Related papers: Studying Morphological Variation: Exploring the Sh…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
Sampling is a basic operation in image processing. In classic literature, a morphological sampling theorem has been established, which shows how sampling interacts by morphological operations with image reconstruction. Many aspects of…
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic. This control is given as a function defined over the image and parameterises the template…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
We often wish to classify objects by their shapes. Indeed, the study of shapes is an important part of many scientific fields such as evolutionary biology, structural biology, image processing, and archaeology. The most widely-used method…
We present a learning framework for abstracting complex shapes by learning to assemble objects using 3D volumetric primitives. In addition to generating simple and geometrically interpretable explanations of 3D objects, our framework also…
This paper presents bone adaptation as a geometric flow. The proposed method is based on two assumptions: first, that the bone surface is smooth (not fractal) permitting the definition of a tangent plane and, second, that the interface…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…
Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…
Statistical shape modeling is the computational process of discovering significant shape parameters from segmented anatomies captured by medical images (such as MRI and CT scans), which can fully describe subject-specific anatomy in the…
Statistical shape models (SSMs) are a popular tool to conduct morphological analysis of anatomical structures which is a crucial step in clinical practices. However, shape representations through SSMs are based on shape coefficients and…
We propose a novel shape representation useful for analyzing and processing shape collections, as well for a variety of learning and inference tasks. Unlike most approaches that capture variability in a collection by using a template model…
We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
Urban theorists, social reformists and philosophers have considered the city as a living organism since Plato. However, despite extraordinary advancements in evolutionary biology, now being used to explain social and cultural phenomena, a…