arXiv subjects

Erchuan Zhang

Publications and source records attributed to Erchuan Zhang.

7 recordsLinked to original sources

arXiv2025

VerteNet -- A Multi-Context Hybrid CNN Transformer for Accurate Vertebral Landmark Localization in Lateral Spine DXA Images

Vertebral Landmarks Localization in Dual-Energy X-ray Absorptiometry based Lateral Spine Imaging plays a critical role in evaluating spinal alignment, Vertebral Fracture Assessment, and facilitating intervertebral guide placement for Abdominal Aortic Calcification quantification. While lateral spine DXA scans offer advantages such as reduced cost and lower radiation exposure, its analysis remains challenging due to a low signal-to-noise ratio and imaging artifacts. Artificial Intelligence presents a promising approach for improving the precision and accuracy of VLL. In this study, we introduce a novel architecture that employs dual-resolution attention mechanisms to capture both fine-grained local details and broader contextual information. Our approach enhances feature integration by leveraging skip connections and decoder layers through dual-resolution self-attention and cross-attention mechanisms. This design improves the ability of the model to learn complex patterns, enabling precise vertebral corner localization while maintaining both local and global contextual awareness. We evaluated the proposed framework on DXA LSI images acquired from multiple machines and found that it outperforms recent state-of-the-art architectures for VLL, achieving a normalized mean error of 4.92 and a normalized median error of 2.35. The proposed framework, VerteNet, enables highly accurate VLL in DXA LSI images from diverse acquisition systems and demonstrates strong robustness to low signal-to-noise ratios, owing to its enhanced ability to capture both fine-grained local details and broader contextual information.

cs.CV↗

arXiv2023

Multi-objective variational curves

Riemannian cubics in tension are critical points of the linear combination of two objective functionals, namely the squared norms of the velocity and acceleration of a curve on a Riemannian manifold. We view this variational problem of finding a curve as a multi-objective optimization problem and construct the Pareto fronts for some given instances where the manifold is a sphere and where the manifold is a torus. The Pareto front for the curves on the torus turns out to be particularly interesting: the front is disconnected and it reveals two distinct Riemannian cubics with the same boundary data, which is the first known nontrivial instance of this kind. We also discuss some convexity conditions involving the Pareto fronts for curves on general Riemannian manifolds.

math.OC↗

arXiv2023

On the Independence Polynomial and Threshold of an Antiregular $k$-Hypergraph

Given an integer $k\geq 3$ and an initial $k-1$ isolated vertices, an {\em antiregular $k$-hypergraph} is constructed by alternatively adding an isolated vertex (connected to no other vertices) or a dominating vertex (connected to every other $k-1$ vertices). Let $a_i$ be the number of independent sets of cardinality $i$ in a hypergraph $H$, then the {\em independence polynomial} of $H$ is defined as $I(H;x)=\sum_{i=0}^m a_i x^i$, where $m$ is the size of a maximum independent set. The main purpose of the present paper is to generalise some results of independence polynomials of antiregular graphs to the case of antiregular $k$-hypergraphs. In particular, we derive (semi-)closed formulas for the independence polynomials of antiregular $k$-hypergraphs and prove their log-concavity. Furthermore, we show that antiregular $k$-hypergraphs are {\em $T2$-threshold}, which means there exist a labeling $c$ of the vertex set and a threshold $τ$ such that for any vertex subset $S$ of cardinality $k$, $\sum_{i\in S}c(i)>τ$ if and only if $S$ is a hyperedge.

math.CO↗

arXiv2022

Maximum Consensus by Weighted Influences of Monotone Boolean Functions

Robust model fitting is a fundamental problem in computer vision: used to pre-process raw data in the presence of outliers. Maximisation of Consensus (MaxCon) is one of the most popular robust criteria and widely used. Recently (Tennakoon et al. CVPR2021), a connection has been made between MaxCon and estimation of influences of a Monotone Boolean function. Equipping the Boolean cube with different measures and adopting different sampling strategies (two sides of the same coin) can have differing effects: which leads to the current study. This paper studies the concept of weighted influences for solving MaxCon. In particular, we study endowing the Boolean cube with the Bernoulli measure and performing biased (as opposed to uniform) sampling. Theoretically, we prove the weighted influences, under this measure, of points belonging to larger structures are smaller than those of points belonging to smaller structures in general. We also consider another "natural" family of sampling/weighting strategies, sampling with uniform measure concentrated on a particular (Hamming) level of the cube. Based on weighted sampling, we modify the algorithm of Tennakoon et al., and test on both synthetic and real datasets. This paper is not promoting a new approach per se, but rather studying the issue of weighted sampling. Accordingly, we are not claiming to have produced a superior algorithm: rather we show some modest gains of Bernoulli sampling, and we illuminate some of the interactions between structure in data and weighted sampling.

cs.CV↗

arXiv2021

Consensus Maximisation Using Influences of Monotone Boolean Functions

Consensus maximisation (MaxCon), which is widely used for robust fitting in computer vision, aims to find the largest subset of data that fits the model within some tolerance level. In this paper, we outline the connection between MaxCon problem and the abstract problem of finding the maximum upper zero of a Monotone Boolean Function (MBF) defined over the Boolean Cube. Then, we link the concept of influences (in a MBF) to the concept of outlier (in MaxCon) and show that influences of points belonging to the largest structure in data would generally be smaller under certain conditions. Based on this observation, we present an iterative algorithm to perform consensus maximisation. Results for both synthetic and real visual data experiments show that the MBF based algorithm is capable of generating a near optimal solution relatively quickly. This is particularly important where there are large number of outliers (gross or pseudo) in the observed data.

cs.CV↗

arXiv2021

Unsupervised Learning for Robust Fitting:A Reinforcement Learning Approach

Robust model fitting is a core algorithm in a large number of computer vision applications. Solving this problem efficiently for datasets highly contaminated with outliers is, however, still challenging due to the underlying computational complexity. Recent literature has focused on learning-based algorithms. However, most approaches are supervised which require a large amount of labelled training data. In this paper, we introduce a novel unsupervised learning framework that learns to directly solve robust model fitting. Unlike other methods, our work is agnostic to the underlying input features, and can be easily generalized to a wide variety of LP-type problems with quasi-convex residuals. We empirically show that our method outperforms existing unsupervised learning approaches, and achieves competitive results compared to traditional methods on several important computer vision problems.

cs.CV↗

arXiv2020

Monotone Boolean Functions, Feasibility/Infeasibility, LP-type problems and MaxCon

This paper outlines connections between Monotone Boolean Functions, LP-Type problems and the Maximum Consensus Problem. The latter refers to a particular type of robust fitting characterisation, popular in Computer Vision (MaxCon). Indeed, this is our main motivation but we believe the results of the study of these connections are more widely applicable to LP-type problems (at least 'thresholded versions', as we describe), and perhaps even more widely. We illustrate, with examples from Computer Vision, how the resulting perspectives suggest new algorithms. Indeed, we focus, in the experimental part, on how the Influence (a property of Boolean Functions that takes on a special form if the function is Monotone) can guide a search for the MaxCon solution.

cs.LG↗