Computer Vision 2. SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung. Computer Vision 2 Dr. Benjamin Guthier

Size: px
Start display at page:

Download "Computer Vision 2. SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung. Computer Vision 2 Dr. Benjamin Guthier"

Transcription

1 Computer Vision 2 SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung Computer Vision 2 Dr. Benjamin Guthier

2 1. IMAGE PROCESSING Computer Vision 2 Dr. Benjamin Guthier

3 Content of this Chapter Non-linear Filtering Morphological Operations Optical Flow Fourier Transformation Computer Vision 2 Dr. Benjamin Guthier 3 1. Image Processing

4 Learning Goals After this chapter, you will be able to Implement an efficient median filter for large window sizes Implement a bilateral filter Implement the morphological operations erosion / dilation Explain the steps to calculate motion vector of one pixel Explain the idea of Fourier Transformation Explain, but not memorize the Fourier transform formulas Describe applications where it is useful Computer Vision 2 Dr. Benjamin Guthier 4 1. Image Processing

5 Recommended Reading R. Szeliski: Computer Vision Algorithms and Applications, Chapter 3 (image processing) and 8.4 (optical flow) Computer Vision 2 Dr. Benjamin Guthier 5 1. Image Processing

6 NON-LINEAR FILTERING Computer Vision 2 Dr. Benjamin Guthier 6 1. Image Processing

7 Motivation So far, only linear filters: Gaussian, Sobel Output is a linear combination of the input Sometimes non-linear operations are preferable To remove salt and pepper noise (random high / low pixels) To preserve edges when smoothing an image Computer Vision 2 Dr. Benjamin Guthier 7 1. Image Processing

8 Motivation Salt and Pepper Noise Gaussian filtering only blurs the noise. It is still visible. The energy of the noise remains in the image. Gaussian Filter Source: wikipedia.org Computer Vision 2 Dr. Benjamin Guthier 8 1. Image Processing

9 Motivation Strong Blurring Large Gaussian filter masks also blur the edges Sometimes we want to preserve edges Gaussian Filter Source: freeimages.com Computer Vision 2 Dr. Benjamin Guthier 9 1. Image Processing

10 Median Filter Uses a filter mask (e.g., 3 3) Calculates median of all pixels in the mask New value of the center pixel is the median Pixels in the mask (sorted): 0, 1, 2, 2, 2, 3, 3, 3, 4 Median is the 5 th value New value of center pixel: 2 Computer Vision 2 Dr. Benjamin Guthier Image Processing

11 Median Filter (2) Noisy pixels are outliers No effect on median 3 3 median filter removes noise without blurring Median Filter Source: wikipedia.org Computer Vision 2 Dr. Benjamin Guthier Image Processing

12 Median Filter Implementation Straightforward algorithm (window size n n): Sort pixels in window by value Pick the middle one For large n, sorting is expensive Complexity of sorting n 2 pixels: O n 2 log n 2 = O(n 2 log n) Better algorithm (for large n): Create histogram of pixels in window Find median from the histogram Update the histogram after moving window Computer Vision 2 Dr. Benjamin Guthier Image Processing

13 Median Filter Implementation (2) Finding median from a histogram Sum of all histogram bins equals window size n n Pixels in histogram are sorted Sum up bins until the sum exceeds half the window size The bin index is the median Window Color / Index # Pixels Sum of bins Histogram median 5 > 3 3 / 2 Computer Vision 2 Dr. Benjamin Guthier Image Processing

14 Median Filter Implementation (3) Updating histogram after moving window to the right Subtract pixels left of the new window from histogram for each pixel I(x, y) in left column decrease hist[i(x, y)] by 1 Add new pixels on the right side to histogram Remove from histogram Add to histogram Computer Vision 2 Dr. Benjamin Guthier Image Processing

15 Median Filter Implementation (4) Finding median from histogram takes 128 steps on average Large constant, but independent of n Updating the histogram takes 2n steps Overall runtime: O(n) Better than O(n 2 log n) for large n Computer Vision 2 Dr. Benjamin Guthier Image Processing

16 Bilateral Filter Motivation: Filter with a large mask without blurring edges Blur textures while maintaining sharp boundaries Application (among others): beautify filters in digital cameras to smoothen the skin Idea: Limit filtering to pixels within a mask with similar intensity value to center pixel Computer Vision 2 Dr. Benjamin Guthier Image Processing

17 Bilateral Filter (2) Bilateral filtering is a weighted sum of pixels (i, j) around a center pixel (x, y): I x, y = σ i,j I i, j w(x, y, i, j) σ i,j w(x, y, i, j) Weighting function w is the product of a domain kernel d and a range kernel r: w x, y, i, j = d x, y, i, j r(x, y, i, j) Domain kernel is the usual Gaussian function d x, y, i, j = exp x i 2 + y j 2 2σ d 2 Computer Vision 2 Dr. Benjamin Guthier Image Processing

18 Bilateral Filter (3) Range kernel measures similarity of intensity r x, y, i, j = exp I x, y I i, j 2 2σ r 2 σ d and σ r define the size of the domain and the range kernel, respectively is the Euclidean norm of the RGB color difference Computer Vision 2 Dr. Benjamin Guthier Image Processing

19 Bilateral Filter Example Original image Filtered image Noise is filtered out Edge is preserved Domain kernel Range kernel Product of the two kernels Source: Durand and Dorsey: Fast bilateral filtering for the display of high-dynamic range images. SIGGRAPH Computer Vision 2 Dr. Benjamin Guthier Image Processing

20 Bilateral Filter Example (2) Bilateral Filter Source: freeimages.com Computer Vision 2 Dr. Benjamin Guthier Image Processing

21 Morphology Computer Vision 2 Dr. Benjamin Guthier Image Processing

22 Morphology Morphological operations are used mainly on binary images Can also be applied to grayscale or color images Working with binary images is very fast E.g., in optical inspection tasks They change the shape of binary objects Make them bigger (dilation) Smaller (erosion) Fill in holes (closing) Remove dots and open gaps (opening) (names assume white objects on black background) Computer Vision 2 Dr. Benjamin Guthier Image Processing

23 Morphology Examples Original Dilation Erosion Closing Opening Computer Vision 2 Dr. Benjamin Guthier Image Processing

24 Morphological Operations Uses structuring element B Defines a square or circular window around center pixel Dilation: I x, y = max I(i, j) i,j B Replace center pixel with maximum pixel within B Erosion: I x, y = min I(i, j) i,j B Replace center pixel with minimum pixel within B Closing: dilation, followed by erosion Opening: erosion, followed by dilation Computer Vision 2 Dr. Benjamin Guthier Image Processing

25 Dilation Example Structuring element B is a circle Dilation: replace center pixel with maximum in B Center pixel becomes white Center pixel remains black Computer Vision 2 Dr. Benjamin Guthier Image Processing

26 OPTICAL FLOW Computer Vision 2 Dr. Benjamin Guthier Image Processing

27 Optical Flow Global image registration only accounts for camera motion E.g., one 3 3 Matrix for motion between two frames Object motion requires fine-grained motion compensation E.g., block-based as in video compression, or Motion of every pixel: Optical flow Input: Two frames of a video I t and I t+1 Output: One 2D motion vector (u, v) for every pixel (x, y) Computer Vision 2 Dr. Benjamin Guthier Image Processing

28 Optical Flow (2) Pixel motion is described by: I t x, y = I t+1 (x + u, y + v) The intensity at (x, y) moves to position (x + u, y + v) from frame t to frame t + 1 Intensity remains constant (assumption of the approach) Approximate intensity at t + 1 by Taylor expansion I t+1 x + u, y + v I t x, y + I t x, y u v + I t x, y t Temporal derivative is approximated by forward difference I t (x, y) t I t+1 x, y I t (x, y) Computer Vision 2 Dr. Benjamin Guthier Image Processing

29 Taylor Expansion Intuition (1D) Cut through one image row The object moves from left to right I t+1 x + u I t x + I t x u + I t+1 x I t x I I t+1 x I t x I t x = I t+1 x + u I t x u x x + u x Computer Vision 2 Dr. Benjamin Guthier Image Processing

30 Gradient Constraint Equation Combining constancy assumption with Taylor expansion gradient constraint equation: u I t x, y v + I t+1 x, y I t x, y = 0 One equation with two unknowns u and v Gradient I t (x, y) and pixel values I t+1 (x, y) and I t (x, y) are known To solve, consider pixels (x, y ) in window W around (x, y). Find (u, v) that minimizes the weighted sum: arg min (u,v) x,y W g x, y I t x, y g(x, y ): Gaussian weighting function u v + I t+1 x, y I t x, y Set partial derivatives w.r.t. u and v to zero and solve equation system 2 Computer Vision 2 Dr. Benjamin Guthier Image Processing

31 Example Direction of motion is encoded as hue, intensity as value Source: docs.opencv.org Computer Vision 2 Dr. Benjamin Guthier Image Processing

32 FOURIER TRANSFORMATION Computer Vision 2 Dr. Benjamin Guthier Image Processing

33 Acknowledgements Some of the slides on Fourier transformation were taken from a lecture by Prof. S. Narasimhan at the Carnegie Mellon University, Pittsburgh, PA. Computer Vision 2 Dr. Benjamin Guthier Image Processing

34 Fourier Transformation Idea Represent a signal as a weighted sum of sines and cosines Signal contains a frequency of 2 Hz with an amplitude of 4, and a frequency of 3 Hz with an amplitude of 0.5 Works similarly in 1D (time varying signals) and 2D (images) 1D: temporal frequencies (change per unit of time) 2D: spatial frequencies (change per unit of distance) Transformation to frequency domain has many advantages! Computer Vision 2 Dr. Benjamin Guthier Image Processing

35 Sum of Sinusoids Target f 1 f 2 f f 0 f 0 + f 1 f 0 + f 1 + f 2 f f Use sinus functions as building block: f i (x) = A i sin(ω i x + φ i ) Adding them up can create any target function 1 0 f f 6 Computer Vision 2 Dr. Benjamin Guthier Image Processing

36 Fourier Transform Goal: For a given signal f(x), find amplitude and phase of all frequencies that are contained in it f(x) (Inverse) Fourier Transform F(ω) f(x): value of the signal at position x F(ω): amplitude A and phase φ at frequency ω F(ω) are complex numbers: F ω = Re ω + i Im(ω) A = ± Re ω 2 + Im ω 2 1 Im(ω) and φ = tan Re(ω) Computer Vision 2 Dr. Benjamin Guthier Image Processing

37 Frequency Spectrum Example f x = sin 2πkx + 1 sin 2π 3k x 3 = + 1 F ω 1 3 k 2k 3k ω Computer Vision 2 Dr. Benjamin Guthier Image Processing

38 Frequency Spectrum Example (2) As we have seen: f(x) = F ω f x A σ k=1 1 k sin(2πkx) ω Computer Vision 2 Dr. Benjamin Guthier Image Processing

39 Discrete Fourier Transform (DFT) Fourier transform for one-dimensional discrete signals with x [0, W 1] and ω [0, W 1] is defined as: W 1 F ω = x=0 f x e 2πi W ωx with e 2πi W ωx = cos 2π W ωx i sin 2π W ωx And its inverse: W 1 f x = 1 W ω=0 F ω e 2πi W ωx Computer Vision 2 Dr. Benjamin Guthier Image Processing

40 DFT Properties For each frequency ωτw, DFT can be viewed as filtering signal f(x) with a complex sinusoid at frequency ωτw F(ω) is the amount of frequency Τ ω W contained in f(x) F(ω) is W-periodic, so ω may also be in W 2, W 2 1 Left and right side will be swapped If all f(x) are real numbers (which they are in images), then F ω = F (W ω) Where F denotes complex conjugation F(ω) is symmetric and only W 2 complex values must be stored Computer Vision 2 Dr. Benjamin Guthier Image Processing

41 DFT Symmetry f(x) F ω F ω : amplitude ω scaled to [ 0.5,0.5] F 0 = σ x=0 W 1 f x, so scales in frequency spectrum vary Computer Vision 2 Dr. Benjamin Guthier Image Processing

42 2D Fourier Transform Discrete Fourier transform for 2D images f(x, y) W 1 F(ω 1, ω 2 ) = x=0 H 1 e 2πi W ω1x y=0 Building blocks are now plane waves ω 1 : horizontal frequency W ω 2 : vertical frequency H e 2πi ω 1 W x+ω2 H y e 2πi H ω 2y f(x, y) Computer Vision 2 Dr. Benjamin Guthier Image Processing

43 Plane Waves Illustration ω 1 = ω 2 = example plane waves (spatial domain) 64 different frequency combinations Image is a linear combination of plane waves Source: wikipedia.org Computer Vision 2 Dr. Benjamin Guthier Image Processing

44 Fourier Domain Examples Images and their Fourier spectrum Spatial lines show up as orthogonal lines in the frequency spectrum Computer Vision 2 Dr. Benjamin Guthier Image Processing

45 Fourier Transform and Convolution Convolution in spatial domain is identical to multiplication in frequency domain: f = f g F = F G f : filtered image, f: original image, g: filter mask F, F, G: Fourier transform of the above : spatial convolution (filtering), : element-wise multiplication Filter images with large filter masks by: f = f g IFT FT FT F = F G Computer Vision 2 Dr. Benjamin Guthier Image Processing

46 Fourier Transform and Convolution (2) f(x, y) F x, y Gaussian filter maintains shape after FT g(x, y) G x, y f (x, y) F x, y Computer Vision 2 Dr. Benjamin Guthier Image Processing

47 Low-Pass Filtering Let low frequencies pass Eliminate high frequencies Creates blurred image, removes detail Computer Vision 2 Dr. Benjamin Guthier Image Processing

48 High-Pass Filtering Let high frequencies pass Eliminate low frequencies Only keeps detail (edges) Computer Vision 2 Dr. Benjamin Guthier Image Processing

49 Application: JPEG Compression Idea: Image distortions are more visible in the low frequency spectrum. Use less bits to store higher frequencies Uses the discrete cosine transform (DCT) Similar to Fourier transform, but using only real values and cosines Better properties for compression Splits image into blocks of 8 8 pixels Processes each block individually Computer Vision 2 Dr. Benjamin Guthier Image Processing

50 Application: JPEG Compression (2) JPEG compression algorithm (simplified) Convert into color space that separates brightness from color Subsample color channels Convert each 8 8 block using the DCT Quantize DCT coefficients, such that high frequencies are stored with less bits (lossy compression) Compress sequence of DCT coefficients using lossless compression Computer Vision 2 Dr. Benjamin Guthier Image Processing

51 Application: JPEG Compression (3) JPEG quality increases from left to right Increased quality = more bits used to encode high frequencies Source: wikipedia.org At low quality, only ω 1, ω 2 = 0 is encoded Only average color of block Computer Vision 2 Dr. Benjamin Guthier Image Processing

52 Application: Eulerian Video Magnification Idea: Use Fourier transform to visualize pulse signal from a video In a video, each pixel is a 1D signal over time If video is perfectly still, signal should be constant Contains only DC frequency (F ω = 0, for ω > 0) However, it is not constant H.-Y. Wu, M. Rubinstein, et al. Eulerian Video Magnification for Revealing Subtle Changes in the World, Siggraph Computer Vision 2 Dr. Benjamin Guthier Image Processing

53 Eulerian Video Magnification (2) Luminance variation of one pixel over time Averaged over multiple pixels pulses Video frame Computer Vision 2 Dr. Benjamin Guthier Image Processing

54 Eulerian Video Magnification (3) Pulse s periodic variation over time shows up as a peak in the frequency spectrum between 0.4 and 4 Hz ( bpm) Video: fps, peak at index 18 Frequency: beats frame 25 frames s 60 s min = 64 beats min Increase amplitude of peak and transform back Pulse signal has been amplified Pulse Harmonics Temporal domain Frequency domain Computer Vision 2 Dr. Benjamin Guthier Image Processing

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 WRI C225 Lecture 04 130131 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Histogram Equalization Image Filtering Linear

More information

EXAM SOLUTIONS. Image Processing and Computer Vision Course 2D1421 Monday, 13 th of March 2006,

EXAM SOLUTIONS. Image Processing and Computer Vision Course 2D1421 Monday, 13 th of March 2006, School of Computer Science and Communication, KTH Danica Kragic EXAM SOLUTIONS Image Processing and Computer Vision Course 2D1421 Monday, 13 th of March 2006, 14.00 19.00 Grade table 0-25 U 26-35 3 36-45

More information

Computer Vision 2. SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung. Computer Vision 2 Dr. Benjamin Guthier

Computer Vision 2. SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung. Computer Vision 2 Dr. Benjamin Guthier Computer Vision 2 SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung Computer Vision 2 Dr. Benjamin Guthier 3. HIGH DYNAMIC RANGE Computer Vision 2 Dr. Benjamin Guthier Pixel Value Content of this

More information

Relationship between Fourier Space and Image Space. Academic Resource Center

Relationship between Fourier Space and Image Space. Academic Resource Center Relationship between Fourier Space and Image Space Academic Resource Center Presentation Outline What is an image? Noise Why do we transform images? What is the Fourier Transform? Examples of images in

More information

Computer Vision I. Announcements. Fourier Tansform. Efficient Implementation. Edge and Corner Detection. CSE252A Lecture 13.

Computer 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 information

Filtering Images. Contents

Filtering 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 information

Computer Vision I - Basics of Image Processing Part 1

Computer Vision I - Basics of Image Processing Part 1 Computer Vision I - Basics of Image Processing Part 1 Carsten Rother 28/10/2014 Computer Vision I: Basics of Image Processing Link to lectures Computer Vision I: Basics of Image Processing 28/10/2014 2

More information

What will we learn? Neighborhood processing. Convolution and correlation. Neighborhood processing. Chapter 10 Neighborhood Processing

What will we learn? Neighborhood processing. Convolution and correlation. Neighborhood processing. Chapter 10 Neighborhood Processing What will we learn? Lecture Slides ME 4060 Machine Vision and Vision-based Control Chapter 10 Neighborhood Processing By Dr. Debao Zhou 1 What is neighborhood processing and how does it differ from point

More information

CS4442/9542b Artificial Intelligence II prof. Olga Veksler

CS4442/9542b Artificial Intelligence II prof. Olga Veksler CS4442/9542b Artificial Intelligence II prof. Olga Veksler Lecture 8 Computer Vision Introduction, Filtering Some slides from: D. Jacobs, D. Lowe, S. Seitz, A.Efros, X. Li, R. Fergus, J. Hayes, S. Lazebnik,

More information

CS4442/9542b Artificial Intelligence II prof. Olga Veksler

CS4442/9542b Artificial Intelligence II prof. Olga Veksler CS4442/9542b Artificial Intelligence II prof. Olga Veksler Lecture 2 Computer Vision Introduction, Filtering Some slides from: D. Jacobs, D. Lowe, S. Seitz, A.Efros, X. Li, R. Fergus, J. Hayes, S. Lazebnik,

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 03 Image Processing Basics 13/01/28 http://www.ee.unlv.edu/~b1morris/ecg782/

More information

Image processing. Reading. What is an image? Brian Curless CSE 457 Spring 2017

Image processing. Reading. What is an image? Brian Curless CSE 457 Spring 2017 Reading Jain, Kasturi, Schunck, Machine Vision. McGraw-Hill, 1995. Sections 4.2-4.4, 4.5(intro), 4.5.5, 4.5.6, 5.1-5.4. [online handout] Image processing Brian Curless CSE 457 Spring 2017 1 2 What is an

More information

Digital Image Fundamentals

Digital Image Fundamentals Digital Image Fundamentals Image Quality Objective/ subjective Machine/human beings Mathematical and Probabilistic/ human intuition and perception 6 Structure of the Human Eye photoreceptor cells 75~50

More information

Image Transformation Techniques Dr. Rajeev Srivastava Dept. of Computer Engineering, ITBHU, Varanasi

Image Transformation Techniques Dr. Rajeev Srivastava Dept. of Computer Engineering, ITBHU, Varanasi Image Transformation Techniques Dr. Rajeev Srivastava Dept. of Computer Engineering, ITBHU, Varanasi 1. Introduction The choice of a particular transform in a given application depends on the amount of

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 Spatial Domain Filtering http://www.ee.unlv.edu/~b1morris/ecg782/ 2 Outline Background Intensity

More information

ME/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 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 information

Part 3: Image Processing

Part 3: Image Processing Part 3: Image Processing Image Filtering and Segmentation Georgy Gimel farb COMPSCI 373 Computer Graphics and Image Processing 1 / 60 1 Image filtering 2 Median filtering 3 Mean filtering 4 Image segmentation

More information

Edge and local feature detection - 2. Importance of edge detection in computer vision

Edge 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 information

Biomedical Image Analysis. Spatial Filtering

Biomedical 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 information

Filters. Advanced and Special Topics: Filters. Filters

Filters. Advanced and Special Topics: Filters. Filters Filters Advanced and Special Topics: Filters Dr. Edmund Lam Department of Electrical and Electronic Engineering The University of Hong Kong ELEC4245: Digital Image Processing (Second Semester, 2016 17)

More information

Digital Image Processing. Prof. P. K. Biswas. Department of Electronic & Electrical Communication Engineering

Digital Image Processing. Prof. P. K. Biswas. Department of Electronic & Electrical Communication Engineering Digital Image Processing Prof. P. K. Biswas Department of Electronic & Electrical Communication Engineering Indian Institute of Technology, Kharagpur Lecture - 21 Image Enhancement Frequency Domain Processing

More information

Computer Vision I - Algorithms and Applications: Basics of Image Processing

Computer Vision I - Algorithms and Applications: Basics of Image Processing Computer Vision I - Algorithms and Applications: Basics of Image Processing Carsten Rother 28/10/2013 Computer Vision I: Basics of Image Processing Link to lectures Computer Vision I: Basics of Image Processing

More information

Filtering and Enhancing Images

Filtering and Enhancing Images KECE471 Computer Vision Filtering and Enhancing Images Chang-Su Kim Chapter 5, Computer Vision by Shapiro and Stockman Note: Some figures and contents in the lecture notes of Dr. Stockman are used partly.

More information

Texture. Outline. Image representations: spatial and frequency Fourier transform Frequency filtering Oriented pyramids Texture representation

Texture. Outline. Image representations: spatial and frequency Fourier transform Frequency filtering Oriented pyramids Texture representation Texture Outline Image representations: spatial and frequency Fourier transform Frequency filtering Oriented pyramids Texture representation 1 Image Representation The standard basis for images is the set

More information

COMPUTER VISION > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE

COMPUTER VISION > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE COMPUTER VISION 2017-2018 > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE OUTLINE Optical flow Lucas-Kanade Horn-Schunck Applications of optical flow Optical flow tracking Histograms of oriented flow Assignment

More information

Tutorial 5. Jun Xu, Teaching Asistant March 2, COMP4134 Biometrics Authentication

Tutorial 5. Jun Xu, Teaching Asistant March 2, COMP4134 Biometrics Authentication Tutorial 5 Jun Xu, Teaching Asistant nankaimathxujun@gmail.com COMP4134 Biometrics Authentication March 2, 2017 Table of Contents Problems Problem 1: Answer The Questions Problem 2: Indeterminate Region

More information

IT Digital Image ProcessingVII Semester - Question Bank

IT Digital Image ProcessingVII Semester - Question Bank UNIT I DIGITAL IMAGE FUNDAMENTALS PART A Elements of Digital Image processing (DIP) systems 1. What is a pixel? 2. Define Digital Image 3. What are the steps involved in DIP? 4. List the categories of

More information

Multimedia Systems Image III (Image Compression, JPEG) Mahdi Amiri April 2011 Sharif University of Technology

Multimedia Systems Image III (Image Compression, JPEG) Mahdi Amiri April 2011 Sharif University of Technology Course Presentation Multimedia Systems Image III (Image Compression, JPEG) Mahdi Amiri April 2011 Sharif University of Technology Image Compression Basics Large amount of data in digital images File size

More information

Digital Image Processing COSC 6380/4393

Digital 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 information

Image Restoration and Reconstruction

Image Restoration and Reconstruction Image Restoration and Reconstruction Image restoration Objective process to improve an image, as opposed to the subjective process of image enhancement Enhancement uses heuristics to improve the image

More information

Final Review. Image Processing CSE 166 Lecture 18

Final Review. Image Processing CSE 166 Lecture 18 Final Review Image Processing CSE 166 Lecture 18 Topics covered Basis vectors Matrix based transforms Wavelet transform Image compression Image watermarking Morphological image processing Segmentation

More information

Filtering and Edge Detection. Computer Vision I. CSE252A Lecture 10. Announcement

Filtering and Edge Detection. Computer Vision I. CSE252A Lecture 10. Announcement Filtering and Edge Detection CSE252A Lecture 10 Announcement HW1graded, will be released later today HW2 assigned, due Wed. Nov. 7 1 Image formation: Color Channel k " $ $ # $ I r I g I b % " ' $ ' = (

More information

Computer Vision I - Basics of Image Processing Part 2

Computer Vision I - Basics of Image Processing Part 2 Computer Vision I - Basics of Image Processing Part 2 Carsten Rother 07/11/2014 Computer Vision I: Basics of Image Processing Roadmap: Basics of Digital Image Processing Computer Vision I: Basics of Image

More information

Robot vision review. Martin Jagersand

Robot vision review. Martin Jagersand Robot vision review Martin Jagersand What is Computer Vision? Computer Graphics Three Related fields Image Processing: Changes 2D images into other 2D images Computer Graphics: Takes 3D models, renders

More information

Computer Vision I - Filtering and Feature detection

Computer Vision I - Filtering and Feature detection Computer Vision I - Filtering and Feature detection Carsten Rother 30/10/2015 Computer Vision I: Basics of Image Processing Roadmap: Basics of Digital Image Processing Computer Vision I: Basics of Image

More information

Artistic Stylization of Images and Video Part III Anisotropy and Filtering Eurographics 2011

Artistic Stylization of Images and Video Part III Anisotropy and Filtering Eurographics 2011 Artistic Stylization of Images and Video Part III Anisotropy and Filtering Eurographics 2011 Hasso-Plattner-Institut, University of Potsdam, Germany Image/Video Abstraction Stylized Augmented Reality for

More information

Linear Operations Using Masks

Linear Operations Using Masks Linear Operations Using Masks Masks are patterns used to define the weights used in averaging the neighbors of a pixel to compute some result at that pixel Expressing linear operations on neighborhoods

More information

CHAPTER 3 IMAGE ENHANCEMENT IN THE SPATIAL DOMAIN

CHAPTER 3 IMAGE ENHANCEMENT IN THE SPATIAL DOMAIN CHAPTER 3 IMAGE ENHANCEMENT IN THE SPATIAL DOMAIN CHAPTER 3: IMAGE ENHANCEMENT IN THE SPATIAL DOMAIN Principal objective: to process an image so that the result is more suitable than the original image

More information

Anno accademico 2006/2007. Davide Migliore

Anno 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 information

[ ] Review. Edges and Binary Images. Edge detection. Derivative of Gaussian filter. Image gradient. Tuesday, Sept 16

[ ] 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 information

EECS 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 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 information

CSci 4968 and 6270 Computational Vision, Fall Semester, 2011 Lectures 2&3, Image Processing. Corners, boundaries, homogeneous regions, textures?

CSci 4968 and 6270 Computational Vision, Fall Semester, 2011 Lectures 2&3, Image Processing. Corners, boundaries, homogeneous regions, textures? 1 Introduction CSci 4968 and 6270 Computational Vision, Fall Semester, 2011 Lectures 2&3, Image Processing How Do We Start Working with Images? Corners, boundaries, homogeneous regions, textures? How do

More information

Image Restoration and Reconstruction

Image Restoration and Reconstruction Image Restoration and Reconstruction Image restoration Objective process to improve an image Recover an image by using a priori knowledge of degradation phenomenon Exemplified by removal of blur by deblurring

More information

Biomedical Image Analysis. Point, Edge and Line Detection

Biomedical 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 information

Lecture 5: Frequency Domain Transformations

Lecture 5: Frequency Domain Transformations #1 Lecture 5: Frequency Domain Transformations Saad J Bedros sbedros@umn.edu From Last Lecture Spatial Domain Transformation Point Processing for Enhancement Area/Mask Processing Transformations Image

More information

Image Processing: Final Exam November 10, :30 10:30

Image Processing: Final Exam November 10, :30 10:30 Image Processing: Final Exam November 10, 2017-8:30 10:30 Student name: Student number: Put your name and student number on all of the papers you hand in (if you take out the staple). There are always

More information

Noise Model. Important Noise Probability Density Functions (Cont.) Important Noise Probability Density Functions

Noise Model. Important Noise Probability Density Functions (Cont.) Important Noise Probability Density Functions Others -- Noise Removal Techniques -- Edge Detection Techniques -- Geometric Operations -- Color Image Processing -- Color Spaces Xiaojun Qi Noise Model The principal sources of noise in digital images

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 14 130307 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Stereo Dense Motion Estimation Translational

More information

EXAM SOLUTIONS. Computer Vision Course 2D1420 Thursday, 11 th of march 2003,

EXAM SOLUTIONS. Computer Vision Course 2D1420 Thursday, 11 th of march 2003, Numerical Analysis and Computer Science, KTH Danica Kragic EXAM SOLUTIONS Computer Vision Course 2D1420 Thursday, 11 th of march 2003, 8.00 13.00 Exercise 1 (5*2=10 credits) Answer at most 5 of the following

More information

PSD2B Digital Image Processing. Unit I -V

PSD2B Digital Image Processing. Unit I -V PSD2B Digital Image Processing Unit I -V Syllabus- Unit 1 Introduction Steps in Image Processing Image Acquisition Representation Sampling & Quantization Relationship between pixels Color Models Basics

More information

Lecture 4: Image Processing

Lecture 4: Image Processing Lecture 4: Image Processing Definitions Many graphics techniques that operate only on images Image processing: operations that take images as input, produce images as output In its most general form, an

More information

Computer Vision and Graphics (ee2031) Digital Image Processing I

Computer Vision and Graphics (ee2031) Digital Image Processing I Computer Vision and Graphics (ee203) Digital Image Processing I Dr John Collomosse J.Collomosse@surrey.ac.uk Centre for Vision, Speech and Signal Processing University of Surrey Learning Outcomes After

More information

JNTUWORLD. 4. Prove that the average value of laplacian of the equation 2 h = ((r2 σ 2 )/σ 4 ))exp( r 2 /2σ 2 ) is zero. [16]

JNTUWORLD. 4. Prove that the average value of laplacian of the equation 2 h = ((r2 σ 2 )/σ 4 ))exp( r 2 /2σ 2 ) is zero. [16] Code No: 07A70401 R07 Set No. 2 1. (a) What are the basic properties of frequency domain with respect to the image processing. (b) Define the terms: i. Impulse function of strength a ii. Impulse function

More information

Computer Vision. Fourier Transform. 20 January Copyright by NHL Hogeschool and Van de Loosdrecht Machine Vision BV All rights reserved

Computer Vision. Fourier Transform. 20 January Copyright by NHL Hogeschool and Van de Loosdrecht Machine Vision BV All rights reserved Van de Loosdrecht Machine Vision Computer Vision Fourier Transform 20 January 2017 Copyright 2001 2017 by NHL Hogeschool and Van de Loosdrecht Machine Vision BV All rights reserved j.van.de.loosdrecht@nhl.nl,

More information

Assignment 3: Edge Detection

Assignment 3: Edge Detection Assignment 3: Edge Detection - EE Affiliate I. INTRODUCTION This assignment looks at different techniques of detecting edges in an image. Edge detection is a fundamental tool in computer vision to analyse

More information

Announcements. Edge Detection. An Isotropic Gaussian. Filters are templates. Assignment 2 on tracking due this Friday Midterm: Tuesday, May 3.

Announcements. 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 information

CoE4TN4 Image Processing. Chapter 5 Image Restoration and Reconstruction

CoE4TN4 Image Processing. Chapter 5 Image Restoration and Reconstruction CoE4TN4 Image Processing Chapter 5 Image Restoration and Reconstruction Image Restoration Similar to image enhancement, the ultimate goal of restoration techniques is to improve an image Restoration: a

More information

Image processing in frequency Domain

Image processing in frequency Domain Image processing in frequency Domain Introduction to Frequency Domain Deal with images in: -Spatial domain -Frequency domain Frequency Domain In the frequency or Fourier domain, the value and location

More information

Point and Spatial Processing

Point and Spatial Processing Filtering 1 Point and Spatial Processing Spatial Domain g(x,y) = T[ f(x,y) ] f(x,y) input image g(x,y) output image T is an operator on f Defined over some neighborhood of (x,y) can operate on a set of

More information

Motion Estimation. There are three main types (or applications) of motion estimation:

Motion Estimation. There are three main types (or applications) of motion estimation: Members: D91922016 朱威達 R93922010 林聖凱 R93922044 謝俊瑋 Motion Estimation There are three main types (or applications) of motion estimation: Parametric motion (image alignment) The main idea of parametric motion

More information

Fourier Transform and Texture Filtering

Fourier Transform and Texture Filtering Fourier Transform and Texture Filtering Lucas J. van Vliet www.ph.tn.tudelft.nl/~lucas Image Analysis Paradigm scene Image formation sensor pre-processing Image enhancement Image restoration Texture filtering

More information

Optic Flow and Basics Towards Horn-Schunck 1

Optic Flow and Basics Towards Horn-Schunck 1 Optic Flow and Basics Towards Horn-Schunck 1 Lecture 7 See Section 4.1 and Beginning of 4.2 in Reinhard Klette: Concise Computer Vision Springer-Verlag, London, 2014 1 See last slide for copyright information.

More information

SECTION 5 IMAGE PROCESSING 2

SECTION 5 IMAGE PROCESSING 2 SECTION 5 IMAGE PROCESSING 2 5.1 Resampling 3 5.1.1 Image Interpolation Comparison 3 5.2 Convolution 3 5.3 Smoothing Filters 3 5.3.1 Mean Filter 3 5.3.2 Median Filter 4 5.3.3 Pseudomedian Filter 6 5.3.4

More information

Image Processing Fundamentals. Nicolas Vazquez Principal Software Engineer National Instruments

Image Processing Fundamentals. Nicolas Vazquez Principal Software Engineer National Instruments Image Processing Fundamentals Nicolas Vazquez Principal Software Engineer National Instruments Agenda Objectives and Motivations Enhancing Images Checking for Presence Locating Parts Measuring Features

More information

EECS490: Digital Image Processing. Lecture #19

EECS490: Digital Image Processing. Lecture #19 Lecture #19 Shading and texture analysis using morphology Gray scale reconstruction Basic image segmentation: edges v. regions Point and line locators, edge types and noise Edge operators: LoG, DoG, Canny

More information

Lecture 4: Spatial Domain Transformations

Lecture 4: Spatial Domain Transformations # Lecture 4: Spatial Domain Transformations Saad J Bedros sbedros@umn.edu Reminder 2 nd Quiz on the manipulator Part is this Fri, April 7 205, :5 AM to :0 PM Open Book, Open Notes, Focus on the material

More information

Chapter 3: Intensity Transformations and Spatial Filtering

Chapter 3: Intensity Transformations and Spatial Filtering Chapter 3: Intensity Transformations and Spatial Filtering 3.1 Background 3.2 Some basic intensity transformation functions 3.3 Histogram processing 3.4 Fundamentals of spatial filtering 3.5 Smoothing

More information

Image Processing. Traitement d images. Yuliya Tarabalka Tel.

Image 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 information

CSci 4968 and 6270 Computational Vision, Fall Semester, Lectures 2&3, Image Processing

CSci 4968 and 6270 Computational Vision, Fall Semester, Lectures 2&3, Image Processing CSci 4968 and 6270 Computational Vision, Fall Semester, 2010-2011 Lectures 2&3, Image Processing 1 Introduction Goals of SIFT Dense, repeatable, matchable features Invariance to scale and rotation Pseudo-invariance

More information

C E N T E R A T H O U S T O N S C H O O L of H E A L T H I N F O R M A T I O N S C I E N C E S. Image Operations II

C E N T E R A T H O U S T O N S C H O O L of H E A L T H I N F O R M A T I O N S C I E N C E S. Image Operations II T H E U N I V E R S I T Y of T E X A S H E A L T H S C I E N C E C E N T E R A T H O U S T O N S C H O O L of H E A L T H I N F O R M A T I O N S C I E N C E S Image Operations II For students of HI 5323

More information

Babu Madhav Institute of Information Technology Years Integrated M.Sc.(IT)(Semester - 7)

Babu Madhav Institute of Information Technology Years Integrated M.Sc.(IT)(Semester - 7) 5 Years Integrated M.Sc.(IT)(Semester - 7) 060010707 Digital Image Processing UNIT 1 Introduction to Image Processing Q: 1 Answer in short. 1. What is digital image? 1. Define pixel or picture element?

More information

Detecting and Identifying Moving Objects in Real-Time

Detecting and Identifying Moving Objects in Real-Time Chapter 9 Detecting and Identifying Moving Objects in Real-Time For surveillance applications or for human-computer interaction, the automated real-time tracking of moving objects in images from a stationary

More information

Edges and Binary Images

Edges 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 information

Lecture: Edge Detection

Lecture: Edge Detection CMPUT 299 Winter 2007 Lecture: Edge Detection Irene Cheng Overview. What is a pixel in an image? 2. How does Photoshop, + human assistance, detect an edge in a picture/photograph? 3. Behind Photoshop -

More information

Announcements. Edges. Last Lecture. Gradients: Numerical Derivatives f(x) Edge Detection, Lines. Intro Computer Vision. CSE 152 Lecture 10

Announcements. Edges. Last Lecture. Gradients: Numerical Derivatives f(x) Edge Detection, Lines. Intro Computer Vision. CSE 152 Lecture 10 Announcements Assignment 2 due Tuesday, May 4. Edge Detection, Lines Midterm: Thursday, May 6. Introduction to Computer Vision CSE 152 Lecture 10 Edges Last Lecture 1. Object boundaries 2. Surface normal

More information

CS 229 Project report: Extracting vital signs from video

CS 229 Project report: Extracting vital signs from video CS 229 Project report: Extracting vital signs from video D.Deriso, N. Banerjee, A. Fallou Abstract In both developing and developed countries, reducing the cost of medical care is a primary goal of science

More information

Fundamentals of Digital Image Processing

Fundamentals of Digital Image Processing \L\.6 Gw.i Fundamentals of Digital Image Processing A Practical Approach with Examples in Matlab Chris Solomon School of Physical Sciences, University of Kent, Canterbury, UK Toby Breckon School of Engineering,

More information

Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects

Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects Intelligent Control Systems Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects Shingo Kagami Graduate School of Information Sciences, Tohoku University swk(at)ic.is.tohoku.ac.jp http://www.ic.is.tohoku.ac.jp/ja/swk/

More information

Dense Image-based Motion Estimation Algorithms & Optical Flow

Dense Image-based Motion Estimation Algorithms & Optical Flow Dense mage-based Motion Estimation Algorithms & Optical Flow Video A video is a sequence of frames captured at different times The video data is a function of v time (t) v space (x,y) ntroduction to motion

More information

Segmentation and Grouping

Segmentation 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 information

Biomedical Image Analysis. Mathematical Morphology

Biomedical Image Analysis. Mathematical Morphology Biomedical Image Analysis Mathematical Morphology Contents: Foundation of Mathematical Morphology Structuring Elements Applications BMIA 15 V. Roth & P. Cattin 265 Foundations of Mathematical Morphology

More information

Review for the Final

Review for the Final Review for the Final CS 635 Review (Topics Covered) Image Compression Lossless Coding Compression Huffman Interpixel RLE Lossy Quantization Discrete Cosine Transform JPEG CS 635 Review (Topics Covered)

More information

Vivekananda. Collegee of Engineering & Technology. Question and Answers on 10CS762 /10IS762 UNIT- 5 : IMAGE ENHANCEMENT.

Vivekananda. Collegee of Engineering & Technology. Question and Answers on 10CS762 /10IS762 UNIT- 5 : IMAGE ENHANCEMENT. Vivekananda Collegee of Engineering & Technology Question and Answers on 10CS762 /10IS762 UNIT- 5 : IMAGE ENHANCEMENT Dept. Prepared by Harivinod N Assistant Professor, of Computer Science and Engineering,

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 11 140311 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Motion Analysis Motivation Differential Motion Optical

More information

Laser sensors. Transmitter. Receiver. Basilio Bona ROBOTICA 03CFIOR

Laser sensors. Transmitter. Receiver. Basilio Bona ROBOTICA 03CFIOR Mobile & Service Robotics Sensors for Robotics 3 Laser sensors Rays are transmitted and received coaxially The target is illuminated by collimated rays The receiver measures the time of flight (back and

More information

Artifacts and Textured Region Detection

Artifacts and Textured Region Detection Artifacts and Textured Region Detection 1 Vishal Bangard ECE 738 - Spring 2003 I. INTRODUCTION A lot of transformations, when applied to images, lead to the development of various artifacts in them. In

More information

Capturing, Modeling, Rendering 3D Structures

Capturing, Modeling, Rendering 3D Structures Computer Vision Approach Capturing, Modeling, Rendering 3D Structures Calculate pixel correspondences and extract geometry Not robust Difficult to acquire illumination effects, e.g. specular highlights

More information

Lossy Coding 2 JPEG. Perceptual Image Coding. Discrete Cosine Transform JPEG. CS559 Lecture 9 JPEG, Raster Algorithms

Lossy Coding 2 JPEG. Perceptual Image Coding. Discrete Cosine Transform JPEG. CS559 Lecture 9 JPEG, Raster Algorithms CS559 Lecture 9 JPEG, Raster Algorithms These are course notes (not used as slides) Written by Mike Gleicher, Sept. 2005 With some slides adapted from the notes of Stephen Chenney Lossy Coding 2 Suppose

More information

Morphological Image Processing

Morphological Image Processing Morphological Image Processing Binary dilation and erosion" Set-theoretic interpretation" Opening, closing, morphological edge detectors" Hit-miss filter" Morphological filters for gray-level images" Cascading

More information

CS4733 Class Notes, Computer Vision

CS4733 Class Notes, Computer Vision CS4733 Class Notes, Computer Vision Sources for online computer vision tutorials and demos - http://www.dai.ed.ac.uk/hipr and Computer Vision resources online - http://www.dai.ed.ac.uk/cvonline Vision

More information

Image Processing. Daniel Danilov July 13, 2015

Image Processing. Daniel Danilov July 13, 2015 Image Processing Daniel Danilov July 13, 2015 Overview 1. Principle of digital images and filters 2. Basic examples of filters 3. Edge detection and segmentation 1 / 25 Motivation For what image processing

More information

Part 3: Image Processing

Part 3: Image Processing Part 3: Image Processing Moving Window Transform Georgy Gimel farb COMPSCI 373 Computer Graphics and Image Processing 1 / 62 1 Examples of linear / non-linear filtering 2 Moving window transform 3 Gaussian

More information

Filtering in frequency domain

Filtering in frequency domain Filtering in frequency domain FFT FFT = Inverse FFT Filtering in frequency domain Can be faster than filtering in spatial domain (for large filters) Can help understand effect of filter Algorithm: 1. Convert

More information

Image Pyramids and Applications

Image Pyramids and Applications Image Pyramids and Applications Computer Vision Jia-Bin Huang, Virginia Tech Golconda, René Magritte, 1953 Administrative stuffs HW 1 will be posted tonight, due 11:59 PM Sept 25 Anonymous feedback Previous

More information

Boundary descriptors. Representation REPRESENTATION & DESCRIPTION. Descriptors. Moore boundary tracking

Boundary descriptors. Representation REPRESENTATION & DESCRIPTION. Descriptors. Moore boundary tracking Representation REPRESENTATION & DESCRIPTION After image segmentation the resulting collection of regions is usually represented and described in a form suitable for higher level processing. Most important

More information

Implementing the Scale Invariant Feature Transform(SIFT) Method

Implementing the Scale Invariant Feature Transform(SIFT) Method Implementing the Scale Invariant Feature Transform(SIFT) Method YU MENG and Dr. Bernard Tiddeman(supervisor) Department of Computer Science University of St. Andrews yumeng@dcs.st-and.ac.uk Abstract The

More information

Computer Vision I. Announcement. Corners. Edges. Numerical Derivatives f(x) Edge and Corner Detection. CSE252A Lecture 11

Computer 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 information

Feature Extraction and Image Processing, 2 nd Edition. Contents. Preface

Feature Extraction and Image Processing, 2 nd Edition. Contents. Preface , 2 nd Edition Preface ix 1 Introduction 1 1.1 Overview 1 1.2 Human and Computer Vision 1 1.3 The Human Vision System 3 1.3.1 The Eye 4 1.3.2 The Neural System 7 1.3.3 Processing 7 1.4 Computer Vision

More information

Line, edge, blob and corner detection

Line, edge, blob and corner detection Line, edge, blob and corner detection Dmitri Melnikov MTAT.03.260 Pattern Recognition and Image Analysis April 5, 2011 1 / 33 Outline 1 Introduction 2 Line detection 3 Edge detection 4 Blob detection 5

More information

Digital Image Processing

Digital Image Processing Digital Image Processing Jen-Hui Chuang Department of Computer Science National Chiao Tung University 2 3 Image Enhancement in the Spatial Domain 3.1 Background 3.4 Enhancement Using Arithmetic/Logic Operations

More information