering = Blur!!!

18 Gaussian kernel A Gaussian kernel gives less weight to pixels further from the center of the window

19 Gaussian filtering This kernel is an approximation of a Gaussian function: What happens if you increase σ?

20 Mean vs. Gaussian filtering

21 Image filtering applications Today: 1. Noise removal 2. Blur 3. Image gradient 4. Edge detection 5. Image pyramids

22 Image gradient as cross-correlation How can we differentiate a digital image F[x,y]? Option 1: reconstruct a continuous image, image, f, then take gradient Option 2: take discrete derivative (finite difference)

23 Image gradient as cross-correlation How can we differentiate a digital image F[x,y]? Option 1: reconstruct a continuous image, image, f, then take gradient Option 2: take discrete derivative (finite difference) How would you implement this as a cross-correlation?

24 Image gradient as cross-correlation How can we differentiate a digital image F[x,y]? Option 1:reconstruct a continuous image, image, f, then take gradient Option 2: take discrete derivative (finite difference) How would you implement this as a cross-correlation?

25 Image gradient as cross-correlation How can we differentiate a digital image F[x,y]? Option 1: reconstruct a continuous image, image, f, then take gradient Option 2: take discrete derivative (finite difference) How would you implement this as a cross-correlation? Forward derivative

26 Image gradient as cross-correlation How can we differentiate a digital image F[x,y]? Option 1: reconstruct a continuous image, image, f, then take gradient Option 2: take discrete derivative (finite difference) How would you implement this as a cross-correlation? Central derivative

27 Image gradient

28 Image gradient The gradient direction is given by: how does this relate to the direction of the edge?

29 Image gradient The gradient direction is given by: how does this relate to the direction of the edge? The edge strength is given by the gradient magnitude

30 Convolution A convolution operation is a cross-correlation where the filter is flipped both horizontally and vertically before being applied to the image: It is written: Suppose H is a Gaussian or mean kernel. How does convolution differ from cross-correlation?

31 Convolution A convolution operation is a cross-correlation where the filter is flipped both horizontally and vertically before being applied to the image: It is written: Suppose H is a Gaussian or mean kernel. How does convolution differ from cross-correlation?

32 Image filtering applications Today: 1. Noise removal 2. Blur 3. Image gradient 4. Edge detection 5. Image pyramids

33 Effects of noise Consider a single row or column of the image Plotting intensity as a function of position gives a signal Where is the edge?

34 Solution: smooth first Where is the edge? Look for peaks in

35 Derivative theorem of convolution This saves us one operation: Where is the edge? Maxima point

36 Laplacian of Gaussian Consider Laplacian of Gaussian operator Where is the edge? Zero-crossings of bottom graph

37 2D edge detection filters Gaussian derivative of Gaussian Laplacian of Gaussian is the Laplacian operator

38 Laplacian filter Gaussian delta function Laplacian of Gaussian (2 nd derivative operator)

39 Laplacian image smoothed (5x5 Gaussian) delta function Laplacian of Gaussian (2 nd derivative operator)

40 Laplacian image smoothed (5x5 Gaussian) original Laplacian of Gaussian (2 nd derivative operator)

41 Laplacian image smoothed (5x5 Gaussian) original Laplacian image smoothed original (scaled by 4, offset +128)

42 Laplacian image smoothed (5x5 Gaussian) original Laplacian image smoothed original (scaled by 4, offset +128) What happens as we change σ?

43 Scale space (Witkin 83) larger Gaussian filtered signal

44 Scale space: insights As the scale is increased edge position can change edges can disappear new edges are not created Bottom line need to consider information at different scales (or else know what scale you care about)

45 Image filtering applications Today: 1. Noise removal 2. Blur 3. Image gradient 4. Edge detection 5. Image pyramids

46 Image Pyramids

47 Image sub-sampling 1/8 1/4 Throw away every other row and column to create a ½ size image

48 Image sub-sampling 1/2 1/4 (2x zoom) 1/8(4x zoom) Why does this look so bad?

49 Even worse for synthetic images

50 Really bad in video

51 Gaussian pre-filtering G 1/8 G 1/4 Gaussian 1/2 Solution: filter the image, image, then subsample In video: filter also temporally

52 Subsampling with Gaussian pre-filtering Gaussian 1/2 Solution: filter the image, G 1/4 G 1/8

53 Compare with... 1/2 1/4 (2x zoom) 1/8(4x zoom)

54 Pyramid Creation

55 Octaves in the Spatial Domain Lowpass Images Bandpass Images

56 Pyramids Advantages of pyramids Faster than Fourier transform Avoids ringing artifacts Many applications small images faster to process good for multiresolution processing compression progressive transmission

57 Example: pyramid blending

58 Laplacian level 4 Laplacian level 2 Laplacian level left pyramid right pyramid blended pyramid

59 Pyramid Blending

60 Video Pyramids Same idea in 3 dimensions x,y,t Space-time pyramid: Temporal pyramid:

61 Example: action recognition

62 Recognizing Actions Use dense information Gradient orientation <--> space-time shape information (behavior) Gradient magnitude <--> photometric information (clothing, lighting, contrast, etc)

63 Behavior-Based Distance Measure Temporal pyramid: Distance measure = the χ2 distance between corresponding empirical distributions

64 Action recognition results

65 Next week:features and descriptors

Edges and Scale. Image Features. Detecting edges. Origin of Edges. Solution: smooth first. Effects of noise

Edges and Scale. Image Features. Detecting edges. Origin of Edges. Solution: smooth first. Effects of noise Edges and Scale Image Features From Sandlot Science Slides revised from S. Seitz, R. Szeliski, S. Lazebnik, etc. Origin of Edges surface normal discontinuity depth discontinuity surface color discontinuity

More information

Subsampling and image pyramids

Subsampling and image pyramids Subsampling and image pyramids http://www.cs.cmu.edu/~16385/ 16-385 Computer Vision Spring 2018, Lecture 3 Course announcements Homework 0 and homework 1 will be posted tonight. - Homework 0 is not required

More information

6.869 Advances in Computer Vision. Bill Freeman, Antonio Torralba and Phillip Isola MIT Oct. 3, 2018

6.869 Advances in Computer Vision. Bill Freeman, Antonio Torralba and Phillip Isola MIT Oct. 3, 2018 6.869 Advances in Computer Vision Bill Freeman, Antonio Torralba and Phillip Isola MIT Oct. 3, 2018 1 Sampling Sampling Pixels Continuous world 3 Sampling 4 Sampling 5 Continuous image f (x, y) Sampling

More information

Image Alignment and Mosaicing

Image Alignment and Mosaicing Image Alignment and Mosaicing Image Alignment Applications Local alignment: Tracking Stereo Global alignment: Camera jitter elimination Image enhancement Panoramic mosaicing Image Enhancement Original

More information

Lecture 3: Linear Filters

Lecture 3: Linear Filters Lecture 3: Linear Filters Professor Fei Fei Li Stanford Vision Lab 1 What we will learn today? Images as functions Linear systems (filters) Convolution and correlation Discrete Fourier Transform (DFT)

More information

Lecture 3: Linear Filters

Lecture 3: Linear Filters Lecture 3: Linear Filters Professor Fei Fei Li Stanford Vision Lab 1 What we will learn today? Images as functions Linear systems (filters) Convolution and correlation Discrete Fourier Transform (DFT)

More information

The Frequency Domain : Computational Photography Alexei Efros, CMU, Fall Many slides borrowed from Steve Seitz

The Frequency Domain : Computational Photography Alexei Efros, CMU, Fall Many slides borrowed from Steve Seitz The Frequency Domain 15-463: Computational Photography Alexei Efros, CMU, Fall 2008 Somewhere in Cinque Terre, May 2005 Many slides borrowed from Steve Seitz Salvador Dali Gala Contemplating the Mediterranean

More information

Lecture 7: Edge Detection

Lecture 7: Edge Detection #1 Lecture 7: Edge Detection Saad J Bedros sbedros@umn.edu Review From Last Lecture Definition of an Edge First Order Derivative Approximation as Edge Detector #2 This Lecture Examples of Edge Detection

More information

Thinking in Frequency

Thinking in Frequency 09/05/17 Thinking in Frequency Computational Photography University of Illinois Derek Hoiem Administrative Matlab/linear algebra tutorial tomorrow, planned for 6:30pm Probably 1214 DCL (will send confirmation

More information

COMP344 Digital Image Processing Fall 2007 Final Examination

COMP344 Digital Image Processing Fall 2007 Final Examination COMP344 Digital Image Processing Fall 2007 Final Examination Time allowed: 2 hours Name Student ID Email Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Total With model answer HK University

More information

Introduction to Computer Vision

Introduction to Computer Vision Introduction to Computer Vision Michael J. Black Sept 2009 Lecture 8: Pyramids and image derivatives Goals Images as functions Derivatives of images Edges and gradients Laplacian pyramids Code for lecture

More information

CSE 473/573 Computer Vision and Image Processing (CVIP)

CSE 473/573 Computer Vision and Image Processing (CVIP) CSE 473/573 Computer Vision and Image Processing (CVIP) Ifeoma Nwogu inwogu@buffalo.edu Lecture 11 Local Features 1 Schedule Last class We started local features Today More on local features Readings for

More information

Lecture 04 Image Filtering

Lecture 04 Image Filtering Institute of Informatics Institute of Neuroinformatics Lecture 04 Image Filtering Davide Scaramuzza 1 Lab Exercise 2 - Today afternoon Room ETH HG E 1.1 from 13:15 to 15:00 Work description: your first

More information

Computer Vision Lecture 3

Computer Vision Lecture 3 Computer Vision Lecture 3 Linear Filters 03.11.2015 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de Demo Haribo Classification Code available on the class website...

More information

CITS 4402 Computer Vision

CITS 4402 Computer Vision CITS 4402 Computer Vision Prof Ajmal Mian Adj/A/Prof Mehdi Ravanbakhsh, CEO at Mapizy (www.mapizy.com) and InFarm (www.infarm.io) Lecture 04 Greyscale Image Analysis Lecture 03 Summary Images as 2-D signals

More information

The Frequency Domain. Many slides borrowed from Steve Seitz

The Frequency Domain. Many slides borrowed from Steve Seitz The Frequency Domain Many slides borrowed from Steve Seitz Somewhere in Cinque Terre, May 2005 15-463: Computational Photography Alexei Efros, CMU, Spring 2010 Salvador Dali Gala Contemplating the Mediterranean

More information

The Frequency Domain, without tears. Many slides borrowed from Steve Seitz

The Frequency Domain, without tears. Many slides borrowed from Steve Seitz The Frequency Domain, without tears Many slides borrowed from Steve Seitz Somewhere in Cinque Terre, May 2005 CS194: Image Manipulation & Computational Photography Alexei Efros, UC Berkeley, Fall 2016

More information

Image Filtering, Edges and Image Representation

Image Filtering, Edges and Image Representation Image Filtering, Edges and Image Representation Capturing what s important Req reading: Chapter 7, 9 F&P Adelson, Simoncelli and Freeman (handout online) Opt reading: Horn 7 & 8 FP 8 February 19, 8 A nice

More information

Filtering and Edge Detection

Filtering and Edge Detection Filtering and Edge Detection Local Neighborhoods Hard to tell anything from a single pixel Example: you see a reddish pixel. Is this the object s color? Illumination? Noise? The next step in order of complexity

More information

Image Enhancement in the frequency domain. GZ Chapter 4

Image Enhancement in the frequency domain. GZ Chapter 4 Image Enhancement in the frequency domain GZ Chapter 4 Contents In this lecture we will look at image enhancement in the frequency domain The Fourier series & the Fourier transform Image Processing in

More information

Templates, Image Pyramids, and Filter Banks

Templates, Image Pyramids, and Filter Banks Templates, Image Pyramids, and Filter Banks 09/9/ Computer Vision James Hays, Brown Slides: Hoiem and others Review. Match the spatial domain image to the Fourier magnitude image 2 3 4 5 B A C D E Slide:

More information

ECE Digital Image Processing and Introduction to Computer Vision

ECE Digital Image Processing and Introduction to Computer Vision ECE592-064 Digital Image Processing and Introduction to Computer Vision Depart. of ECE, NC State University Instructor: Tianfu (Matt) Wu Spring 2017 Outline Recap, image degradation / restoration Template

More information

Gaussian derivatives

Gaussian derivatives Gaussian derivatives UCU Winter School 2017 James Pritts Czech Tecnical University January 16, 2017 1 Images taken from Noah Snavely s and Robert Collins s course notes Definition An image (grayscale)

More information

Image Stitching II. Linda Shapiro CSE 455

Image Stitching II. Linda Shapiro CSE 455 Image Stitching II Linda Shapiro CSE 455 RANSAC for Homography Initial Matched Points RANSAC for Homography Final Matched Points RANSAC for Homography Image Blending What s wrong? Feathering + 1 0 1 0

More information

Edge Detection. Introduction to Computer Vision. Useful Mathematics Funcs. The bad news

Edge Detection. Introduction to Computer Vision. Useful Mathematics Funcs. The bad news Edge Detection Introduction to Computer Vision CS / ECE 8B Thursday, April, 004 Edge detection (HO #5) Edge detection is a local area operator that seeks to find significant, meaningful changes in image

More information

Linear Operators and Fourier Transform

Linear Operators and Fourier Transform Linear Operators and Fourier Transform DD2423 Image Analysis and Computer Vision Mårten Björkman Computational Vision and Active Perception School of Computer Science and Communication November 13, 2013

More information

Reading. 3. Image processing. Pixel movement. Image processing Y R I G Q

Reading. 3. Image processing. Pixel movement. Image processing Y R I G Q Reading Jain, Kasturi, Schunck, Machine Vision. McGraw-Hill, 1995. Sections 4.-4.4, 4.5(intro), 4.5.5, 4.5.6, 5.1-5.4. 3. Image processing 1 Image processing An image processing operation typically defines

More information

SIFT: SCALE INVARIANT FEATURE TRANSFORM BY DAVID LOWE

SIFT: SCALE INVARIANT FEATURE TRANSFORM BY DAVID LOWE SIFT: SCALE INVARIANT FEATURE TRANSFORM BY DAVID LOWE Overview Motivation of Work Overview of Algorithm Scale Space and Difference of Gaussian Keypoint Localization Orientation Assignment Descriptor Building

More information

Image Stitching II. Linda Shapiro EE/CSE 576

Image Stitching II. Linda Shapiro EE/CSE 576 Image Stitching II Linda Shapiro EE/CSE 576 RANSAC for Homography Initial Matched Points RANSAC for Homography Final Matched Points RANSAC for Homography Image Blending What s wrong? Feathering + 1 0 ramp

More information

Multimedia Databases. Previous Lecture. 4.1 Multiresolution Analysis. 4 Shape-based Features. 4.1 Multiresolution Analysis

Multimedia Databases. Previous Lecture. 4.1 Multiresolution Analysis. 4 Shape-based Features. 4.1 Multiresolution Analysis Previous Lecture Multimedia Databases Texture-Based Image Retrieval Low Level Features Tamura Measure, Random Field Model High-Level Features Fourier-Transform, Wavelets Wolf-Tilo Balke Silviu Homoceanu

More information

Multimedia Databases. Wolf-Tilo Balke Philipp Wille Institut für Informationssysteme Technische Universität Braunschweig

Multimedia Databases. Wolf-Tilo Balke Philipp Wille Institut für Informationssysteme Technische Universität Braunschweig Multimedia Databases Wolf-Tilo Balke Philipp Wille Institut für Informationssysteme Technische Universität Braunschweig http://www.ifis.cs.tu-bs.de 4 Previous Lecture Texture-Based Image Retrieval Low

More information

CS 3710: Visual Recognition Describing Images with Features. Adriana Kovashka Department of Computer Science January 8, 2015

CS 3710: Visual Recognition Describing Images with Features. Adriana Kovashka Department of Computer Science January 8, 2015 CS 3710: Visual Recognition Describing Images with Features Adriana Kovashka Department of Computer Science January 8, 2015 Plan for Today Presentation assignments + schedule changes Image filtering Feature

More information

Introduction to Computer Vision. 2D Linear Systems

Introduction to Computer Vision. 2D Linear Systems Introduction to Computer Vision D Linear Systems Review: Linear Systems We define a system as a unit that converts an input function into an output function Independent variable System operator or Transfer

More information

Digital Image Processing COSC 6380/4393

Digital Image Processing COSC 6380/4393 Digital Image Processing COSC 6380/4393 Lecture 11 Oct 3 rd, 2017 Pranav Mantini Slides from Dr. Shishir K Shah, and Frank Liu Review: 2D Discrete Fourier Transform If I is an image of size N then Sin

More information

Vlad Estivill-Castro (2016) Robots for People --- A project for intelligent integrated systems

Vlad Estivill-Castro (2016) Robots for People --- A project for intelligent integrated systems 1 Vlad Estivill-Castro (2016) Robots for People --- A project for intelligent integrated systems V. Estivill-Castro 2 Perception Concepts Vision Chapter 4 (textbook) Sections 4.3 to 4.5 What is the course

More information

Wavelets and Multiresolution Processing

Wavelets and Multiresolution Processing Wavelets and Multiresolution Processing Wavelets Fourier transform has it basis functions in sinusoids Wavelets based on small waves of varying frequency and limited duration In addition to frequency,

More information

CEE598 - Visual Sensing for Civil Infrastructure Eng. & Mgmt.

CEE598 - Visual Sensing for Civil Infrastructure Eng. & Mgmt. CEE598 - Visual Sensing for Civil Infrastructure Eng. & Mgmt. Session 8- Linear Filters From Spatial Domain to Frequency Domain Mani Golparvar-Fard Department of Civil and Environmental Engineering 329D,

More information

Blobs & Scale Invariance

Blobs & Scale Invariance Blobs & Scale Invariance Prof. Didier Stricker Doz. Gabriele Bleser Computer Vision: Object and People Tracking With slides from Bebis, S. Lazebnik & S. Seitz, D. Lowe, A. Efros 1 Apertizer: some videos

More information

Additional Pointers. Introduction to Computer Vision. Convolution. Area operations: Linear filtering

Additional Pointers. Introduction to Computer Vision. Convolution. Area operations: Linear filtering Additional Pointers Introduction to Computer Vision CS / ECE 181B andout #4 : Available this afternoon Midterm: May 6, 2004 W #2 due tomorrow Ack: Prof. Matthew Turk for the lecture slides. See my ECE

More information

Digital Image Processing COSC 6380/4393

Digital Image Processing COSC 6380/4393 Digital Image Processing COSC 6380/4393 Lecture 13 Oct 2 nd, 2018 Pranav Mantini Slides from Dr. Shishir K Shah, and Frank Liu Review f 0 0 0 1 0 0 0 0 w 1 2 3 2 8 Zero Padding 0 0 0 0 0 0 0 1 0 0 0 0

More information

Multimedia Databases. 4 Shape-based Features. 4.1 Multiresolution Analysis. 4.1 Multiresolution Analysis. 4.1 Multiresolution Analysis

Multimedia Databases. 4 Shape-based Features. 4.1 Multiresolution Analysis. 4.1 Multiresolution Analysis. 4.1 Multiresolution Analysis 4 Shape-based Features Multimedia Databases Wolf-Tilo Balke Silviu Homoceanu Institut für Informationssysteme Technische Universität Braunschweig http://www.ifis.cs.tu-bs.de 4 Multiresolution Analysis

More information

Announcements. Filtering. Image Filtering. Linear Filters. Example: Smoothing by Averaging. Homework 2 is due Apr 26, 11:59 PM Reading:

Announcements. Filtering. Image Filtering. Linear Filters. Example: Smoothing by Averaging. Homework 2 is due Apr 26, 11:59 PM Reading: Announcements Filtering Homework 2 is due Apr 26, :59 PM eading: Chapter 4: Linear Filters CSE 52 Lecture 6 mage Filtering nput Output Filter (From Bill Freeman) Example: Smoothing by Averaging Linear

More information

CS5670: Computer Vision

CS5670: Computer Vision CS5670: Computer Vision Noah Snavely Lecture 5: Feature descriptors and matching Szeliski: 4.1 Reading Announcements Project 1 Artifacts due tomorrow, Friday 2/17, at 11:59pm Project 2 will be released

More information

Linear Diffusion and Image Processing. Outline

Linear Diffusion and Image Processing. Outline Outline Linear Diffusion and Image Processing Fourier Transform Convolution Image Restoration: Linear Filtering Diffusion Processes for Noise Filtering linear scale space theory Gauss-Laplace pyramid for

More information

Lecture 6: Edge Detection. CAP 5415: Computer Vision Fall 2008

Lecture 6: Edge Detection. CAP 5415: Computer Vision Fall 2008 Lecture 6: Edge Detection CAP 5415: Computer Vision Fall 2008 Announcements PS 2 is available Please read it by Thursday During Thursday lecture, I will be going over it in some detail Monday - Computer

More information

Multiresolution image processing

Multiresolution image processing Multiresolution image processing Laplacian pyramids Some applications of Laplacian pyramids Discrete Wavelet Transform (DWT) Wavelet theory Wavelet image compression Bernd Girod: EE368 Digital Image Processing

More information

Feature extraction: Corners and blobs

Feature extraction: Corners and blobs Feature extraction: Corners and blobs Review: Linear filtering and edge detection Name two different kinds of image noise Name a non-linear smoothing filter What advantages does median filtering have over

More information

Multiresolution schemes

Multiresolution schemes Multiresolution schemes Fondamenti di elaborazione del segnale multi-dimensionale Multi-dimensional signal processing Stefano Ferrari Università degli Studi di Milano stefano.ferrari@unimi.it Elaborazione

More information

Topic 7. Convolution, Filters, Correlation, Representation. Bryan Pardo, 2008, Northwestern University EECS 352: Machine Perception of Music and Audio

Topic 7. Convolution, Filters, Correlation, Representation. Bryan Pardo, 2008, Northwestern University EECS 352: Machine Perception of Music and Audio Topic 7 Convolution, Filters, Correlation, Representation Short time Fourier Transform Break signal into windows Calculate DFT of each window The Spectrogram spectrogram(y,1024,512,1024,fs,'yaxis'); A

More information

Lecture 8: Interest Point Detection. Saad J Bedros

Lecture 8: Interest Point Detection. Saad J Bedros #1 Lecture 8: Interest Point Detection Saad J Bedros sbedros@umn.edu Review of Edge Detectors #2 Today s Lecture Interest Points Detection What do we mean with Interest Point Detection in an Image Goal:

More information

Fourier Transforms 1D

Fourier Transforms 1D Fourier Transforms 1D 3D Image Processing Alireza Ghane 1 Overview Recap Intuitions Function representations shift-invariant spaces linear, time-invariant (LTI) systems complex numbers Fourier Transforms

More information

Edge Detection. CS 650: Computer Vision

Edge Detection. CS 650: Computer Vision CS 650: Computer Vision Edges and Gradients Edge: local indication of an object transition Edge detection: local operators that find edges (usually involves convolution) Local intensity transitions are

More information

Review Smoothing Spatial Filters Sharpening Spatial Filters. Spatial Filtering. Dr. Praveen Sankaran. Department of ECE NIT Calicut.

Review Smoothing Spatial Filters Sharpening Spatial Filters. Spatial Filtering. Dr. Praveen Sankaran. Department of ECE NIT Calicut. Spatial Filtering Dr. Praveen Sankaran Department of ECE NIT Calicut January 7, 203 Outline 2 Linear Nonlinear 3 Spatial Domain Refers to the image plane itself. Direct manipulation of image pixels. Figure:

More information

Multiscale Image Transforms

Multiscale Image Transforms Multiscale Image Transforms Goal: Develop filter-based representations to decompose images into component parts, to extract features/structures of interest, and to attenuate noise. Motivation: extract

More information

Frequency2: Sampling and Aliasing

Frequency2: Sampling and Aliasing CS 4495 Computer Vision Frequency2: Sampling and Aliasing Aaron Bobick School of Interactive Computing Administrivia Project 1 is due tonight. Submit what you have at the deadline. Next problem set stereo

More information

Multiresolution schemes

Multiresolution schemes Multiresolution schemes Fondamenti di elaborazione del segnale multi-dimensionale Stefano Ferrari Università degli Studi di Milano stefano.ferrari@unimi.it Elaborazione dei Segnali Multi-dimensionali e

More information

Image preprocessing in spatial domain

Image preprocessing in spatial domain Image preprocessing in spatial domain Sharpening, image derivatives, Laplacian, edges Revision: 1.2, dated: May 25, 2007 Tomáš Svoboda Czech Technical University, Faculty of Electrical Engineering Center

More information

CS 4495 Computer Vision. Frequency and Fourier Transforms. Aaron Bobick School of Interactive Computing. Frequency and Fourier Transform

CS 4495 Computer Vision. Frequency and Fourier Transforms. Aaron Bobick School of Interactive Computing. Frequency and Fourier Transform CS 4495 Computer Vision Frequency and Fourier Transforms Aaron Bobick School of Interactive Computing Administrivia Project 1 is (still) on line get started now! Readings for this week: FP Chapter 4 (which

More information

Roadmap. Introduction to image analysis (computer vision) Theory of edge detection. Applications

Roadmap. Introduction to image analysis (computer vision) Theory of edge detection. Applications Edge Detection Roadmap Introduction to image analysis (computer vision) Its connection with psychology and neuroscience Why is image analysis difficult? Theory of edge detection Gradient operator Advanced

More information

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Lesson 7 Delta Modulation and DPCM Instructional Objectives At the end of this lesson, the students should be able to: 1. Describe a lossy predictive coding scheme.

More information

ECG782: Multidimensional Digital Signal Processing

ECG782: Multidimensional Digital Signal Processing Professor Brendan Morris, SEB 3216, brendan.morris@unlv.edu ECG782: Multidimensional Digital Signal Processing Spring 2014 TTh 14:30-15:45 CBC C313 Lecture 05 Image Processing Basics 13/02/04 http://www.ee.unlv.edu/~b1morris/ecg782/

More information

Scale-space image processing

Scale-space image processing Scale-space image processing Corresponding image features can appear at different scales Like shift-invariance, scale-invariance of image processing algorithms is often desirable. Scale-space representation

More information

ECG782: Multidimensional Digital Signal Processing

ECG782: Multidimensional Digital Signal Processing Professor Brendan Morris, SEB 3216, brendan.morris@unlv.edu ECG782: Multidimensional Digital Signal Processing Filtering in the Frequency Domain http://www.ee.unlv.edu/~b1morris/ecg782/ 2 Outline Background

More information

Edge Detection. Image Processing - Computer Vision

Edge Detection. Image Processing - Computer Vision Image Processing - Lesson 10 Edge Detection Image Processing - Computer Vision Low Level Edge detection masks Gradient Detectors Compass Detectors Second Derivative - Laplace detectors Edge Linking Image

More information

EECS490: Digital Image Processing. Lecture #11

EECS490: Digital Image Processing. Lecture #11 Lecture #11 Filtering Applications: OCR, scanning Highpass filters Laplacian in the frequency domain Image enhancement using highpass filters Homomorphic filters Bandreject/bandpass/notch filters Correlation

More information

Recap: edge detection. Source: D. Lowe, L. Fei-Fei

Recap: edge detection. Source: D. Lowe, L. Fei-Fei Recap: edge detection Source: D. Lowe, L. Fei-Fei Canny edge detector 1. Filter image with x, y derivatives of Gaussian 2. Find magnitude and orientation of gradient 3. Non-maximum suppression: Thin multi-pixel

More information

Frequency Filtering CSC 767

Frequency Filtering CSC 767 Frequency Filtering CSC 767 Outline Fourier transform and frequency domain Frequency view of filtering Hybrid images Sampling Slide: Hoiem Why does the Gaussian give a nice smooth image, but the square

More information

Lecture 8: Interest Point Detection. Saad J Bedros

Lecture 8: Interest Point Detection. Saad J Bedros #1 Lecture 8: Interest Point Detection Saad J Bedros sbedros@umn.edu Last Lecture : Edge Detection Preprocessing of image is desired to eliminate or at least minimize noise effects There is always tradeoff

More information

Midterm Summary Fall 08. Yao Wang Polytechnic University, Brooklyn, NY 11201

Midterm Summary Fall 08. Yao Wang Polytechnic University, Brooklyn, NY 11201 Midterm Summary Fall 8 Yao Wang Polytechnic University, Brooklyn, NY 2 Components in Digital Image Processing Output are images Input Image Color Color image image processing Image Image restoration Image

More information

Machine vision. Summary # 4. The mask for Laplacian is given

Machine vision. Summary # 4. The mask for Laplacian is given 1 Machine vision Summary # 4 The mask for Laplacian is given L = 0 1 0 1 4 1 (6) 0 1 0 Another Laplacian mask that gives more importance to the center element is L = 1 1 1 1 8 1 (7) 1 1 1 Note that the

More information

Why does a lower resolution image still make sense to us? What do we lose? Image:

Why does a lower resolution image still make sense to us? What do we lose? Image: 2D FREQUENCY DOMAIN 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 information

Digital Image Processing

Digital Image Processing Digital Image Processing, 2nd ed. Digital Image Processing Chapter 7 Wavelets and Multiresolution Processing Dr. Kai Shuang Department of Electronic Engineering China University of Petroleum shuangkai@cup.edu.cn

More information

CAP 5415 Computer Vision

CAP 5415 Computer Vision CAP 545 Computer Vision Dr. Mubarak Sa Univ. o Central Florida Filtering Lecture-2 Contents Filtering/Smooting/Removing Noise Convolution/Correlation Image Derivatives Histogram Some Matlab Functions General

More information

Taking derivative by convolution

Taking derivative by convolution Taking derivative by convolution Partial derivatives with convolution For 2D function f(x,y), the partial derivative is: For discrete data, we can approximate using finite differences: To implement above

More information

Computational Photography

Computational Photography Computational Photography Si Lu Spring 208 http://web.cecs.pdx.edu/~lusi/cs50/cs50_computati onal_photography.htm 04/0/208 Last Time o Digital Camera History of Camera Controlling Camera o Photography

More information

SYDE 575: Introduction to Image Processing. Image Compression Part 2: Variable-rate compression

SYDE 575: Introduction to Image Processing. Image Compression Part 2: Variable-rate compression SYDE 575: Introduction to Image Processing Image Compression Part 2: Variable-rate compression Variable-rate Compression: Transform-based compression As mentioned earlier, we wish to transform image data

More information

Outline. Convolution. Filtering

Outline. Convolution. Filtering Filtering Outline Convolution Filtering Logistics HW1 HW2 - out tomorrow Recall: what is a digital (grayscale) image? Matrix of integer values Images as height fields Let s think of image as zero-padded

More information

Corners, Blobs & Descriptors. With slides from S. Lazebnik & S. Seitz, D. Lowe, A. Efros

Corners, Blobs & Descriptors. With slides from S. Lazebnik & S. Seitz, D. Lowe, A. Efros Corners, Blobs & Descriptors With slides from S. Lazebnik & S. Seitz, D. Lowe, A. Efros Motivation: Build a Panorama M. Brown and D. G. Lowe. Recognising Panoramas. ICCV 2003 How do we build panorama?

More information

Edge Detection in Computer Vision Systems

Edge Detection in Computer Vision Systems 1 CS332 Visual Processing in Computer and Biological Vision Systems Edge Detection in Computer Vision Systems This handout summarizes much of the material on the detection and description of intensity

More information

Machine vision, spring 2018 Summary 4

Machine vision, spring 2018 Summary 4 Machine vision Summary # 4 The mask for Laplacian is given L = 4 (6) Another Laplacian mask that gives more importance to the center element is given by L = 8 (7) Note that the sum of the elements in the

More information

Today s lecture. Local neighbourhood processing. The convolution. Removing uncorrelated noise from an image The Fourier transform

Today s lecture. Local neighbourhood processing. The convolution. Removing uncorrelated noise from an image The Fourier transform Cris Luengo TD396 fall 4 cris@cbuuse Today s lecture Local neighbourhood processing smoothing an image sharpening an image The convolution What is it? What is it useful for? How can I compute it? Removing

More information

Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials

Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials Philipp Krähenbühl and Vladlen Koltun Stanford University Presenter: Yuan-Ting Hu 1 Conditional Random Field (CRF) E x I = φ u

More information

Reprinted from Proceedings of the Pattern Recognition and Information Processing Conference (pp ), Dallas, TX (1981).

Reprinted from Proceedings of the Pattern Recognition and Information Processing Conference (pp ), Dallas, TX (1981). Reprinted from Proceedings of the Pattern Recognition and Information Processing Conference (pp. 18-3), Dallas, TX (1981). IMAGE DATA COMPRESSION WITH THE LAPLACIAN PYRAMID* Edward H. Adelson Psychology

More information

Colorado School of Mines Image and Multidimensional Signal Processing

Colorado School of Mines Image and Multidimensional Signal Processing Image and Multidimensional Signal Processing Professor William Hoff Department of Electrical Engineering and Computer Science Spatial Filtering Main idea Spatial filtering Define a neighborhood of a pixel

More information

INTEREST POINTS AT DIFFERENT SCALES

INTEREST POINTS AT DIFFERENT SCALES INTEREST POINTS AT DIFFERENT SCALES Thank you for the slides. They come mostly from the following sources. Dan Huttenlocher Cornell U David Lowe U. of British Columbia Martial Hebert CMU Intuitively, junctions

More information

Detectors part II Descriptors

Detectors part II Descriptors EECS 442 Computer vision Detectors part II Descriptors Blob detectors Invariance Descriptors Some slides of this lectures are courtesy of prof F. Li, prof S. Lazebnik, and various other lecturers Goal:

More information

Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials

Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials by Phillip Krahenbuhl and Vladlen Koltun Presented by Adam Stambler Multi-class image segmentation Assign a class label to each

More information

CS4495/6495 Introduction to Computer Vision. 2A-L6 Edge detection: 2D operators

CS4495/6495 Introduction to Computer Vision. 2A-L6 Edge detection: 2D operators CS4495/6495 Introduction to Computer Vision 2A-L6 Edge detection: 2D operators Derivative theorem of convolution - 1D This saves us one operation: ( ) ( ) x h f h f x f h h x h x ( ) f Derivative of Gaussian

More information

Chapter 4: Filtering in the Frequency Domain. Fourier Analysis R. C. Gonzalez & R. E. Woods

Chapter 4: Filtering in the Frequency Domain. Fourier Analysis R. C. Gonzalez & R. E. Woods Fourier Analysis 1992 2008 R. C. Gonzalez & R. E. Woods Properties of δ (t) and (x) δ : f t) δ ( t t ) dt = f ( ) f x) δ ( x x ) = f ( ) ( 0 t0 x= ( 0 x0 1992 2008 R. C. Gonzalez & R. E. Woods Sampling

More information

Image matching. by Diva Sian. by swashford

Image matching. by Diva Sian. by swashford Image matching by Diva Sian by swashford Harder case by Diva Sian by scgbt Invariant local features Find features that are invariant to transformations geometric invariance: translation, rotation, scale

More information

Digital Image Processing. Chapter 4: Image Enhancement in the Frequency Domain

Digital Image Processing. Chapter 4: Image Enhancement in the Frequency Domain Digital Image Processing Chapter 4: Image Enhancement in the Frequency Domain Image Enhancement in Frequency Domain Objective: To understand the Fourier Transform and frequency domain and how to apply

More information

6.003: Signals and Systems. Sampling and Quantization

6.003: Signals and Systems. Sampling and Quantization 6.003: Signals and Systems Sampling and Quantization December 1, 2009 Last Time: Sampling and Reconstruction Uniform sampling (sampling interval T ): x[n] = x(nt ) t n Impulse reconstruction: x p (t) =

More information

FILTERING IN THE FREQUENCY DOMAIN

FILTERING IN THE FREQUENCY DOMAIN 1 FILTERING IN THE FREQUENCY DOMAIN Lecture 4 Spatial Vs Frequency domain 2 Spatial Domain (I) Normal image space Changes in pixel positions correspond to changes in the scene Distances in I correspond

More information

Department of Electrical Engineering, Polytechnic University, Brooklyn Fall 05 EL DIGITAL IMAGE PROCESSING (I) Final Exam 1/5/06, 1PM-4PM

Department of Electrical Engineering, Polytechnic University, Brooklyn Fall 05 EL DIGITAL IMAGE PROCESSING (I) Final Exam 1/5/06, 1PM-4PM Department of Electrical Engineering, Polytechnic University, Brooklyn Fall 05 EL512 --- DIGITAL IMAGE PROCESSING (I) Y. Wang Final Exam 1/5/06, 1PM-4PM Your Name: ID Number: Closed book. One sheet of

More information

Laplacian Eigenimages in Discrete Scale Space

Laplacian Eigenimages in Discrete Scale Space Laplacian Eigenimages in Discrete Scale Space Martin Tschirsich and Arjan Kuijper,2 Technische Universität Darmstadt, Germany 2 Fraunhofer IGD, Darmstadt, Germany Abstract. Linear or Gaussian scale space

More information

CSCI 1290: Comp Photo

CSCI 1290: Comp Photo CSCI 1290: Comp Photo Fall 2018 @ Brown University James Tompkin Many slides thanks to James Hays old CS 129 course, along with all of its acknowledgements. Capture Frequency - Rolling `Shutter James

More information

Image pyramids and frequency domain

Image pyramids and frequency domain Image pyramids and frequency domain http://www.cs.cmu.edu/~16385/ 16-385 Computer Vision Spring 2019, Lecture 3 Course announcements Homework 1 will be posted tonight. - Homework 1 is due on February 6

More information

Chapter 4 Image Enhancement in the Frequency Domain

Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain Yinghua He School of Computer Science and Technology Tianjin University Background Introduction to the Fourier Transform and the Frequency Domain Smoothing

More information

Advanced Edge Detection 1

Advanced Edge Detection 1 Advanced Edge Detection 1 Lecture 4 See Sections 2.4 and 1.2.5 in Reinhard Klette: Concise Computer Vision Springer-Verlag, London, 2014 1 See last slide for copyright information. 1 / 27 Agenda 1 LoG

More information