Shape Representation via Harmonic Embedding
نویسندگان
چکیده
We present a novel representation of shape for closed planar contours explicitly designed to possess a linear structure. This greatly simplifies linear operations such as averaging, principal component analysis or differentiation in the space of shapes. The representation relies upon embedding the contour on a subset of the space of harmonic functions of which the original contour is the zero level set.
منابع مشابه
Boundaries of Planar Graphs, via Circle Packings
We provide a geometric representation of the Poisson and Martin boundaries of a transient, bounded degree triangulation of the plane in terms of its circle packing in the unit disc (this packing is unique up to Möbius transformations). More precisely, we show that any bounded harmonic function on the graph is the harmonic extension of some measurable function on the boundary of the disk, and th...
متن کاملA contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies
In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet's principles, is concurrently able to be expanded in Taylor's representation, over a particular interval of their do...
متن کاملCurvature in image and shape processing
The laplacian operator applied to the coordinates of a manifold provides the mean curvature vector. Manipulating the metric of the manifold or interpreting its coordinates in various ways provide useful tools for shape and image processing and representation. We will review some of these tools focusing on scale invariant geometry, curvature flow with respect to an embedding of the image manifol...
متن کاملModular irreducible representations of the symmetric group as linear codes
We describe a particularly easy way of evaluating the modular irreducible matrix representations of the symmetric group. It shows that Specht’s approach to the ordinary irreducible representations, along Specht polynomials, can be unified with Clausen’s approach to the modular irreducible representations using symmetrized standard bideterminants. The unified method, using symmetrized Specht pol...
متن کاملHarmonic Galois theory for finite graphs
This paper develops a harmonic Galois theory for finite graphs, thereby classifying harmonic branched G-covers of a fixed base X in terms of homomorphisms from a suitable fundamental group of X together with G-inertia structures on X. As applications, we show that finite embedding problems for graphs have proper solutions and prove a Grunwald-Wang type result stating that an arbitrary collectio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003