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.
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.
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.
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.
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.
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.
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.
Here we describe a new image representation technique based on the mathematics of transport and optimal transport. The method relies on the combination of the well-known Radon transform for images and a recent signal representation method called the Signed Cumulative Distribution Transform. The newly proposed method generalizes previous transport-related image representation methods to arbitrary functions (images), and thus can be used in more applications. We describe the new transform, and some of its mathematical properties and demonstrate its ability to partition image classes with real and simulated data. In comparison to existing transport transform methods, as well as deep learning-based classification methods, the new transform more accurately represents the information content of signed images, and thus can be used to obtain higher classification accuracies. The implementation of the proposed method in Python language is integrated as a part of the software package PyTransKit, available on Github.
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of closed-form solutions for the one-dimensional optimal transport problem and the associated computational advantages. While such schemes have already been successfully utilized in data science applications, not too many results on their convergence are available. The main contribution of this paper is an almost sure convergence proof for stochastic slicing-and-matching schemes. The proof builds on an interpretation as a stochastic gradient descent scheme on the Wasserstein space. Numerical examples on step-wise image morphing are demonstrated as well.
We introduce Omni-LOS, a neural computational imaging method for conducting holistic shape reconstruction (HSR) of complex objects utilizing a Single-Photon Avalanche Diode (SPAD)-based time-of-flight sensor. As illustrated in Fig. 1, our method enables new capabilities to reconstruct near-$360^\circ$ surrounding geometry of an object from a single scan spot. In such a scenario, traditional line-of-sight (LOS) imaging methods only see the front part of the object and typically fail to recover the occluded back regions. Inspired by recent advances of non-line-of-sight (NLOS) imaging techniques which have demonstrated great power to reconstruct occluded objects, Omni-LOS marries LOS and NLOS together, leveraging their complementary advantages to jointly recover the holistic shape of the object from a single scan position. The core of our method is to put the object nearby diffuse walls and augment the LOS scan in the front view with the NLOS scans from the surrounding walls, which serve as virtual ``mirrors'' to trap lights toward the object. Instead of separately recovering the LOS and NLOS signals, we adopt an implicit neural network to represent the object, analogous to NeRF and NeTF. While transients are measured along straight rays in LOS but over the spherical wavefronts in NLOS, we derive differentiable ray propagation models to simultaneously model both types of transient measurements so that the NLOS reconstruction also takes into account the direct LOS measurements and vice versa. We further develop a proof-of-concept Omni-LOS hardware prototype for real-world validation. Comprehensive experiments on various wall settings demonstrate that Omni-LOS successfully resolves shape ambiguities caused by occlusions, achieves high-fidelity 3D scan quality, and manages to recover objects of various scales and complexity.