Digital Images in Computer Vision TP2 - Sampling, Quantization, and More
Explore the world of digital images in Computer Vision TP2, covering topics such as sampling, quantization, image structures, and components of a computer vision system. Learn about the pinhole camera model, simple image representation, analog-to-digital conversion, and images as matrices. Understand the fundamentals of image processing and the importance of sampling theory in digital imagery.
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Presentation Transcript
Computer Vision TP2 Digital Images Miguel Coimbra, Francesco Renna
Outline Sampling and quantization Data structures for digital images Computer Vision TP2 - Digital Images
Topic: Sampling and quantization Sampling and quantization Data structures for digital images Computer Vision TP2 - Digital Images
Components of a Computer Vision System Camera Lighting Computer Scene Scene Interpretation Computer Vision TP2 - Digital Images
Digital Images What we see What a computer sees Computer Vision TP2 - Digital Images
Pinhole and the Perspective Projection Is an image being formed on the screen? (x,y) screen YES! But, not a clear one. scene image plane = r ( , , ) x y z y effective focal length, f z optical axis pinhole x r r ' ' ' x x y y = = = = r ' ( , ' x , ' y ) ' f ' ' ' f z f z f z Computer Vision TP2 - Digital Images
Simple Image Model Image as a 2D light- intensity function f ( , ) x y Continuous Non-zero, finite value ( 0 f Intensity , ) x y Position [Gonzalez & Woods] Computer Vision TP2 - Digital Images
Analog to Digital The scene is: projected on a 2D plane, sampled on a regular grid, and each sample is quantized (rounded to the nearest integer) ( ) ( ) = i j , Quantize , f i j f Computer Vision TP2 - Digital Images
Images as Matrices 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) (0,0) (0,N-1) (M-1,0) Pixel Computer Vision TP2 - Digital Images
Sampling Theorem ( ) x f Continuous signal: x Shah function (Impulse train): ( ) x ( ) = n ( ) x = s x nx s 0 x 0x ( ) x ( ) ( ) s x ( ) x ( ) = n = = f f x f x nx Sampled function: 0 s Computer Vision TP2 - Digital Images
Sampling Theorem 1 x Sampled function: ( ) x ( ) ( ) s x ( ) x ( ) = n Sampling frequency = = f f x f x nx 0 s 0 FSu ( )= F u ( ) S u ( )= F u ( ) 1 u n n= x0 x0 ( ) u ( ) u A FS F A 0x u u u u max max 1 x 1x u Only if 0 max 2 0 Computer Vision TP2 - Digital Images
Nyquist Theorem ( ) u FS 1 x u If max 2 A Aliasing 0x 0 u u max 1x 0 2u Sampling frequency must be greater than max Computer Vision TP2 - Digital Images
Aliasing Input signal: Matlab output: Picket fence receding into the distance will produce aliasing WHY? x = 0:.05:5; imagesc(sin((2.^x).*x)) Computer Vision TP2 - Digital Images
Quantization Analog: Digital: Infinite storage space per pixel! Quantization 0 ( , ) f x y Computer Vision TP2 - Digital Images
Quantization Levels G - number of levels m storage bits Round each value to its nearest level = m 2 G Computer Vision TP2 - Digital Images
Effect of quantization Computer Vision TP2 - Digital Images
Effect of quantization Computer Vision TP2 - Digital Images
Image Size Storage space Spatial resolution: N x M Quantization: m bits per pixel Required bits b: = b N M m Rule of thumb: More storage space means more image quality Computer Vision TP2 - Digital Images
Image Scaling This image is too big to fit on the screen. How can we reduce it? How to generate a half- sized version? Computer Vision TP2 - Digital Images
Sub-sampling 1/8 1/4 Throw away every other row and column to create a 1/2 size image - called image sub-sampling Computer Vision TP2 - Digital Images
Sub-sampling 1/2 1/4 (2x zoom) 1/8 (4x zoom) Computer Vision TP2 - Digital Images
Topic: Data structures for digital images Sampling and quantization Data structures for digital images Computer Vision TP2 - Digital Images
Data Structures for Digital Images Are there other ways to represent digital images? What we see What a computer sees Computer Vision TP2 - Digital Images
Chain codes Chains represent the borders of objects. Coding with chain codes. Relative. Assume an initial starting point for each object. Needs segmentation! Freeman Chain Code Using a Freeman Chain Code and considering the top-left pixel as the starting point: 70663422 Computer Vision TP2 - Digital Images
Topological Data Structures Region Adjacency Graph Nodes - Regions Arcs Relationships Describes the elements of an image and their spatial relationships. Needs segmentation! Region Adjacency Graph Computer Vision TP2 - Digital Images
Relational Structures Stores relations between objects. Important semantic information of an image. Needs segmentation and an image description (features)! Relational Table Computer Vision TP2 - Digital Images
Resources Szeliski, Computer Vision: Algorithms and Applications , Springer, 2011 Chapter 2 Image Formation Computer Vision TP2 - Digital Images
