03346nam 2200685Ia 450 991076816670332120200520144314.09786613569516978128039159012803915969783642046117364204611810.1007/978-3-642-04611-7(CKB)2670000000007016(SSID)ssj0000399632(PQKBManifestationID)11250031(PQKBTitleCode)TC0000399632(PQKBWorkID)10376321(PQKB)11710124(DE-He213)978-3-642-04611-7(MiAaPQ)EBC3064932(PPN)149078552(EXLCZ)99267000000000701620091009d2010 uy 0engurnn#008mamaatxtccrGeometric description of images as topographic maps /Vicent Caselles, Pascal Monasse1st ed. 2010.Heidelberg Springerc20101 online resource (XVII, 192 p.)Lecture notes in mathematics,0075-8434 ;1984Bibliographic Level Mode of Issuance: Monograph9783642046100 364204610X 9783642046247 364204624X Includes bibliographical references and index.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 -- Applications.This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented. The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8.Lecture Notes in Mathematics,0075-8434 ;1984Image processingMathematical modelsGeometric analysisTopographic mapsImage processingMathematical models.Geometric analysis.Topographic maps.003.5468U1094A0805C05mscCaselles Vicent1960-281922Monasse Pascal506784MiAaPQMiAaPQMiAaPQBOOK9910768166703321Geometric description of images as topographic maps778550UNINA