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Mestrado em Ciência de Computadores

VC 17/18 – TP3 Digital Images. Mestrado em Ciência de Computadores Mestrado Integrado em Engenharia de Redes e Sistemas Informáticos. Miguel Tavares Coimbra. Outline. Sampling and quantization Data structures for digital images Histograms. Topic: Sampling and quantization.

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Mestrado em Ciência de Computadores

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  1. VC 17/18 – TP3Digital Images Mestrado em Ciência de Computadores Mestrado Integrado em Engenharia de Redes e Sistemas Informáticos Miguel Tavares Coimbra

  2. Outline • Sampling and quantization • Data structures for digital images • Histograms VC 17/18 - TP3 - Digital Images

  3. Topic: Sampling and quantization • Sampling and quantization • Data structures for digital images • Histograms VC 17/18 - TP3 - Digital Images

  4. Scene Interpretation Components of a Computer Vision System Camera Lighting Computer Scene VC 17/18 - TP3 - Digital Images

  5. What we see What a computer sees Digital Images VC 17/18 - TP3 - Digital Images

  6. Pinhole and the Perspective Projection Is an image being formed on the screen? YES! But, not a “clear” one. (x,y) screen scene image plane y effective focal length, f’ z optical axis pinhole x VC 17/18 - TP3 - Digital Images

  7. Intensity Position Simple Image Model • Image as a 2D light-intensity function • Continuous • Non-zero, finite value [Gonzalez & Woods] VC 17/18 - TP3 - Digital Images

  8. The scene is: projected on a 2D plane, sampled on a regular grid, and each sample is quantized (rounded to the nearest integer) Analog to Digital VC 17/18 - TP3 - Digital Images

  9. Each point is a pixel with amplitude: f(x,y) An image is a matrix with size N x M M = [(0,0) (0,1) … [(1,0) (1,1) … … Images as Matrices (0,0) (0,N-1) (M-1,0) Pixel VC 17/18 - TP3 - Digital Images

  10. Sampling Theorem Continuous signal: Shah function (Impulse train): Sampled function: VC 17/18 - TP3 - Digital Images

  11. Sampling frequency Only if Sampling Theorem Sampledfunction: VC 17/18 - TP3 - Digital Images

  12. If Sampling frequency must be greater than Nyquist Theorem Aliasing VC 17/18 - TP3 - Digital Images

  13. Input signal: Matlab output: WHY? x = 0:.05:5; imagesc(sin((2.^x).*x)) Aliasing Picket fence receding into the distance will produce aliasing… VC 17/18 - TP3 - Digital Images

  14. Quantization • Analog: • Digital: Infinite storage space per pixel! • Quantization VC 17/18 - TP3 - Digital Images

  15. G - number of levels m – storage bits Round each value to its nearest level Quantization Levels VC 17/18 - TP3 - Digital Images

  16. Effect of quantization VC 17/18 - TP3 - Digital Images

  17. Effect of quantization VC 17/18 - TP3 - Digital Images

  18. Image Size • Storage space • Spatial resolution: N x M • Quantization: m bits per pixel • Required bits b: • Rule of thumb: • More storage space means more image quality VC 17/18 - TP3 - Digital Images

  19. Image Scaling This image is too big to fit on the screen. How can we reduce it? How to generate a half- sized version? VC 17/18 - TP3 - Digital Images

  20. Sub-sampling 1/8 1/4 Throw away every other row and column to create a 1/2 size image - called image sub-sampling VC 17/18 - TP3 - Digital Images

  21. Sub-sampling 1/2 1/4 (2x zoom) 1/8 (4x zoom) VC 17/18 - TP3 - Digital Images

  22. Topic: Data structures for digital images • Sampling and quantization • Data structures for digital images • Histograms VC 17/18 - TP3 - Digital Images

  23. What we see What a computer sees Data Structures for Digital Images • Are there other ways to represent digital images? VC 17/18 - TP3 - Digital Images

  24. Chains represent the borders of objects. Coding with chain codes. Relative. Assume an initial starting point for each object. Needs segmentation! Chain codes Freeman Chain Code Using a Freeman Chain Code and considering the top-left pixel as the starting point: 70663422 VC 17/18 - TP3 - Digital Images

  25. Region Adjacency Graph Nodes - Regions Arcs – Relationships Describes the elements of an image and their spatial relationships. Needs segmentation! Topological Data Structures Region Adjacency Graph VC 17/18 - TP3 - Digital Images

  26. Stores relations between objects. Important semantic information of an image. Needs segmentation and an image description (features)! Relational Structures Relational Table VC 17/18 - TP3 - Digital Images

  27. Topic: Histograms • Sampling and quantization • Data structures for digital images • Histograms VC 17/18 - TP3 - Digital Images

  28. “In statistics, a histogram is a graphical display of tabulated frequencies.” [Wikipedia] Typically represented as a bar chart: Histograms VC 17/18 - TP3 - Digital Images

  29. Colour or Intensity distribution. Typically: Reduced number of bins. Normalization. Compressed representation of an image. No spatial information whatsoever! Image Histograms VC 17/18 - TP3 - Digital Images

  30. As many histograms as axis of the colour space. Ex: RGB Colour space - Red Histogram - Green Histogram - Blue Histogram Combined histogram. Colour Histogram Red Green Blue VC 17/18 - TP3 - Digital Images

  31. Resources • R. Gonzalez, and R. Woods – Chapter 2 VC 17/18 - TP3 - Digital Images

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