PPT-38655 BMED-2300-02 Lecture 4: Convolution

Ge Wang PhD Biomedical Imaging Center CBISBME RPI wangg6rpiedu January 26 2018 Tue Topic Fri Topic 116 I ntro d u ction 119 MatLab I Basics 123 System 126 Convolution. Convolution is a general purpos e filter effect for images Is a matrix applied to an image and a mathematical operation comprised of integers It works by determining the value of a central pixel by adding the weighted values of all its neighbors tog e LSI Linear shift invariant systems We shall define the term Impulse response in context to LSI systems We shall learn Convolution an operation which helps us find the output of the LTI system given the impulse response and the input signal NOTE I Solution Then N 1 Index of the first nonzero value of xn M 2 Index of the first nonzero value of hn Next write an array brPage 5br DiscreteTime Convolution Example 1 2 3 4 1 5 3 1 2 3 4 5 10 15 20 3 6 9 12 1 3 10 17 29 12 Coefficients of x Convolution op erates on two signals in 1D or two images in 2D you can think of one as the input signal or image and the other called the kernel as a 64257lter on the input image pro ducing an output image so convolution takes two images as input an LTI: . h(t). g(t). g(t) . . h(t). Example: g[n] = u[n] – u[3-n]. h[n] = . . [n] + . . [n-1]. LTI: . h[n]. g[n]. g[n] . . h[n]. Convolution methods:. Method 1: “running sum”. Plot . Dawei Fan. Contents. Introduction. 1. Methodology. 2. RTL Design and Optimization. 3. Physical Layout Design. 4. Conclusion. 5. Introduction. What is convolution?. Convolution . is defined as the . Advanced applications of the GLM, . SPM MEEG Course 2016. Ashwani. . Jha. , UCL . Outline. Experimental Scenario (stop-signal task). Difficulties arising from experimental design. Baseline correction. Advanced applications of the GLM, . SPM MEEG Course 2017. Ashwani. . Jha. , UCL . Outline. Experimental Scenario (stop-signal task). Difficulties arising from experimental design. Baseline correction. CNN. KH Wong. CNN. V7b. 1. Introduction. Very Popular: . Toolboxes: . tensorflow. , . cuda-convnet. and . caffe. (user friendlier). A high performance Classifier (multi-class). Successful in object recognition, handwritten optical character OCR recognition, image noise removal etc.. Fall 2016. Review. Iso. -contours in grayscale images and volumes . Piece-wise linear representations. Polylines . (2D). and . meshes . (3D). Primal and dual methods. Marching Squares (2D) and Cubes (3D). Cross correlation. Convolution. Last time: Convolution and cross-correlation. Properties. Shift-invariant: a sensible thing to require. Linearity: convenient. Can be used for smoothing, sharpening. Also main component of CNNs. C. ă. t. ă. lin. . Ciobanu. Georgi. . Gaydadjiev. Computer Engineering Laboratory. Delft University of Technology. The Netherlands. and. Department of Computer Science . and Engineering. Chalmers University of . Recap. Some algorithms are “less obviously parallelizable”:. Reduction. Sorts. FFT (and certain recursive algorithms). Parallel FFT structure (radix-2). Bit-reversed access. http://staff.ustc.edu.cn/~csli/graduate/algorithms/book6/chap32.htm. Ge Wang, PhD. Biomedical . Imaging . Center. CBIS/BME. , . RPI. wangg6@rpi.edu. March . 9. , 2018. Tue. Topic. Fri. Topic. 1/16. I. ntro. d. u. ction. 1/19. MatLab I (Basics). 1/23. System. 1/26. Convolution.