ÐAutomatic transformation of paper documents into electronic documents requires geometric document layout analysis at the first stage. However, variations in character font sizes, text line spacing, and document layout structures have made it difficult to design a general-purpose document layout analysis algorithm for many years. The use of some parameters has therefore been unavoidable in prev...

Bones are composed of hierarchical bio-composite materials characterized by complex multiscale structural geometry and behavior. The architecture and the mechanical properties of bone tissue differ at each level of hierarchy. Thus, a multiscale approach for mechanical analysis of bone is imperative. This paper proposes a new approach for 3D multiscale finite element analysis of trabecular bone ...

We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scale...

Since their introduction a little more than 10 years ago, wavelets have revolutionized image processing. Wavelet based algorithms define the state-of-the-art for applications including image coding (JPEG2000), restoration, and segmentation. Despite their success, wavelets have significant shortcomings in their treatment of edges. Wavelets do not parsimoniously capture even the simplest geometri...

We generalize some characterizations of uniformly rectifiable (UR) sets to whose Hausdorff content is lower regular (and in particular, do not need be Ahlfors regular). For example, David and Semmes showed that, given an $d$-regular set $E$, if we consider the $\mathscr{B}$ surface cubes (in sense Christ David) near which $E$ does look approximately like a union planes, then UR only satisfies C...

Image Compression using Multiscale Geometric Edge Models

Representing geometric properties of objects in medical images independent of object size necessarily requires a multiscale, or scale space, analysis. We describe means called cores for representing middle and width properties of greyscale image objects via scale space measurements and describe an efficient algorithm for their computation called stimulated cores. We present applications of stim...

Introduction Multiscale image analysis has gained firm ground in computer vision, image processing and models of biological vision. The approaches however have been characterised by a wide variety of techniques, many of them chosen ad hoc. Scale-space theory, as a relatively new field, has been established as a well founded, general and promising multiresolution technique for image structure an...

The widely used feature representation scheme for magnetic resonance (MR) image classification based on low-frequency subband (LFS) coefficients of wavelet transform (WT) is ineffective in presence of common MR imaging (MRI) artifacts (small rotation, low dynamic range etc.). The directional information present in the high-frequency subbands (HFSs) can be used to improve the performance. Moreov...