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Caselles V., Monasse P. Geometric Description of Images as Topographic Maps

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Caselles V., Monasse P. Geometric Description of Images as Topographic Maps
Springer, 2010. — 200 p.
This book discusses the basic geometric contents of an image and presents a tree data structure to handle ifficiently. It analyzes also some morphological operators that simplify this geometric contents and their implementation in terms of the data structures introduced. It finally reviews several applications to image comparison and registration, to edge and corner computation, and the selection of features associated to a given scale in images.
A gray level image is usually modeled as a function defined in a bounded N domain D⊆RN (typically N=2 for usual snapshots, N=3 for medical images or movies) with values in R. The sensors of a camera or a CCD array transform the continuum of light energies to a finite interval of values by means of a nonlinear function g. The contrast change g depends on the properties of the sensors, but also on the illumination conditions and there reflection properties of the objects, and those conditions are generally unknown. Images are thus observed modulo an arbitrary and unknown contrast change.
The use of a topographic description of images, surfaces, or 3D data has been introduced and motivated in different areas of research, including image processing, computer graphics, and geographic information systems (GIS). The motivations for such a description differ depending on the field of application. In all cases these descriptions aim to achieve an efficient description of the basic shapes in the given image and their topological changes as a function of a physical quantity that depends on the type of data (intensity in images, height in data elevation models, etc.). In computer graphics and geographic information
The Tree of Shapes of an Image
Grain Filters
A Topological Description of the Topographic Map
Merging the Component Trees
Computation of the Tree of Shapes of a Digital Image
Computation of the Tree of Bilinear Level Lines
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