Geometric Description of Images as Topographic Maps

1. Front Matter

   Pages 1-14

   PDF

2. Introduction

   • Vicent Caselles, Pascal Monasse

   Pages 1-7

3. The Tree of Shapes of an Image

   • Vicent Caselles, Pascal Monasse

   Pages 9-34

4. Grain Filters

   • Vicent Caselles, Pascal Monasse

   Pages 35-73

5. A Topological Description of the Topographic Map

   • Vicent Caselles, Pascal Monasse

   Pages 75-102

6. Merging the Component Trees

   • Vicent Caselles, Pascal Monasse

   Pages 103-113

7. Computation of the Tree of Shapes of a Digital Image

   • Vicent Caselles, Pascal Monasse

   Pages 115-140

8. Computation of the Tree of Bilinear Level Lines

   • Vicent Caselles, Pascal Monasse

   Pages 141-153

9. Applications

   • Vicent Caselles, Pascal Monasse

   Pages 155-171

10. Back Matter

    Pages 1-18

    PDF

This book discusses the basic geometric contents of an image and presents a treedatastructuretohandleite?ciently.Itanalyzesalsosomemorphological operators that simplify this geometric contents and their implementation in termsofthe datastructuresintroduced.It?nallyreviewsseveralapplications to image comparison and registration, to edge and corner computation, and the selection of features associated to a given scale in images. Let us ?rst say that, to avoid a long list, we shall not give references in this summary; they are obviously contained in this monograph. A gray level image is usually modeled as a function de?ned in a bounded N domain D? R (typically N = 2 for usual snapshots, N=3formedical images or movies) with values in R. The sensors of a camera or a CCD array transform the continuum of light energies to a ?nite interval of values by means of a nonlinear function g. The contrast change g depends on the pr- ertiesofthesensors,butalsoontheilluminationconditionsandthere?ection propertiesofthe objects,andthoseconditionsaregenerallyunknown.Images are thus observed modulo an arbitrary and unknown contrast change.

• Algorithms
• Graph
• Node
• Sim
• algorithm
• data structure
• image processing
• information
• information and communication, circuits
• combinatorics

• Depto. Tecnologia, Universidad Pompeu Fabra, Barcelona, Spain

  Vicent Caselles

• IMAGINE, Ecole des Ponts ParisTech, Marne-la-Vallée CX 2, France

  Pascal Monasse

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