{"product_id":"9783031870156","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eTari, Farid; Salarinoghabi, Mostafa; Hasegawa, Masaru\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp class=\"MsoNormal\" style=\"margin-bottom: .0001pt; line-height: normal; background: white;\"\u003e\u003cspan lang=\"EN-GB\"\u003eThis book presents new and original results on the deformations of apparent contours of surfaces in Euclidean 3-space and the discriminants of plane-to-plane map-germs. Given a viewing direction, the apparent contour (also called the profile or outline) is the projection of the set of points on the surface where the viewing direction is tangent to the surface. Apparent contours are extensively used in computer vision and image analysis and pose significant mathematical challenges. \u003c\/span\u003e\u003c\/p\u003e\n\u003cp class=\"MsoNormal\" style=\"margin-bottom: .0001pt; line-height: normal; background: white;\"\u003e\u003cspan lang=\"EN-GB\"\u003e \u003c\/span\u003e\u003cspan lang=\"EN-GB\"\u003eAs the viewing direction varies, the apparent contour deforms, with emerging and vanishing inflections and vertices. The book provides a complete catalog of these bifurcations for generic surfaces as the viewing direction changes. Additionally, it explores geometric invariants that determine the maximum number of inflections and vertices that may appear in such deformations of an apparent contour. Aimed at researchers working in differential geometry, singularity theory, computer vision, and related areas, the text can also serve as material for an undergraduate reading course.\u003c\/span\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2025-04-25\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031870156\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-87016-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 186\u003c\/p\u003e ","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":45369841254540,"sku":"9783031870156","price":76.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031870156.jpg?v=1777979532","url":"https:\/\/lateknightbooks.com\/products\/9783031870156","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}