This paper proposes a novel Subdivision-Fusion Model (SFM) to recognize human actions. In most action recognition tasks, overlapping feature distribution is a common problem leading to overfitting. In the subdivision stage of the proposed SFM, samples in each category are clustered. Then, such samples are grouped into multiple more concentrated subcategories. Boundaries for the subcategories ar...

We investigate whether dual triangular √ 3 subdivision can be made practical. We conclude that it has serious drawbacks. Our analysis provides insights into the sorts of problem which occur with subdivision schemes which break symmetry.

During the development of subdivision surface methods one of the important questions has been the degree of continuity of the limit surface. In particular whether continuity of curvature can be achieved at the extraordinary points. However, there are several different curvature behaviours, not just two, and this note demonstrates them by examples. q 2003 Elsevier Science Ltd. All rights reserved.

The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link. These tilings define a combinatorial space at infinity, similar to the space at infinity for word hyperbolic groups.

Two planar triangulations with a correspondence between two vertex sets are compatible (isomorphic) if they are topologically equivalent. This work presents a simple and robust method for morphing two compatible planar triangulations with identical convex boundaries that locally preserves the intrinsic geometric properties of triangles throughout the morph. The method is based on the barycentri...

A net is a graph consisting of a triangle C and three more vertices, each of degree one and with its neighbour in C, and all adjacent to different vertices of C. We give a polynomial-time algorithm to test whether an input graph has an induced subgraph which is a subdivision of a net. Unlike many similar questions, this does not seem to be solvable by an application of the “three-in-a-tree” sub...

The k-wheel Wk is the graph obtained as a join of a vertex and the cycle of length k. It is proved that a subdivided wheel G embeds isometrically into a hypercube if and only if G is the subdivision graph S(K4) of K4 or G is obtained from the wheel Wk (k¿ 3) by subdividing any of its outer-edges with an odd number of vertices. c © 2003 Elsevier B.V. All rights reserved.

An efficient algorithm for embedding graphs in the torus is presented. Given a graph G, the algorithm either returns an embedding ofG in the torus or a subgraph ofG which is a subdivision of a minimal nontoroidal graph. The algorithm based on [13] avoids the most complicated step of [13] by applying a recent result of Fiedler, Huneke, Richter, and Robertson [5] about the genus of graphs in the ...

It is shown that if T is a connected nontrivial graph and X is an arbitrary finite simplicial complex, then there is a graph G such that the complex Hom(T, G) is homotopy equivalent to X. The proof is constructive, and uses a nerve lemma. Along the way several results regarding Hom complexes, exponentials, and subdivision are established that may be of independent interest.

Gyárfás and Sumner independently conjectured that for every tree T and integer k there is an integer f(k, T ) such that every graph G with χ(G) > f(k, T ) contains either Kk or an induced copy of T . We prove a ‘topological’ version of the conjecture: for every tree T and integer k there is g(k, T ) such that every graph G with χ(G) > g(k, T ) contains either Kk or an induced copy of a subdivis...