Two Handy Geometric Prediction Methods of Cancer Growth

In present day societies, cancer is a widely spread disease that affects a large proportion of the human population, many research teams are developing algorithms to help medics to understand this disease. In particular, tumor growth has been studied from different viewpoints and different mathematical models have been proposed. Our aim is to make predictions about shape growth, where shapes are given as domains bounded by a closed curve in R2. These predictions are based on geometric properties of plane curves and vectors. We propose two methods of prediction and a comparison between them is shared. Both methods can be used to study the evolution in time of any 2D and 3D geometrical forms such as cancer skin and other types of cancer boundary. The first method is based on observations in the normal direction to the plane curve (boundary) at each point (normal method). The second method is based on observations at the growing boundaries in radial directions from the "center" of the shape (radius method). The real data consist of at least two input curves that bind a plane domain

Detecting Thalamic Abnormalities in Autism Using Cylinder Conformal Mapping

Abstract. A number of studies have documented that autism has a neurobiological basis, but the anatomical extent of these neurobiological abnormalities is largely unknown. In this paper, we applied advanced computational techniques to extract 3D surface models of the thalamus and subsequently analyze highly localized shape variations in a homogeneous group of autism children. In particular, a new conformal parameterization for high genus surfaces is applied in our shape analysis work, which maps the surfaces onto a cylinder domain. Surface matching among different individual meshes is achieved by re-triangulating each mesh according to the template. Children with autism and their controls are compared, and statistical significant abnormalities in thalamus of autism are detected