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Example-based mesh deformation methods are powerful tools for realistic shape editing. However, existing techniques typically combine all the example deformation modes, which can lead to overfitting, i.e. using a overly complicated model to…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
Quantifying aleatoric uncertainty in medical image segmentation is critical since it is a reflection of the natural variability observed among expert annotators. A conventional approach is to model the segmentation distribution using the…
The stochastic density functional theory (sDFT) has exhibited advantages over the standard Kohn-Sham DFT method and has become an attractive approach for large-scale electronic structure calculations. The sDFT method avoids the expensive…
Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…
We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in…
Recent studies have demonstrated advantages of information fusion based on sparsity models for multimodal classification. Among several sparsity models, tree-structured sparsity provides a flexible framework for extraction of…
Medical image segmentation is inherently uncertain. For a given image, there may be multiple plausible segmentation hypotheses, and physicians will often disagree on lesion and organ boundaries. To be suited to real-world application,…
This review presents various image segmentation methods using complex networks. Image segmentation is one of the important steps in image analysis as it helps analyze and understand complex images. At first, it has been tried to classify…
Foreground segmentation is an essential task in the field of image understanding. Under unsupervised conditions, different images and instances always have variable expressions, which make it difficult to achieve stable segmentation…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the…
Recently, Mamba-based methods have become popular in medical image segmentation due to their lightweight design and long-range dependency modeling capabilities. However, current segmentation methods frequently encounter challenges in fetal…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
Recent advancements in multi-modal large language models have propelled the development of joint probabilistic models capable of both image understanding and generation. However, we have identified that recent methods suffer from loss of…
Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential…
Multi-modal image fusion integrates complementary information from different modalities to produce enhanced and informative images. Although State-Space Models, such as Mamba, are proficient in long-range modeling with linear complexity,…
Stochastic partition models tailor a product space into a number of rectangular regions such that the data within each region exhibit certain types of homogeneity. Due to constraints of partition strategy, existing models may cause…
Deep stochastic processes have recently become a central paradigm for image enhancement, with many methods explicitly conditioning the stochastic trajectory on the degraded input. However, the relationship between these conditional…
This paper proposes an Allen-Cahn Chan-Vese model to settle the multi-phase image segmentation. We first integrate the Allen--Cahn term and the Chan--Vese fitting energy term to establish an energy functional, whose minimum locates the…