filters - 1 Filtering Most slides from Steve Seitz 2 What...

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Unformatted text preview: 1 Filtering Most slides from Steve Seitz 2 What is an image? We can think of an image as a function, f , from R 2 to R: f ( x, y ) gives the intens ity at position ( x, y ) Realistically, we expect the image only to be defined over a rectangle, with a finite range: f : [ a , b ] x [ c , d ] [0,1] A color image is just three functions pasted together. We can write this as a vector-valued function: ( , ) ( , ) ( , ) ( , ) r x y f x y g x y b x y = 3 Images as functions 4 What is a digital image? In computer vision we usually operate on digital ( dis crete ) images: Sample the 2D space on a regular grid Quantize each sample (round to nearest integer) If our samples are apart, we can write this as: f [ i , j ] = Quantize{ f ( i , j ) } The image can now be represented as a matrix of integer values 5 Image proces s ing An image proces s ing operation typically defines a new image g in terms of an existing image f. We can transform either the domain or the range of f . Range trans formation : Whats kinds of operations can this perform? 6 Image proces s ing Some operations preserve the range but change the domain of f : What kinds of operations can this perform? 7...
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filters - 1 Filtering Most slides from Steve Seitz 2 What...

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