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Image Processing. Introduction and Overview. Instructor: Juyong Zhang juyong@ustc.edu.cn http://staff.ustc.edu.cn/~juyong. . 1. %. {. . {. Introduction and Overview. This presentation is an overview of some of the ideas and techniques to be covered during the course. Topics.

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## Image Processing

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**Image Processing**Introduction and Overview Instructor: Juyong Zhang juyong@ustc.edu.cn http://staff.ustc.edu.cn/~juyong . 1. %. {. . {. . . . . . . .**Introduction and Overview**This presentation is an overview of some of the ideas and techniques to be covered during the course.**Topics**1. Image formation 2. Point processing and equalization 3. The Fourier transform 4. Convolution 5. Spatial filtering 6. Image restoration 7.Advanced topics (sparse fft, total variation, non-local mean, compressed sensing, graph cut, image inpainting…)**References**• Rafael C. Gonzalez, Richard E. Woods, Digital Image Processing • G. Sapiro, Geometric Partial Differential Equations and Image Analysis • IEEE Trans On Image Processing • Siam Journal On Image Science**Grades**• Small projects: 25% • Paper Reading: 25% • Big project: 50%**Projects and paper reading**• Small project: basic image operation • Big project: select one paper in recent years (ICCP, Siggraph, Siggraph Asia, Eurographics) • Paper Reading: A short presentation/report**lens**object image plane Image Formation**light source**Image Formation**Image Formation**projection through lens image of object**Image Formation**projection onto discrete sensor array. digital camera**Image Formation**sampled image**Image Formation**discrete real-valued image**Digital Image Formation: Quantization**discrete color output continuous colors mapped to a finite, discrete set of colors. continuous color input**Digital Image**Color images have 3 values per pixel; monochrome images have 1 value per pixel. a grid of squares, each of which contains a single color each square is called a pixel (for picture element)**Are constructed from three intensity maps.**Each intensity map is pro-jected through a color filter (e.g., red, green, or blue, or cyan, magenta, or yellow) to create a monochrome image. The intensity maps are overlaid to create a color image. Each pixel in a color image is a three element vector. Color Images**- gamma**- brightness original + brightness + gamma histogram mod - contrast original + contrast histogram EQ Point Processing**Color Sensing / Color Perception**The eye has 3 types of photoreceptors: sensitive to red, green, or blue light. luminance hue saturation The brain transforms RGB into separate brightness and color channels (e.g., LHS). brain photo receptors**these complex exponentials are 2D sinusoids.**The 2D Fourier Transform of a Digital Image Let I(r,c) be a single-band (intensity) digital image with R rows and C columns. Then, I(r,c) has Fourier representation where are the R x C Fourier coefficients.**2D Sinusoids:**... are plane waves with grayscale amplitudes, periods in terms of lengths, ... A**The Fourier Transform of an Image**magnitude phase Ð[F{I}] I |F{I}|**sFFT**DFT: O(n*n) FFT: O(n*logn) sFFT: O(k*logn), if signal is k-sparse**Convolution**Sums of shifted and weighted copies of images or Fourier transforms. Sum times 1/5**Convolution Property of the Fourier Transform**The Fourier Transform of a product equals the convolution of the Fourier Transforms. Similarly, the Fourier Transform of a convolution is the product of the Fourier Transforms**Frequency Domain (FD) Filtering**Power Spectrum Original Image**FD Filtering: Lowpass**Image size: 512x512 SD filter sigma = 8 Filtered Image Filtered Power Spectrum Original Image**FD Filtering: Highpass**Image size: 512x512 FD notch sigma = 8 Filtered Image Filtered Power Spectrum Original Image**Spatial Filtering**blurred original sharpened**Spatial Filtering**Bandpass filter original**Motion Blur**regional vertical original rotational zoom**Motion deblur**Input Output**High dynamic range imaging**• A greater dynamic range between the lightest and darkest areas of an image than current standard digital image methods**Image Compression**Original image is 5244w x 4716h @ 1200 ppi: 127MBytes**Image Compression: JPEG**File size in bytes JPEG quality level**Image Compositing**• Combine parts from separate images to form a new image. • It’s difficult to do well. • Requires relative positions, orientations, and scales to be correct. • Lighting of objects must be consistent within the separate images. • Brightness, contrast, color balance, and saturation must match. • Noise color, amplitude, and patterns must be seamless.**Image Compositing Example**Prof. Peters in his home office. Needs a better shirt.**Image Compositing Example**This shirt demands a monogram.**Image Compositing Example**He needs some more color.**Image Compositing Example**Nice. Now for the way he’d wear his hair if he had any.**Image Compositing Example**He can’t stay in the office like this.**Image Compositing Example**Where’s a hepcat Daddy-O like this belong?**Image Compositing Example**Collar this jive, Jackson. Like crazy, Man ! In the studio!**Outline**1. Non linear PDEs 2. Variational Methods 3. Geometrical Schemes**Noisy image**Denoised image**Total variation model**input output**Medical image segmentation**Initial contour Final contour

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