Image Processing ITodayImage FormationSampling and QuantizationSlide 5What is an image?Images as functionsWhat is a digital image?Image processingPoint ProcessingBasic Point ProcessingNegativeLogPower-law transformationsGamma CorrectionImage EnhancementContrast StrechingImage HistogramsCumulative HistogramsHistogram EqualizationHistogram MatchingMatch-histogram codeNeighborhood Processing (filtering)Programming Assignment #1Image Processing I15-463: Rendering and Image ProcessingAlexei Efros…with most slides shamelessly stolenfrom Steve Seitz and Gonzalez & WoodsTodayImage FormationRange Transformations•Point ProcessingProgramming Assignment #1 OUTReading for this week:•Gonzalez & Woods, Ch. 3•Forsyth & Ponce, Ch. 7Image Formationf(x,y) = reflectance(x,y) * illumination(x,y)Reflectance in [0,1], illumination in [0,inf]Sampling and QuantizationSampling and QuantizationWhat is an image?We can think of an image as a function, f, from R2 to R:•f( x, y ) gives the intensity 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 yf x y g x yb x y� �� �=� �� �� �Images as functionsWhat is a digital image?We usually operate on digital (discrete) 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 valuesImage processingAn image processing operation typically defines a new image g in terms of an existing image f.We can transform either the range of f.Or the domain of f:What kinds of operations can each perform?Point ProcessingThe simplest kind of range transformations are these independent of position x,y:g = t(f)This is called point processing.What can they do?What’s the form of t?Important: every pixel for himself – spatial information completely lost!Basic Point ProcessingNegativeLogPower-law transformationsGamma CorrectionGamma Measuring Applet: http://www.cs.berkeley.edu/~efros/java/gamma/gamma.htmlImage EnhancementContrast StrechingImage HistogramsCumulative HistogramsHistogram EqualizationHistogram MatchingMatch-histogram codeNeighborhood Processing (filtering)Q: What happens if I reshuffle all pixels within the image?A: It’s histogram won’t change. No point processing will be affected…Need spatial information to capture this.Programming Assignment #1Easy stuff to get you started with Matlab•James will hold tutorial this weekDistance Functions•SSD•Normalized CorrelationBells and Whistles•Point Processing (color?)•Neighborhood Processing•Using your data (3 copies!)•Using your data (other
View Full Document
Unlocking...