PDEs for tensor image processing

Methods based on partial differential equations (PDEs) belong to those image processing techniques that can be extended in a particularly elegant way to tensor fields. In this survey paper the most important PDEs for discontinuity-preserving denoising of tensor fields are reviewed such that the underlying design principles becomes evident. We consider isotropic and anisotropic diffusion filters and their corresponding variational methods, mean curvature motion, and selfsnakes. These filters preserve positive semidefiniteness of any positive semidefinite initial tensor field. Finally we discuss geodesic active contours for segmenting tensor fields. Experiments are presented that illustrate the behaviour of all these methods

Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

In Llanas and Lantarón, J. Sci. Comput. 46, 485–518 (2011) we proposed an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of ℝ d . This procedure is based on adaptive splitting of the domain of the function guided by the value of an average integral. The above study was limited to the 1D and 2D versions of the algorithm. In this paper we address the three-dimensional problem. We prove an integral inequality (in the case d=3) which constitutes the basis of EDAS-3. We have performed detailed computational experiments demonstrating effective edge detection in 3D function models with different interface topologies. EDAS-1 and EDAS-2 appealing properties are extensible to the 3D cas

Osteocrin, a novel bone-specific secreted protein that modulates the osteoblast phenotype

Although a number of secreted factors have been demonstrated to be bone regulators, none of these are unique to bone. Using a viral- based signal- trap strategy we have identified a novel gene we have termed " osteocrin." A 1280- bp mRNA encodes osteocrin producing a mature protein of 103 amino acids with a molecular mass of 11.4 kDa. Osteocrin shows no homology with any known gene except for two conserved sequence motifs reminiscent of dibasic cleavage sites found in peptide hormone precursors. Immunofluorescence and Western blot analysis confirmed the secretory nature of osteocrin. Two protein species were identified in the medium of cells overexpressing osteocrin, a full- length 11.4 kDa species and a processed similar to 5 kDa species. Mutation of the (KKKR79)-K-76 dibasic cleavage site abolished the appearance of this smaller osteocrin fragment. By in situ hybridization in mouse embryos, osteocrin was expressed specifically in Cbfa- 1- positive, osteocalcin- negative osteoblasts. Immunohistochemistry on adult mouse bone showed osteocrin localization in osteoblasts and young osteocytes. By Northern blot analysis, osteocrin expression was only detected in bone, expression peaking just after birth and decreasing markedly with age. In primary osteoblastic cell cultures osteocrin expression coincided with matrix formation then decreased in very mature cultures. Treatment of cultures with 1,25- dihydroxyvitamin D-3 resulted in a rapid dose- dependent down- regulation of osteocrin expression, suggesting direct regulation. Chronic treatment of primary cultures with osteocrin- conditioned media inhibited mineralization and reduced osteocalcin and alkaline phosphatase expression. These results suggest that osteocrin represents a novel, unique vitamin D- regulated bone- specific protein that appears to act as a soluble osteoblast regulator

A new sharpness measure based on Gaussian Lines And Edges

We measure the sharpness of natural (complex) images using Gaussian models. We first locate lines and edges in the image. We apply Gaussian derivatives at different scales to the lines and edges. This yields a response function, to which we can fit the response function of model lines and edges. We can thus estimate the width and amplitude of the line or edge. As measure of the sharpness we propose the 5 of the sigmas or the number of line/edge pixels with a sigma smaller than 1

Designing 3-D Nonlinear Diffusion Filters for High Performance Cluster Computing

This paper deals with parallelization and implementation aspects of PDE based image processing models for large cluster environments with distributed memory. As an example we focus on nonlinear isotropic di#usion filtering which we discretize by means of an additive operator splitting (AOS). We start by decomposing the algorithm into small modules that shall be parallelized separately. For this purpose image partitioning strategies are discussed and their impact on the communication pattern and volume is analyzed. Based on the results we develop an algorithmic implementation with excellent scaling properties on massively connected low latency networks. Test runs on a high--end Myrinet cluster yield almost linear speedup factors up to 209 for 256 processors. This results in typical denoising times of 0.5 seconds for five iterations on a 256 128 data cube