Optimal Random Matchings, Tours, and Spanning Trees in Hierarchically Separated Trees

We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and {\it bichromatic} versions of the minimum matching, minimum spanning tree, and traveling salesman problems. We also present tight concentration results for the monochromatic problems.Comment: 24 pages, to appear in TC

A Graph Theoretic Approach for Object Shape Representation in Compositional Hierarchies Using a Hybrid Generative-Descriptive Model

A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid generative-descriptive model. First, statistical relationships between parts are learned using a Minimum Conditional Entropy Clustering algorithm. Then, selection of descriptive parts is defined as a frequent subgraph discovery problem, and solved using a Minimum Description Length (MDL) principle. Finally, part compositions are constructed by compressing the internal data representation with discovered substructures. Shape representation and computational complexity properties of the proposed approach and algorithms are examined using six benchmark two-dimensional shape image datasets. Experiments show that CHOP can employ part shareability and indexing mechanisms for fast inference of part compositions using learned shape vocabularies. Additionally, CHOP provides better shape retrieval performance than the state-of-the-art shape retrieval methods.Comment: Paper : 17 pages. 13th European Conference on Computer Vision (ECCV 2014), Zurich, Switzerland, September 6-12, 2014, Proceedings, Part III, pp 566-581. Supplementary material can be downloaded from http://link.springer.com/content/esm/chp:10.1007/978-3-319-10578-9_37/file/MediaObjects/978-3-319-10578-9_37_MOESM1_ESM.pd

Salient Regions for Query by Image Content

Much previous work on image retrieval has used global features such as colour and texture to describe the content of the image. However, these global features are insufficient to accurately describe the image content when different parts of the image have different characteristics. This paper discusses how this problem can be circumvented by using salient interest points and compares and contrasts an extension to previous work in which the concept of scale is incorporated into the selection of salient regions to select the areas of the image that are most interesting and generate local descriptors to describe the image characteristics in that region. The paper describes and contrasts two such salient region descriptors and compares them through their repeatability rate under a range of common image transforms. Finally, the paper goes on to investigate the performance of one of the salient region detectors in an image retrieval situation

Measures of Similarity Between Objects Based on Qualitative Shape Descriptions

A computational approach for comparing qualitative shape descriptions (QSDs) of objects within digital images is presented. First, the dissimilarity of qualitative features of shape is measured: (i) intuitively using conceptual neighbourhood diagrams; and (ii) mathematically using interval distances. Then, a similarity measure between QSDs is defined and tested using images of different categories of the MPEG-7-CE-Shape-1 library, images of tiles used to build mosaics, and a collection of Clipart images. The results obtained show the effectiveness of the similarity measure defined, which is invariant to translations, rotations and scaling, and which implicitly manages deformation of shape parts and incompleteness

Homogenization of Heterogeneous Tissue Scaffold: A Comparison of Mechanics, Asymptotic Homogenization, and Finite Element Approach

Actual prediction of the effective mechanical properties of tissue scaffolds is very important for tissue engineering applications. Currently common homogenization methods are based on three available approaches: standard mechanics modeling, homogenization theory, and finite element methods. Each of these methods has advantages and limitations. This paper presents comparisons and applications of these approaches for the prediction of the effective properties of a tissue scaffold. Derivations and formulations of mechanics, homogenization, and finite element approach as they relate to tissue engineering are described. The process for the development of a computational algorithm, finite element implementation, and numerical solution for calculating the effective mechanical properties of porous tissue scaffolds are also given. A comparison of the results based upon these different approaches is presented. Parametric analyses using the homogenization approach to study the effects of different scaffold materials and pore shapes on the properties of the scaffold are conducted, and the results of the analyses are also presented