SELFSIMILAR EXPANDING SOLUTIONS IN A SECTOR FOR A CRYSTALLINE FLOW

For a given sector a selfsimilar expanding solution to a crystalline flow is constructed. The solution is shown to be unique. Because of selfsimilarity the problem is reduced to solve a system of algebraic equations of degree two. The solution is constructed by a method of continuity and obtained by solving associated ordinary differential equations. The selfsimilar expanding solution is useful to construct a crystalline flow from an arbitrary polygon not necessarily admissible

Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis

AbstractA numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations (ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour figure

Case-based similar image retrieval for weakly annotated large histopathological images of malignant lymphoma using deep metric learning

In the present study, we propose a novel case-based similar image retrieval (SIR) method for hematoxylin and eosin (H&E)-stained histopathological images of malignant lymphoma. When a whole slide image (WSI) is used as an input query, it is desirable to be able to retrieve similar cases by focusing on image patches in pathologically important regions such as tumor cells. To address this problem, we employ attention-based multiple instance learning, which enables us to focus on tumor-specific regions when the similarity between cases is computed. Moreover, we employ contrastive distance metric learning to incorporate immunohistochemical (IHC) staining patterns as useful supervised information for defining appropriate similarity between heterogeneous malignant lymphoma cases. In the experiment with 249 malignant lymphoma patients, we confirmed that the proposed method exhibited higher evaluation measures than the baseline case-based SIR methods. Furthermore, the subjective evaluation by pathologists revealed that our similarity measure using IHC staining patterns is appropriate for representing the similarity of H&E-stained tissue images for malignant lymphoma

SELFSIMILAR EXPANDING SOLUTIONS IN A SECTOR FOR A CRYSTALLINE FLOW

For a given sector a selfsimilar expanding solution to a crystalline flow is constructed. The solution is shown to be unique. Because of selfsimilarity the problem is reduced to solve a system of algebraic equations of degree two. The solution is constructed by a method of continuity and obtained by solving associated ordinary differential equations. The selfsimilar expanding solution is useful to construct a crystalline flow from an arbitrary polygon not necessarily admissible