Irregular graph pyramids and representative cocycles of cohomology generators

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed

A New Phase Field Model of a `Gas of Circles' for Tree Crown Extraction from Aerial Images

We describe a model for tree crown extraction from aerial images, a problem of great practical importance for the forestry industry. The novelty lies in the prior model of the region occupied by tree crowns in the image, which is a phase field version of the higher-order active contour inflection point 'gas of circles' model. The model combines the strengths of the inflection point model with those of the phase field framework: it removes the 'phantom circles' produced by the original 'gas of circles' model, while executing two orders of magnitude faster than the contour-based inflection point model. The model has many other areas of application e.g., to imagery in nanotechnology, biology, and physics

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

A Revision of Pyramid Segmentation

Dual graph contraction reduces the number of vertices and of edges of a pair of dual image graphs while, at the same time, the topological relations among the 'surviving ' components are preserved. Repeated application produces a stack of successively smaller graphs: a pair of dual irregular pyramids. The process is controlled by selected decimation parameters which consist of a subset of surviving vertices and associated contraction kernels. Equivalent contraction kernels (ECKs) combine two or more contraction kernels into one single contraction kernel which generates the same result in one single dual contraction. This is the basis to the proof that any segmentation can be represented in one single level of such a pyramid. Experimental results demonstrate the applicability on synthetic and real images respectively. 1 Introduction Pyramids, considered as a stack of interrelated images with decreasing resolution, are useful when dealing with image processing tasks and feature extract..

Z.: Integral Trees: Subtree Depth and Diameter

Abstract. Regions in an image graph can be described by their spanning tree. A graph pyramid is a stack of image graphs at different granularities. Integral features capture important properties of these regions and the associated trees. We compute the depth of a rooted tree, its diameter and the center which becomes the root in the top-down decomposition of a region. The integral tree is an intermediate representation labeling each vertex of the tree with the integral feature(s) of the subtree. Parallel algorithms efficiently compute the integral trees for subtree depth and diameter enabling local decisions with global validity in subsequent top-down processes.

Hierarchy of Partitions with Dual Graph Contraction

We present a hierarchical partitioning of images using a pairwise similarity function on a graph-based representation of an image

A simplified human vision model applied to a blocking artifact metric

A novel approach towards a simplified, though still reliable human vision model based on the spatial masking properties of the human visual system (HVS) is presented. The model contains two basic characteristics of the HVS, namely texture masking and luminance masking. These masking effects are implemented as simple spatial filtering followed by a weighting function, and are efficiently combined into a single visibility coefficient. This HVS model is applied to a blockiness metric by using its output to scale the block-edge strength. To validate the proposed model, its performance in the blockiness metric is determined by comparing it to the same blockiness metric having different HVS-based models embedded. The results show that the proposed model is indeed simple, without compromising its accuracy. © Springer-Verlag Berlin Heidelberg 2007

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