By Victor Patrangenaru, Leif Ellingson
ISBN-10: 1439820503
ISBN-13: 9781439820506
A New method of interpreting item facts from a Nonparametric Viewpoint
Nonparametric data on Manifolds and Their functions to item information Analysis presents one of many first thorough remedies of the speculation and method for reading info on manifolds. It additionally offers in-depth purposes to functional difficulties bobbing up in quite a few fields, together with records, scientific imaging, computing device imaginative and prescient, trend attractiveness, and bioinformatics.
The publication starts off with a survey of illustrative examples of item information sooner than relocating to a evaluate of options from mathematical facts, differential geometry, and topology. The authors subsequent describe conception and strategies for engaged on a variety of manifolds, giving a historic point of view of suggestions from arithmetic and records. They then current difficulties from a wide selection of parts, together with diffusion tensor imaging, similarity form research, directional information research, and projective form research for desktop imaginative and prescient. The e-book concludes with a dialogue of present similar examine and graduate-level educating subject matters in addition to issues on the topic of computational statistics.
Researchers in varied fields needs to mix statistical technique with options from projective geometry, differential geometry, and topology to investigate info gadgets bobbing up from non-Euclidean item areas. An expert-driven consultant to this technique, this ebook covers the final nonparametric idea for interpreting facts on manifolds, tools for operating with particular areas, and wide functions to useful examine difficulties. those difficulties convey how item facts research opens an impressive door to the area of massive info analysis.
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Extra resources for Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis
Sample text
Jective shape of the scene. Instead, if one has at least two images of the scene, the scene’s 3D projective shape can be extracted, as shown in Chapter 22. We consider a case of 3D projective shape in our next example. 13. 13 and have sides, from top to bottom, of four, six, and ten units. 13 displays a digital image of the object with visible corners, taken as landmarks, numbered from 1 to 19. Sixteen randomly selected pictures of the object that show all of the selected landmarks were paired into eight pairs of images.
5 Coordinates of landmarks in a normal children growth study measured from X-rays at 8 and 14 years of age – part II. 6 Coordinates of landmarks in a normal children growth study measured from X-rays at 8 and 14 years of age – part III. 7 Coordinates of landmarks in a normal children growth study measured from X-rays at 8 and 14 years of age – part IV. 8 Coordinates of landmarks in Apert children, including their age and gender. 42 -0. 84 -0. 3. 3. 3. 3. 3. 3. 3. 3. 17 Coordinates of five landmarks in a normal eye (n) and in a treated eye (0) measured in 12 Rhesus monkeys.
3. 3. 3. 3. 3. 3. 3. 3. 17 Coordinates of five landmarks in a normal eye (n) and in a treated eye (0) measured in 12 Rhesus monkeys.