Lehrveranstaltungsinhalt aus - Institute for Computer Graphics and ...

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44 CHAPTER 1. CHARACTERIZATION OF IMAGES a distance depending on the neighborhood-relationships that we have defined. The Euclidian distance of course is simply obtained by the pythagorean sum of the coordinate differences. But if we take a 4-neighborhood as the base for distance measurements than we have a “city block distance”, two blocks up, two blocks over. Or if we have the 8-neighborhood than we have a “chessboard type of distance”. Let’s define an “edge”. This is important because there is a mathematical definition that is a little different from what one would define an edge to be in a sort casual way. An edge e in an image is a property of a pair of pixels which are neighbors of one another. That is thus a property of a pair of pixels and one needs to consider two pixels to define this. It is important that the two pixels are neighbors under a neighborhood relationship. Any pair of pixels that are neighbors of one another represent an edge. The edge has a “direction” and a “strength”. Clearly the strength of the edge is what is important to us. The edge is defined on an image B and an edge image is obtained by taking each edge value at each pixel. We can apply a threshold to the weight and the direction of the edge. All edges with a weight beyond a certain value become 1 and all edges less than a certain value become 0. In that case now we have converted our image into a binary edge image. What is a line? A line is a finite sequence of edges, with each edge e i , i = 1, . . . n. A line is a sequence of edges where the edges need to be one another’s neighbor under a neighborhood relationship. The edges must be connected. A line has a length, the length is the number of the edges that form that line. What’s a region in the image? A region is a connected set R of pixels from an image B. A region has a contour. A contour is a line composed of edges and the edges are defined with the property of two neighboring pixels P and Q. P must be part of the region R, Q must not be. This sounds all pretty intuitive, but gets pretty complicated once one starts doing operations. Prüfungsfragen: • Wenn wir eine ” Distanz“ zwischen zwei Pixeln in einem Digitalbild anzugeben haben, stehen uns verschiedene Distanzmaße zur Verfügung. Zählen Sie bitte auf, welche Distanzmaße Sie kennen. Sie sind eingeladen, für die Beantwortung Formeln zu nutzen. • Bei der Betrachtung von Pixeln bestehen Nachbarschaften“ von Pixeln. Zählen Sie alle ” Arten von Nachbarschaften auf, die in der Vorlesung behandelt wurden, und beschreiben Sie diese Nachbarschaften mittels je einer Skizze. • Welche Möglichkeiten gibt es, Pixel in einem digitalen Rasterbild als zusammenhängend zu definieren? Erläutern Sie jede Definition anhand einer Skizze. • Zu welchen Zwecken definiert man Nachbarschafts- und Zusammenhangsbeziehungen zwischen Pixeln in digitalen Rasterbildern? • Geben Sie die Definitionen der Begriffe ” Kante“, ” Linie“ und ” Region“ in einem digitalen Rasterbild an. 1.7 Algebraic Operations on Images We can add two images, subtract, multiply, divide them, we can compare images by some logical operations and we can look at one image using a second image as a mask. Suppose we have a source image, an operator and a destination image. Now, depending on the operator we obtain a resulting image. We take a particular source and destination image and make our operator the function “replace” or the function “or” or the function “X or” or the function “and” to then obtain different results. We may have mask operations. In this case we take an image A to
1.7. ALGEBRAIC OPERATIONS ON IMAGES 45 Algorithm 5 Logical mask operations This is an example for a mask operation. Two images are linked with the Boolean OR-operator, pixel by pixel. 1: for all i=0, i
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94 CHAPTER 5. COLOR A monitor prese
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96 CHAPTER 5. COLOR Color in image
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122 CHAPTER 6. IMAGE QUALITY Resolv
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142 CHAPTER 7. FILTERING appearance
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144 CHAPTER 7. FILTERING Getting An
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148 CHAPTER 7. FILTERING Slide 7.29
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150 CHAPTER 7. FILTERING
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152 CHAPTER 8. TEXTURE µ n (z) =
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154 CHAPTER 8. TEXTURE Algorithm 23
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162 CHAPTER 9. TRANSFORMATIONS In t
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256 CHAPTER 15. RESAMPLING images,
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276 CHAPTER 20. IMAGE REPRESENTATIO
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286 APPENDIX A. ALGORITHMEN UND DEF
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290 APPENDIX B. FRAGENÜBERSICHT
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352 INDEX Entzerrung, 287 Erosion,
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354 INDEX Skalierung, 157, 303 Sobe
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356 LIST OF ALGORITHMS 29 z-buffer
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358 LIST OF DEFINITIONS 29 Boundary
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360 LIST OF FIGURES B.12 Lineare Tr
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362 LIST OF FIGURES
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