arXiv subjects

Mohsen Taheri

Publications and source records attributed to Mohsen Taheri.

5 recordsLinked to original sources

arXiv2026

Model Fitting and Analysis of the Discrete Swept Skeletal Representation for Ellipsoidal Objects

Statistical shape analysis of quasi-ellipsoidal objects, such as groups of hippocampi, is crucial for advancing medical research by aiding in the diagnosis and understanding of various diseases. This work presents a novel object representation method, termed the Locally Parameterized Discrete Swept Skeletal Representation (LPDSSRep). We discuss the model fitting and analysis techniques for this representation, which rely on boundary division and surface flattening. The quality of the model fitting is assessed based on the symmetry and tidiness of the skeletal structure and the volume of the implied boundary. The power of the method is demonstrated by visual inspection and statistical analysis of a synthetic and an actual data set in comparison with an available skeletal representation.

stat.ME↗

arXiv2025

Interior Object Geometry via Fitted Frames

We propose a means of computing fitted frames on the boundary and in the interior of objects and using them to provide the basis for producing geometric features from them that are not only alignment-free but most importantly can be made to correspond locally across a population of objects. We describe a representation targeted for anatomic objects which is designed to enable this strong locational correspondence within object populations and thus to provide powerful object statistics. It accomplishes this by understanding an object as the diffeomorphic deformation of the closure of the interior of an ellipsoid and by using a skeletal representation fitted throughout the deformation to produce a model of the target object, where the object is provided initially in the form of a boundary mesh. Via classification performance on hippocampi shape between individuals with a disorder vs. others, we compare our method to two state-of-theart methods for producing object representations that are intended to capture geometric correspondence across a population of objects and to yield geometric features useful for statistics, and we show notably improved classification performance by this new representation, which we call the evolutionary s-rep. The geometric features that are derived from each of the representations, especially via fitted frames, are discussed.

cs.CV↗

arXiv2024

The Mean Shape under the Relative Curvature Condition

Guaranteeing that Fréchet means of object populations do not locally self-intersect or are thereby affected is a serious challenge for object representations because the objects' shape space typically includes elements corresponding to geometrically invalid objects. We show how to produce a shape space guaranteeing no local self-intersections for specific but important cases where objects are represented by swept elliptical disks. This representation can model a variety of anatomic objects, such as the colon and hippocampus. Our approach of computing geodesic paths in this shape space enables detailed comparisons of structural variations between groups, such as patients and controls. The guarantee is met by constraining the shape space using the Relative Curvature Condition (RCC) of swept regions. This study introduces the Elliptical Tube Representation (ETRep) framework to provide a systematic approach to ensure valid mean shapes, effectively addressing the challenges of complex non-convex spaces while adhering to the RCC. The ETRep shape space incorporates an intrinsic distance metric defined based on the skeletal coordinate system of the shape space. The proposed methodology is applied to statistical shape analysis, facilitating the development of both global and partial hypothesis testing methods, which were employed to investigate hippocampal structures in early Parkinson's disease.

stat.ME↗

arXiv2021

Non-Euclidean Analysis of Joint Variations in Multi-Object Shapes

This paper considers joint analysis of multiple functionally related structures in classification tasks. In particular, our method developed is driven by how functionally correlated brain structures vary together between autism and control groups. To do so, we devised a method based on a novel combination of (1) non-Euclidean statistics that can faithfully represent non-Euclidean data in Euclidean spaces and (2) a non-parametric integrative analysis method that can decompose multi-block Euclidean data into joint, individual, and residual structures. We find that the resulting joint structure is effective, robust, and interpretable in recognizing the underlying patterns of the joint variation of multi-block non-Euclidean data. We verified the method in classifying the structural shape data collected from cases that developed and did not develop into Autistic Spectrum Disorder (ASD).

stat.ML↗

arXiv2021

Statistical analysis of locally parameterized shapes

The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most commonly used method and state of the art. In this work, we uncover that alignment might seriously affect the statistical analysis. For example, alignment can induce false shape differences and lead to misleading results and interpretations. We propose a novel hierarchical shape parameterization based on local coordinate systems. The local parameterized shapes are translation and rotation invariant. Thus, the inherent alignment problems from the commonly used global coordinate system for shape representation can be avoided using this parameterization. The new parameterization is also superior for shape deformation and simulation. The method's power is demonstrated on the hypothesis testing of simulated data as well as the left hippocampi of patients with Parkinson's disease and controls.

stat.ME↗