LBP and irregular graph pyramids

In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes the topological category (local max, min, slope, saddle) of the gray level landscape around the center region. Given a 2D grayscale image I, our goal is to obtain a simplified image which can be seen as “minimal” representation in terms of topological characterization of I. For this, a method is developed based on merging regions and Minimum Contrast Algorithm

Dual graph contraction with LEDA

Graphs are useful tools for modeling problems that occur in a variety of fields. In machine vision graphs based solutions have been successfully applied to many image processing problem e.g. quad trees for image compression and regional adjacency graphs for segmentation. The application of graphs to machine vision problems poses special problems due to the underlying size of the image e.g. a graph representing the base level of a 512x512 image has over 200.000 nodes. The large size of the graphs make issues of both space and time complexity important when designing algorithms for machine vision problems. We present an implementation under LEDA (Library of Efficient Data structures andAlgorithms) of DGC (dual graph contraction) for irregular pyramids. In the first section we present the theory behind DGC, in the second an algorithmic specification is derived, and in the third an implementation under LEDAis given followed by a short conclusion. 1 Theory of DGC The pres..

Calculating the Number of Tunnels

This paper considers 2-regions of grid cubes and proposes an algorithm for calculating the number of tunnels of such a. region. The graph-theoretical algorithm proceeds layer by layer; a proof of its correctness is provided, and its time complexity is also given

Congratulations! Dual Graphs are Now Orientated!

A digital image can be perceived as a 2.5D surface consisting of pixel coordinates and the intensity of pixel as height of the point in the surface. Such surfaces can be e ciently represented by the pair of dual plane graphs: neighborhood (primal) graph and its dual. By de ning ori- entation of edges in the primal graph and use of Local Binary Patters (LBPs), we can categorize the vertices corresponding to the pixel into critical (maximum, minimum, saddle) or slope points. Basic operation of contraction and removal of edges in primal graph result in con guration of graphs with di erent combinations of critical and non-critical points. The faces of graph resemble a slope region after restoration of the contin- uous surface by successive monotone cubic interpolation. In this paper, we de ne orientation of edges in the dual graph such that it remains consistent with the primal graph. Further we deliver the necessary and su cient conditions for merging of two adjacent slope regions

On the Space Between Critical Points

The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifold M with critical points (maxima, minima, saddles), slopes and plateaus being the ones recognized by local binary patterns (LBPs). Neighborhood graph produces a cell decomposition of M: each 0-cell is a vertex in the neighborhood graph, each 1-cell is an edge in the neighborhood graph and, if P is well-composed, each 2-cell is a slope region in M in the sense that every pair of s in the region can be connected by a monotonically increasing or decreasing path. In our previous research, we produced superpixel hierarchies (combinatorial graph pyramids) that are multiresolution segmentations of the given picture. Critical points of P are preserved along the pyramid. Each level of the pyramid produces a slope complex which is a cell decomposition of M preserving critical points of P and such that each 2-cell is a slope region. Slope complexes in different levels of the pyramid are always homeomorphic. Our aim in this research is to explore the configuration at the top level of the pyramid which consists of a slope complex with vertices being only the critical points of P. We also study the number of slope regions on the top