Related papers: Shape theory via SVD decomposition I
We present the first utterly self-supervised network for dense correspondence mapping between non-isometric shapes. The task of alignment in non-Euclidean domains is one of the most fundamental and crucial problems in computer vision. As 3D…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach.…
We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…
Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using…
Anatomical shape analysis plays a pivotal role in clinical research and hypothesis testing, where the relationship between form and function is paramount. Correspondence-based statistical shape modeling (SSM) facilitates population-level…
In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…
Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space.…
We derive analytical expressions for the shape of the invariant mass distributions of massless Standard Model endproducts in cascade decays involving massive New Physics (NP) particles, D -> Cc -> Bbc -> Aabc, where the final NP particle A…
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…
Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…
Because of their strong theoretical properties, Shapley values have become very popular as a way to explain predictions made by black box models. Unfortuately, most existing techniques to compute Shapley values are computationally very…
This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal blood-vessel (RBV) networks. The shape graphs are represented by…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
Shape information is a strong and valuable prior in segmenting organs in medical images. However, most current deep learning based segmentation algorithms have not taken shape information into consideration, which can lead to bias towards…
The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs)…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
Binary image based classification and retrieval of documents of an intellectual nature is a very challenging problem. Variations in the binary image generation mechanisms which are subject to the document artisan designer including drawing…