Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axis

The medial axis, a lower-dimensional shape descriptor, plays an important role in the field of digital geometry processing. Despite its importance, robust computation of the medial axis transform from diverse inputs, especially point clouds with defects, remains a significant challenge. In this paper, we tackle the challenge by proposing a new implicit method that diverges from mainstream explicit medial axis computation techniques. Our key technical insight is the difference between the signed distance field (SDF) and the medial field (MF) of a solid shape is the unsigned distance field (UDF) of the shape's medial axis. This allows for formulating medial axis computation as an implicit reconstruction problem. Utilizing a modified double covering method, we extract the medial axis as the zero level-set of the UDF. Extensive experiments show that our method has enhanced accuracy and robustness in learning compact medial axis transform from thorny meshes and point clouds compared to existing methods.

Topological Feature Search Method for Multichannel EEG: Application in ADHD classification

In recent years, the preliminary diagnosis of Attention Deficit Hyperactivity Disorder (ADHD) using electroencephalography (EEG) has garnered attention from researchers. EEG, known for its expediency and efficiency, plays a pivotal role in the diagnosis and treatment of ADHD. However, the non-stationarity of EEG signals and inter-subject variability pose challenges to the diagnostic and classification processes. Topological Data Analysis (TDA) offers a novel perspective for ADHD classification, diverging from traditional time-frequency domain features. Yet, conventional TDA models are restricted to single-channel time series and are susceptible to noise, leading to the loss of topological features in persistence diagrams.This paper presents an enhanced TDA approach applicable to multi-channel EEG in ADHD. Initially, optimal input parameters for multi-channel EEG are determined. Subsequently, each channel's EEG undergoes phase space reconstruction (PSR) followed by the utilization of k-Power Distance to Measure (k-PDTM) for approximating ideal point clouds. Then, multi-dimensional time series are re-embedded, and TDA is applied to obtain topological feature information. Gaussian function-based Multivariate Kernel Density Estimation (MKDE) is employed in the merger persistence diagram to filter out desired topological feature mappings. Finally, persistence image (PI) method is utilized to extract topological features, and the influence of various weighting functions on the results is discussed.The effectiveness of our method is evaluated using the IEEE ADHD dataset. Results demonstrate that the accuracy, sensitivity, and specificity reach 85.60%, 83.61%, and 88.33%, respectively. Compared to traditional TDA methods, our method was effectively improved and outperforms typical nonlinear descriptors. These findings indicate that our method exhibits higher precision and robustness.