We explore the oscillatory behavior observed in inversion methods applied to large-scale flow models, including text-to-image and text-to-video. By employing an augmented fixed-point-inspired iterative approach to invert real-world images, we observe that the solution does not achieve convergence, instead oscillating between distinct clusters. Through both experiments on synthetic data, text-to-image and text-to-video, we demonstrate that these oscillating clusters exhibit notable semantic coherence. We offer theoretical insights, showing that this behavior arises from oscillatory dynamics in flow models. Building on this understanding, we introduce a simple and fast distribution transfer technique that facilitates training-free image and video editing/enhancement. Furthermore, we provide quantitative results demonstrating the effectiveness of our method on tasks such as image enhancement, editing, and reconstruction. Notably, our approach enables the transformation of image-only enhancers and editors into lightweight, video-capable tools—without additional training—highlighting its practical versatility and impact.

We present Parametric Piecewise Linear Networks (PPLNs) for temporal vision inference. Motivated by the neuromorphic principles that regulate biological neural behaviors, PPLNs are ideal for processing data captured by event cameras, which are built to simulate neural activities in the human retina. We discuss how to represent the membrane potential of an artificial neuron by a parametric piecewise linear function with learnable coefficients. This design echoes the idea of building deep models from learnable parametric functions recently popularized by Kolmogorov–Arnold Networks (KANs). Experiments demonstrate the state-of-the-art performance of PPLNs in event-based and image-based vision applications, including steering prediction, human pose estimation, and motion deblurring.

A fundamental problem in scan-based 3D reconstruction is to align the depth scans under different camera poses into the same coordinate system. While there are abundant algorithms on aligning depth scans, few methods have focused on assessing the quality of a solution. This quality checking problem is vital, as we need to determine whether the current scans are sufficient or not and where to install additional scans to improve the reconstruction. On the other hand, this problem is fundamentally challenging because the underlying ground-truth is generally unavailable, and it is challenging to predict alignment errors such as global drifts manually. In this paper, we introduce a local uncertainty framework for geometric alignment algorithms. Our approach enjoys several appealing properties, such as it does not require re-sampling the input, no need for the underlying ground-truth, informative, and high computational efficiency. We apply this framework to two multi-scan alignment formulations, one minimizes geometric distances between pairs of scans, and another simultaneously aligns the input scans with a deforming model. The output of our approach can be seamlessly integrated with view selection, enabling uncertainty-aware view planning. Experimental results and user studies justify the effectiveness of our approach on both synthetic and real datasets.

Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps. The first step estimates relative transformations between pairs of scans using an off-the-shelf technique. Due to limited information presented between pairs of scans, the resulting relative transformations are generally noisy. The second step then jointly optimizes the relative transformations among all input depth scans. A natural constraint used in this step is the cycle-consistency constraint, which allows us to prune incorrect relative transformations by detecting inconsistent cycles. The performance of such approaches, however, heavily relies on the quality of the input relative transformations. Instead of merely using the relative transformations as the input to perform transformation synchronization, we propose to use a neural network to learn the weights associated with each relative transformation. Our approach alternates between transformation synchronization using weighted relative transformations and predicting new weights of the input relative transformations using a neural network. We demonstrate the usefulness of this approach across a wide range of datasets.

Optimizing a network of maps among a collection of objects/domains (or map synchronization) is a central problem across computer vision and many other relevant fields. Compared to optimizing pairwise maps in isolation, the benefit of map synchronization is that there are natural constraints among a map network that can improve the quality of individual maps. While such self-supervision constraints are well-understood for undirected map networks (e.g., the cycle-consistency constraint), they are under-explored for directed map networks, which naturally arise when maps are given by parametric maps (e.g., a feed-forward neural network). In this paper, we study a natural self-supervision constraint for directed map networks called path-invariance, which enforces that composite maps along different paths between a fixed pair of source and target domains are identical. We introduce path-invariance bases for efficient encoding of the path-invariance constraint and present an algorithm that outputs a path-variance basis with polynomial time and space complexities. We demonstrate the effectiveness of our formulation on optimizing object correspondences, estimating dense image maps via neural networks, and 3D scene segmentation via map networks of diverse 3D representations. In particular, our approach only requires 8\% labeled data from ScanNet to achieve the same performance as training a single 3D semantic segmentation network with 30\% to 100\% labeled data.

A recent trend in optimizing maps such as dense correspondences between objects or neural networks between pairs of domains is to optimize them jointly. In this context, there is a natural \textsl{cycle-consistency} constraint, which regularizes composite maps associated with cycles, i.e., they are forced to be identity maps. However, as there is an exponential number of cycles in a graph, how to sample a subset of cycles becomes critical for efficient and effective enforcement of the cycle-consistency constraint. This paper presents an algorithm that select a subset of weighted cycles to minimize a condition number of the induced joint optimization problem. Experimental results on benchmark datasets justify the effectiveness of our approach for optimizing dense correspondences between 3D shapes and neural networks for predicting dense image flows.

Establishing high-quality correspondence maps between geometric shapes has been shown to be the fundamental problem in managing geometric shape collections. Prior work has focused on computing efficient maps between pairs of shapes, and has shown a quantifiable benefit of joint map synchronization, where a collection of shapes are used to improve (denoise) the pairwise maps for consistency and correctness. However, these existing map synchronization techniques place very strong assumptions on the input shapes collection such as all the input shapes fall into the same category and/or the majority of the input pairwise maps are correct. In this paper, we present a multiple map synchronization approach that takes a heterogeneous shape collection as input and simultaneously outputs consistent dense pairwise shape maps. We achieve our goal by using a novel tensor-based representation for map synchronization, which is efficient and robust than all prior matrix-based representations. We demonstrate the usefulness of this approach across a wide range of geometric shape datasets and the applications in shape clustering and shape co-segmentation.

We introduce a principled approach for simultaneous mapping and clustering (SMAC) for establishing consistent maps across heterogeneous object collections (e.g., 2D images or 3D shapes). Our approach takes as input a heterogeneous object collection and a set of maps computed between some pairs of objects, and outputs a homogeneous object clustering together with a new set of maps possessing optimal intra- and inter-cluster consistency. Our approach is based on the spectral decomposition of a data matrix storing all pairwise maps in its blocks. We additionally provide tight theoretical guarantees on the exactness of SMAC under established noise models. We also demonstrate the usefulness of the approach on synthetic and real datasets.

In this paper, we introduce a robust algorithm, \textsl{TranSync}, for the 1D translation synchronization problem, in which the aim is to recover the global coordinates of a set of nodes from noisy measurements of relative coordinates along an observation graph. The basic idea of TranSync is to apply truncated least squares, where the solution at each step is used to gradually prune out noisy measurements. We analyze TranSync under both deterministic and randomized noisy models, demonstrating its robustness and stability. Experimental results on synthetic and real datasets show that TranSync is superior to state-of-the-art convex formulations in terms of both efficiency and accuracy.