Metric properties of partial and robust Gromov-Wasserstein distances

The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct metric spaces. They are particularly useful in areas such as network analysis and geometry processing, as computation of a GW distance involves solving for registration between the objects which minimizes geometric distortion. Although GW distances have proven useful for various applications in the recent machine learning literature, it has been observed that they are inherently sensitive to outlier noise and cannot accommodate partial matching. This has been addressed by various constructions building on the GW framework; in this article, we focus specifically on a natural relaxation of the GW optimization problem, introduced by Chapel et al., which is aimed at addressing exactly these shortcomings. Our goal is to understand the theoretical properties of this relaxed optimization problem, from the viewpoint of metric geometry. While the relaxed problem fails to induce a metric, we derive precise characterizations of how it fails the axioms of non-degeneracy and triangle inequality. These observations lead us to define a novel family of distances, whose construction is inspired by the Prokhorov and Ky Fan distances, as well as by the recent work of Raghvendra et al.\ on robust versions of classical Wasserstein distance. We show that our new distances define true metrics, that they induce the same topology as the GW distances, and that they enjoy additional robustness to perturbations. These results provide a mathematically rigorous basis for using our robust partial GW distances in applications where outliers and partial matching are concerns.

SAM-OCTA2: Layer Sequence OCTA Segmentation with Fine-tuned Segment Anything Model 2

Segmentation of indicated targets aids in the precise analysis of optical coherence tomography angiography (OCTA) samples. Existing segmentation methods typically perform on 2D projection targets, making it challenging to capture the variance of segmented objects through the 3D volume. To address this limitation, the low-rank adaptation technique is adopted to fine-tune the Segment Anything Model (SAM) version 2, enabling the tracking and segmentation of specified objects across the OCTA scanning layer sequence. To further this work, a prompt point generation strategy in frame sequence and a sparse annotation method to acquire retinal vessel (RV) layer masks are proposed. This method is named SAM-OCTA2 and has been experimented on the OCTA-500 dataset. It achieves state-of-the-art performance in segmenting the foveal avascular zone (FAZ) on regular 2D en-face and effectively tracks local vessels across scanning layer sequences. The code is available at: https://github.com/ShellRedia/SAM-OCTA2.

Snake with Shifted Window: Learning to Adapt Vessel Pattern for OCTA Segmentation

Segmenting specific targets or structures in optical coherence tomography angiography (OCTA) images is fundamental for conducting further pathological studies. The retinal vascular layers are rich and intricate, and such vascular with complex shapes can be captured by the widely-studied OCTA images. In this paper, we thus study how to use OCTA images with projection vascular layers to segment retinal structures. To this end, we propose the SSW-OCTA model, which integrates the advantages of deformable convolutions suited for tubular structures and the swin-transformer for global feature extraction, adapting to the characteristics of OCTA modality images. Our model underwent testing and comparison on the OCTA-500 dataset, achieving state-of-the-art performance. The code is available at: https://github.com/ShellRedia/Snake-SWin-OCTA.

Linear optimal transport subspaces for point set classification

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. Furthermore, our approach exhibits robustness in out-of-distribution scenarios where training and test distributions vary in terms of deformation magnitudes.

Visual Decoding and Reconstruction via EEG Embeddings with Guided Diffusion

How to decode human vision through neural signals has attracted a long-standing interest in neuroscience and machine learning. Modern contrastive learning and generative models improved the performance of fMRI-based visual decoding and reconstruction. However, the high cost and low temporal resolution of fMRI limit their applications in brain-computer interfaces (BCIs), prompting a high need for EEG-based visual reconstruction. In this study, we present an EEG-based visual reconstruction framework. It consists of a plug-and-play EEG encoder called the Adaptive Thinking Mapper (ATM), which is aligned with image embeddings, and a two-stage EEG guidance image generator that first transforms EEG features into image priors and then reconstructs the visual stimuli with a pre-trained image generator. Our approach allows EEG embeddings to achieve superior performance in image classification and retrieval tasks. Our two-stage image generation strategy vividly reconstructs images seen by humans. Furthermore, we analyzed the impact of signals from different time windows and brain regions on decoding and reconstruction. The versatility of our framework is demonstrated in the magnetoencephalogram (MEG) data modality. We report that EEG-based visual decoding achieves SOTA performance, highlighting the portability, low cost, and high temporal resolution of EEG, enabling a wide range of BCI applications. The code of ATM is available at https://github.com/dongyangli-del/EEG_Image_decode.

Approximation properties of slice-matching operators

Iterative slice-matching procedures are efficient schemes for transferring a source measure to a target measure, especially in high dimensions. These schemes have been successfully used in applications such as color transfer and shape retrieval, and are guaranteed to converge under regularity assumptions. In this paper, we explore approximation properties related to a single step of such iterative schemes by examining an associated slice-matching operator, depending on a source measure, a target measure, and slicing directions. In particular, we demonstrate an invariance property with respect to the source measure, an equivariance property with respect to the target measure, and Lipschitz continuity concerning the slicing directions. We furthermore establish error bounds corresponding to approximating the target measure by one step of the slice-matching scheme and characterize situations in which the slice-matching operator recovers the optimal transport map between two measures. We also investigate connections to affine registration problems with respect to (sliced) Wasserstein distances. These connections can be also be viewed as extensions to the invariance and equivariance properties of the slice-matching operator and illustrate the extent to which slice-matching schemes incorporate affine effects.

SAM-OCTA: Prompting Segment-Anything for OCTA Image Segmentation

In the analysis of optical coherence tomography angiography (OCTA) images, the operation of segmenting specific targets is necessary. Existing methods typically train on supervised datasets with limited samples (approximately a few hundred), which can lead to overfitting. To address this, the low-rank adaptation technique is adopted for foundation model fine-tuning and proposed corresponding prompt point generation strategies to process various segmentation tasks on OCTA datasets. This method is named SAM-OCTA and has been experimented on the publicly available OCTA-500 and ROSE datasets. This method achieves or approaches state-of-the-art segmentation performance metrics. The effect and applicability of prompt points are discussed in detail for the retinal vessel, foveal avascular zone, capillary, artery, and vein segmentation tasks. Furthermore, SAM-OCTA accomplishes local vessel segmentation and effective artery-vein segmentation, which was not well-solved in previous works. The code is available at https://github.com/ShellRedia/SAM-OCTA.

SAM-OCTA: A Fine-Tuning Strategy for Applying Foundation Model to OCTA Image Segmentation Tasks

In the analysis of optical coherence tomography angiography (OCTA) images, the operation of segmenting specific targets is necessary. Existing methods typically train on supervised datasets with limited samples (approximately a few hundred), which can lead to overfitting. To address this, the low-rank adaptation technique is adopted for foundation model fine-tuning and proposed corresponding prompt point generation strategies to process various segmentation tasks on OCTA datasets. This method is named SAM-OCTA and has been experimented on the publicly available OCTA-500 dataset. While achieving state-of-the-art performance metrics, this method accomplishes local vessel segmentation as well as effective artery-vein segmentation, which was not well-solved in previous works. The code is available at: https://github.com/ShellRedia/SAM-OCTA.

An Accurate and Efficient Neural Network for OCTA Vessel Segmentation and a New Dataset

Optical coherence tomography angiography (OCTA) is a noninvasive imaging technique that can reveal high-resolution retinal vessels. In this work, we propose an accurate and efficient neural network for retinal vessel segmentation in OCTA images. The proposed network achieves accuracy comparable to other SOTA methods, while having fewer parameters and faster inference speed (e.g. 110x lighter and 1.3x faster than U-Net), which is very friendly for industrial applications. This is achieved by applying the modified Recurrent ConvNeXt Block to a full resolution convolutional network. In addition, we create a new dataset containing 918 OCTA images and their corresponding vessel annotations. The data set is semi-automatically annotated with the help of Segment Anything Model (SAM), which greatly improves the annotation speed. For the benefit of the community, our code and dataset can be obtained from https://github.com/nhjydywd/OCTA-FRNet.

Nonrigid Object Contact Estimation With Regional Unwrapping Transformer

Acquiring contact patterns between hands and nonrigid objects is a common concern in the vision and robotics community. However, existing learning-based methods focus more on contact with rigid ones from monocular images. When adopting them for nonrigid contact, a major problem is that the existing contact representation is restricted by the geometry of the object. Consequently, contact neighborhoods are stored in an unordered manner and contact features are difficult to align with image cues. At the core of our approach lies a novel hand-object contact representation called RUPs (Region Unwrapping Profiles), which unwrap the roughly estimated hand-object surfaces as multiple high-resolution 2D regional profiles. The region grouping strategy is consistent with the hand kinematic bone division because they are the primitive initiators for a composite contact pattern. Based on this representation, our Regional Unwrapping Transformer (RUFormer) learns the correlation priors across regions from monocular inputs and predicts corresponding contact and deformed transformations. Our experiments demonstrate that the proposed framework can robustly estimate the deformed degrees and deformed transformations, which makes it suitable for both nonrigid and rigid contact.