Defining a sound shift operator for signals existing on a certain graphical structure, similar to the well-defined shift operator in classical signal processing, is a crucial problem in graph signal processing. Since almost all operations, such as filtering, transformation, prediction, etc., are directly related to the graph shift operator. We define a unique shift operator that satisfies all p...

In this paper we propose a novel rotation normalization technique for point cloud processing using an oriented bounding box. We use method to create annotation tool part segmentation on real camera data. Custom data sets are used train our network classification and tasks. Successful deployment is completed embedded device with limited power. A comparison made other rotation-invariant features ...

In a linear forest, each component is a path. The linear arboricity ~(G) of a graph G is defined in Harary [8] as the minimum number of linear forests whose union is G. This invariant first arose in a study [i0] of information retrieval in file systems. A quite similar covering invariant which is well known to the linear arboricity is the arboricity of a graph, which is defined as the minimum n...

It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper we reformulate this conjecture using a matroid obtained from the Tait graph (checkerboard graph) G of a knot diagram K. The spanning trees of G provide a filtration and a spectral sequence that converges to the reduced Khovanov homology of K. We show that the E2–term of this spectral sequence is a ...

In graph theory, Graph Isomorphism is an important issue. Information in the database can be stored in the form of graph. Graph represents the structural information in an efficient way. Graph Isomorphism problem is to determine if there exists one to one correspondence between the structures of two graphs. Graph isomorphism problem arises in many fields such as chemistry, switching theory, inf...

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This construction suggests an extension of the Kauffman bracket to an invariant of looped graphs, and an extension of Reidemeister equivalence to an equivalence relation on looped graphs. The graph bracke...