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Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…

A key approach to state abstraction is approximating behavioral metrics (notably, bisimulation metrics) in the observation space and embedding these learned distances in the representation space. While promising for robustness to…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…

This paper introduces a novel paradigm for the generalizable neural radiance field (NeRF). Previous generic NeRF methods combine multiview stereo techniques with image-based neural rendering for generalization, yielding impressive results,…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Dynamic brain data, teeming with biological and functional insights, are becoming increasingly accessible through advanced measurements, providing a gateway to understanding the inner workings of the brain in living subjects. However, the…

Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…

Breadth First Search (BFS) and other graph traversal techniques are widely used for measuring large unknown graphs, such as online social networks. It has been empirically observed that an incomplete BFS is biased toward high degree nodes.…

Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is…

A common setting for scientific inference is the ability to sample from a high-fidelity forward model (simulation) without having an explicit probability density of the data. We propose a simulation-based maximum likelihood deconvolution…

Deep neural networks are able to learn multi-layered representation via back propagation (BP). Although the gradient boosting decision tree (GBDT) is effective for modeling tabular data, it is non-differentiable with respect to its input,…

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Black materials play a critical role in applications such as image registration, camera calibration, stray light suppression, and visual design. Although many such materials appear similarly dark under diffuse illumination, their…

Detailed microstructures on specular objects often exhibit intriguing glinty patterns under high-frequency lighting, which is challenging to render using a conventional normal-mapped BRDF. In this paper, we present a manifold-based…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

The realistic rendering of woven and knitted fabrics has posed significant challenges throughout many years. Previously, fiber-based micro-appearance models have achieved considerable success in attaining high levels of realism. However,…

Bidirectional Scattering Distribution Functions (BSDFs) encode how a material reflects or transmits the incoming light. The most commonly used model is the Microfacet BSDF. It computes material response from the micro-geometry of the…

We address the problem of estimating realistic, spatially varying reflectance for complex planetary surfaces such as the lunar regolith, which is critical for high-fidelity rendering and vision-based navigation. Existing lunar rendering…