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 CSE 190 [Spring 2015]. , Lecture . 4. Ravi Ramamoorthi. http://. www.cs.ucsd.edu. /~. ravir. To Do . Assignment . 1, Due . Apr 24. . Please . START . EARLY. This lecture completes all the material you need. Vallary S. Bhopatkar. FFT Convolution. Convolution theorem. Convolution theorem for continuous case:. h(t) and g(t) are two functions and H(f) and G(f) are their corresponding Fourier Transform, then convolution is defined as . 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 . Overview. Images. Pixel Filters. Neighborhood Filters. Dithering. Image as a Function. We can think of an . image . as a function, . f. , . f:. . R. 2. . . . R. f . (. x, y. ). . gives the . intensity. 25 50 75 100 125 150 2000 2100 2200 2300 2400 2500 0 25 50 75 100 125 150 2000 2100 2200 2300 2400 2500 0 10 20 30 40 WETE Index of desertification P Goswami and K V Ramesh CSIR Centre for Mathematic Page 2301 Load Pickup ToolsCatalog 2300 November 2013 November 2013 Jumpers & Load Pickup Tools – 2300 Phone: 573-682-5521 Email: hpsliterature@hubbell.com Web: hubbellpowersystems.com Page Zwick. Tel Aviv University. March 2016. Last updated: March 16, 2016. Algorithms . in Action. Fast Fourier Transform. 2. Discrete Fourier Transform (DFT). A very special . linear transformation.  .  . They replace the value of an image pixel with a combination of its neighbors. Basic operations in images. Shift Invariant. Linear. Thanks to David Jacobs for the use of some slides. Consider 1D images. Carl . Doersch. Joint work with Alexei A. . Efros. . & . Abhinav. Gupta. ImageNet. + Deep Learning. Beagle. - Image Retrieval. - Detection (RCNN). - Segmentation (FCN). - Depth Estimation. - …. 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.. 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.