Lecture 2 : Stat 238 . Winter 2012 . A . L . Yuille

1 Lecture 2: Edge Detection and Multi-Scale 1. What is an Image? It is a set of intensity values (usually {0, 255} for a black and white image) defined over a lattice. Each lattice element is called a pixel. The pizel’s intensity is called the pixel value (each pixel will have three values for a color image). Hence the input to a computer vision system is a matrix of numbers (the pixel values). 2. Given a matrix-image, how could you segment it into two regions? There are two types of cues. There are big intensity changes – edges – at the boundary between the two regions. Also the intensity values are similar within each region (foreground and background). Assumes that images are piecewise smooth. Show a clean number-image and a noisy number-image with cross-sections. 3. Filtering images. Smoothing filters and derivative filters. Filterbanks (represent local properties). Convolution and Fourier theory. 4. Piecewise smooth images – a 1980’s model of images. Motivates edge detection and region grouping (by similar intensity values). Empirical justification for this model based on statistics of natural images – weakness of this justification. Texture and image structures at multiple scales. 5. Multiscale. blurring. Aude Oliva – Chuck Close – Dali – Dennis Peli New York Times article. Fourier components – low frequency, high frequency. Blur with Gaussian – eliminates the high frequencies. Limitations of linear smoothing – destroys structure – alternatives later. 6. Statistical Edge Detection. 7. Bayes Decision Theory and Learning. Techniques: 1. Calculus (derivatives and integrals). 2. Filter Theory. Fourier Theory. 3. The Diffusion/Heat equation. Nonlinear diffusion. Differential equations. 4. Basis functions – over-complete bases. Wavelets. Harmonic analysis. 5. Histrograms (non-parameteric probability distributions). 6. Log-likelihood ratio test, Bayes rule, Bayes Decision Theory. 7. Theory of Learning — memorization and generalization – cross-validation. 8. Mixtures of Distributions. Robust and non-robust distributions.