Deep learning has been used as a powerful tool for various tasks in computer vision, such as image segmentation, object recognition and data generation. A key part of end-to-end training is designing the appropriate encoder to extract specific features from the input data. However, few encoders maintain the topological properties of data, such as connection structures and global contours. In this paper, we introduce a Voronoi Diagram encoder based on convex set distance (CSVD) and apply it in edge encoding. The boundaries of Voronoi cells is related to detected edges of structures and contours. The CSVD model improves contour extraction in CNN and structure generation in GAN. We also show the experimental results and demonstrate that the proposed model has great potentiality in different visual problems where topology information should be involved.
This paper presents a method of page segmentation based on the approximated area Voronoi diagram. The characteristics of the proposed method are as follows: (1) The Voronoi diagram enables us to obtain the candidates of boundaries of document components from page images with non-Manhattan layout and a skew. (2) The candidates are utilized to estimate the intercharacter and interline gaps without the use of domain-specific parameters to select the boundaries. From the experimental results for 128 images with non-Manhattan layout and the skew of 0° 45° as well as 98 images with Manhattan layout, we have confirmed that the method is effective for extraction of body text regions, and it is as efficient as other methods based on connected component analysis. We develop and evaluate a novel 3D computational bone framework, which is capable of enabling quantitative assessment of bone micro-architecture, bone mineral density and fracture risks. Our model for bone mineral is developed and its parameters are estimated from imaging data obtained with dual energy x-ray absorptiometry and x-ray imaging methods. Using these parameters, we propose a proper 3D microstructure bone model. The research starts by developing a spatio-temporal 3D microstructure bone model using Voronoi tessellation. Then, we simulate and analyze the architecture of human normal bone network and osteoporotic bone network with edge pruning process in an appropriate ratio. Finally, we design several measurements to analyze Bone Mineral Density (BMD) and bone strength based on our model. The validation results clearly demonstrate our 3D Microstructure Bone Model is robust to reflect the properties of bone in the real world. Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however, so far only with flat hyper-surfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein–Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae.  Segmentation of human faces from still images is a research field of rapidly increasing interest. Although the field encounters several challenges, this paper seeks to present a novel face segmentation and facial feature extraction algorithm for gray intensity images (each containing a single face object). Face location and extraction must first be performed to obtain the approximate, if not exact, representation of a given face in an image. The proposed approach is based on the Voronoi diagram (VD), a well-known technique in computational geometry, which generates clusters of intensity values using information from the vertices of the external boundary of Delaunay triangulation (DT). In this way, it is possible to produce segmented image regions. A greedy search algorithm looks for a particular face candidate by focusing its action in elliptical-like regions. VD is presently employed in many fields, but researchers primarily focus on its use in skeletonization and for generating Euclidean distances; this work exploits the triangulations (i.e., Delaunay) generated by the VD for use in this field. A distance transformation is applied to segment face features. We used the BioID face database to test our algorithm. We obtained promising results: 95.14 of faces were correctly segmented; 90.2 of eyes were detected and a 98.03 detection rate was obtained for mouth and nose.