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Lok Ming Lui

Publications and source records attributed to Lok Ming Lui.

At least 37 records · Page 2Linked to original sources
arXiv2025

Enhancing Facial Classification and Recognition using 3D Facial Models and Deep Learning

Accurate analysis and classification of facial attributes are essential in various applications, from human-computer interaction to security systems. In this work, a novel approach to enhance facial classification and recognition tasks through the integration of 3D facial models with deep learning methods was proposed. We extract the most useful information for various tasks using the 3D Facial Model, leading to improved classification accuracy. Combining 3D facial insights with ResNet architecture, our approach achieves notable results: 100% individual classification, 95.4% gender classification, and 83.5% expression classification accuracy. This method holds promise for advancing facial analysis and recognition research.

cs.CV↗
arXiv2025

Learning-based density-equalizing map

Density-equalizing map (DEM) serves as a powerful technique for creating shape deformations with the area changes reflecting an underlying density function. In recent decades, DEM has found widespread applications in fields such as data visualization, geometry processing, and medical imaging. Traditional approaches to DEM primarily rely on iterative numerical solvers for diffusion equations or optimization-based methods that minimize handcrafted energy functionals. However, these conventional techniques often face several challenges: they may suffer from limited accuracy, produce overlapping artifacts in extreme cases, and require substantial algorithmic redesign when extended from 2D to 3D, due to the derivative-dependent nature of their energy formulations. In this work, we propose a novel learning-based density-equalizing mapping framework (LDEM) using deep neural networks. Specifically, we introduce a loss function that enforces density uniformity and geometric regularity, and utilize a hierarchical approach to predict the transformations at both the coarse and dense levels. Our method demonstrates superior density-equalizing and bijectivity properties compared to prior methods for a wide range of simple and complex density distributions, and can be easily applied to surface remeshing with different effects. Also, it generalizes seamlessly from 2D to 3D domains without structural changes to the model architecture or loss formulation. Altogether, our work opens up new possibilities for scalable and robust computation of density-equalizing maps for practical applications.

cs.GR↗
arXiv2025

Point Cloud Surface Parametrization with HAND and LEG: Hausdorff Approximation from Node-wise Distances and Localized Energy for Geometry

Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on triangular meshes. On the contrary, the theories and methods of point cloud surface parametrization are less researched, despite its rising significance. In this work, we compute surface parametrization in an optimization approach using neural networks, with novel loss functions introduced without extrinsic information, together with theoretical analyses. Based on the theory, we develop an optimization algorithm to improve the parametrization quality. Using our methods, general open surfaces can be parametrized in either free-boundary manner or with arbitrary domain constraints. Landmark matching can also be enforced under our framework. Numerical experiments are conducted and presented, along with applications including surface reconstruction and boundary detection.

cs.CG↗
arXiv2024

QIS : Interactive Segmentation via Quasi-Conformal Mappings

Image segmentation plays a crucial role in extracting important objects of interest from images, enabling various applications. While existing methods have shown success in segmenting clean images, they often struggle to produce accurate segmentation results when dealing with degraded images, such as those containing noise or occlusions. To address this challenge, interactive segmentation has emerged as a promising approach, allowing users to provide meaningful input to guide the segmentation process. However, an important problem in interactive segmentation lies in determining how to incorporate minimal yet meaningful user guidance into the segmentation model. In this paper, we propose the quasi-conformal interactive segmentation (QIS) model, which incorporates user input in the form of positive and negative clicks. Users mark a few pixels belonging to the object region as positive clicks, indicating that the segmentation model should include a region around these clicks. Conversely, negative clicks are provided on pixels belonging to the background, instructing the model to exclude the region near these clicks from the segmentation mask. Additionally, the segmentation mask is obtained by deforming a template mask with the same topology as the object of interest using an orientation-preserving quasiconformal mapping. This approach helps to avoid topological errors in the segmentation results. We provide a thorough analysis of the proposed model, including theoretical support for the ability of QIS to include or exclude regions of interest or disinterest based on the user's indication. To evaluate the performance of QIS, we conduct experiments on synthesized images, medical images, natural images and noisy natural images. The results demonstrate the efficacy of our proposed method.

cs.CV↗
arXiv2024

Shape Prior Segmentation Guided by Harmonic Beltrami Signature

This paper presents a novel shape prior segmentation method guided by the Harmonic Beltrami Signature (HBS). The HBS is a shape representation fully capturing 2D simply connected shapes, exhibiting resilience against perturbations and invariance to translation, rotation, and scaling. The proposed method integrates the HBS within a quasi-conformal topology preserving segmentation framework, leveraging shape prior knowledge to significantly enhance segmentation performance, especially for low-quality or occluded images. The key innovation lies in the bifurcation of the optimization process into two iterative stages: 1) The computation of a quasi-conformal deformation map, which transforms the unit disk into the targeted segmentation area, driven by image data and other regularization terms; 2) The subsequent refinement of this map is contingent upon minimizing the $L_2$ distance between its Beltrami coefficient and the reference HBS. This shape-constrained refinement ensures that the segmentation adheres to the reference shape(s) by exploiting the inherent invariance, robustness, and discerning shape discriminative capabilities afforded by the HBS. Extensive experiments on synthetic and real-world images validate the method's ability to improve segmentation accuracy over baselines, eliminate preprocessing requirements, resist noise corruption, and flexibly acquire and apply shape priors. Overall, the HBS segmentation framework offers an efficient strategy to robustly incorporate the shape prior knowledge, thereby advancing critical low-level vision tasks.

cs.CV↗
arXiv2024

A deep neural network framework for dynamic multi-valued mapping estimation and its applications

This paper addresses the problem of modeling and estimating dynamic multi-valued mappings. While most mathematical models provide a unique solution for a given input, real-world applications often lack deterministic solutions. In such scenarios, estimating dynamic multi-valued mappings is necessary to suggest different reasonable solutions for each input. This paper introduces a deep neural network framework incorporating a generative network and a classification component. The objective is to model the dynamic multi-valued mapping between the input and output by providing a reliable uncertainty measurement. Generating multiple solutions for a given input involves utilizing a discrete codebook comprising finite variables. These variables are fed into a generative network along with the input, producing various output possibilities. The discreteness of the codebook enables efficient estimation of the output's conditional probability distribution for any given input using a classifier. By jointly optimizing the discrete codebook and its uncertainty estimation during training using a specially designed loss function, a highly accurate approximation is achieved. The effectiveness of our proposed framework is demonstrated through its application to various imaging problems, using both synthetic and real imaging data. Experimental results show that our framework accurately estimates the dynamic multi-valued mapping with uncertainty estimation.

cs.CV↗
arXiv2024

A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings

We propose the Topology-Preserving Segmentation Network, a deformation-based model that can extract objects in an image while maintaining their topological properties. This network generates segmentation masks that have the same topology as the template mask, even when trained with limited data. The network consists of two components: the Deformation Estimation Network, which produces a deformation map that warps the template mask to enclose the region of interest, and the Beltrami Adjustment Module, which ensures the bijectivity of the deformation map by truncating the associated Beltrami coefficient based on Quasiconformal theories. The proposed network can also be trained in an unsupervised manner, eliminating the need for labeled training data. This is achieved by incorporating an unsupervised segmentation loss. Our experimental results on various image datasets show that TPSN achieves better segmentation accuracy than state-of-the-art models with correct topology. Furthermore, we demonstrate TPSN's ability to handle multiple object segmentation.

cs.CV↗
arXiv2024

Deep Learning-Based Quasi-Conformal Surface Registration for Partial 3D Faces Applied to Facial Recognition

3D face registration is an important process in which a 3D face model is aligned and mapped to a template face. However, the task of 3D face registration becomes particularly challenging when dealing with partial face data, where only limited facial information is available. To address this challenge, this paper presents a novel deep learning-based approach that combines quasi-conformal geometry with deep neural networks for partial face registration. The proposed framework begins with a Landmark Detection Network that utilizes curvature information to detect the presence of facial features and estimate their corresponding coordinates. These facial landmark features serve as essential guidance for the registration process. To establish a dense correspondence between the partial face and the template surface, a registration network based on quasiconformal theories is employed. The registration network establishes a bijective quasiconformal surface mapping aligning corresponding partial faces based on detected landmarks and curvature values. It consists of the Coefficients Prediction Network, which outputs the optimal Beltrami coefficient representing the surface mapping. The Beltrami coefficient quantifies the local geometric distortion of the mapping. By controlling the magnitude of the Beltrami coefficient through a suitable activation function, the bijectivity and geometric distortion of the mapping can be controlled. The Beltrami coefficient is then fed into the Beltrami solver network to reconstruct the corresponding mapping. The surface registration enables the acquisition of corresponding regions and the establishment of point-wise correspondence between different partial faces, facilitating precise shape comparison through the evaluation of point-wise geometric differences at these corresponding regions. Experimental results demonstrate the effectiveness of the proposed method.

cs.CV↗
arXiv2024

Spherical Density-Equalizing Map for Genus-0 Closed Surfaces

Density-equalizing maps are a class of mapping methods in which the shape deformation is driven by prescribed density information. In recent years, they have been widely used for data visualization on planar domains and planar parameterization of open surfaces. However, the theory and computation of density-equalizing maps for closed surfaces are much less explored. In this work, we develop a novel method for computing spherical density-equalizing maps for genus-0 closed surfaces. Specifically, we first compute a conformal parameterization of the given genus-0 closed surface onto the unit sphere. Then, we perform density equalization on the spherical domain based on the given density information to achieve a spherical density-equalizing map. The bijectivity of the mapping is guaranteed using quasi-conformal theory. We further propose a method for incorporating the harmonic energy and landmark constraints into our formulation to achieve landmark-aligned spherical density-equalizing maps balancing different distortion measures. Using the proposed methods, a large variety of spherical parameterizations can be achieved. Applications to surface registration, remeshing, and data visualization are presented to demonstrate the effectiveness of our methods.

cs.GR↗
arXiv2023

Bijective Density-Equalizing Quasiconformal Map for Multiply-Connected Open Surfaces

This paper proposes a novel method for computing bijective density-equalizing quasiconformal (DEQ) flattening maps for multiply-connected open surfaces. In conventional density-equalizing maps, shape deformations are solely driven by prescribed constraints on the density distribution, defined as the population per unit area, while the bijectivity and local geometric distortions of the mappings are uncontrolled. Also, prior methods have primarily focused on simply-connected open surfaces but not surfaces with more complicated topologies. Our proposed method overcomes these issues by formulating the density diffusion process as a quasiconformal flow, which allows us to effectively control the local geometric distortion and guarantee the bijectivity of the mapping by solving an energy minimization problem involving the Beltrami coefficient of the mapping. To achieve an optimal parameterization of multiply-connected surfaces, we develop an iterative scheme that optimizes both the shape of the target planar circular domain and the density-equalizing quasiconformal map onto it. In addition, landmark constraints can be incorporated into our proposed method for consistent feature alignment. The method can also be naturally applied to simply-connected open surfaces. By changing the prescribed population, a large variety of surface flattening maps with different desired properties can be achieved. The method is tested on both synthetic and real examples, demonstrating its efficacy in various applications in computer graphics and medical imaging.

cs.CG↗
arXiv2023

Fast MRI Reconstruction via Edge Attention

Fast and accurate MRI reconstruction is a key concern in modern clinical practice. Recently, numerous Deep-Learning methods have been proposed for MRI reconstruction, however, they usually fail to reconstruct sharp details from the subsampled k-space data. To solve this problem, we propose a lightweight and accurate Edge Attention MRI Reconstruction Network (EAMRI) to reconstruct images with edge guidance. Specifically, we design an efficient Edge Prediction Network to directly predict accurate edges from the blurred image. Meanwhile, we propose a novel Edge Attention Module (EAM) to guide the image reconstruction utilizing the extracted edge priors, as inspired by the popular self-attention mechanism. EAM first projects the input image and edges into Q_image, K_edge, and V_image, respectively. Then EAM pairs the Q_image with K_edge along the channel dimension, such that 1) it can search globally for the high-frequency image features that are activated by the edge priors; 2) the overall computation burdens are largely reduced compared with the traditional spatial-wise attention. With the help of EAM, the predicted edge priors can effectively guide the model to reconstruct high-quality MR images with accurate edges. Extensive experiments show that our proposed EAMRI outperforms other methods with fewer parameters and can recover more accurate edges.

eess.IV↗
arXiv2022

Automatic Landmark Detection and Registration of Brain Cortical Surfaces via Quasi-Conformal Geometry and Convolutional Neural Networks

In medical imaging, surface registration is extensively used for performing systematic comparisons between anatomical structures, with a prime example being the highly convoluted brain cortical surfaces. To obtain a meaningful registration, a common approach is to identify prominent features on the surfaces and establish a low-distortion mapping between them with the feature correspondence encoded as landmark constraints. Prior registration works have primarily focused on using manually labeled landmarks and solving highly nonlinear optimization problems, which are time-consuming and hence hinder practical applications. In this work, we propose a novel framework for the automatic landmark detection and registration of brain cortical surfaces using quasi-conformal geometry and convolutional neural networks. We first develop a landmark detection network (LD-Net) that allows for the automatic extraction of landmark curves given two prescribed starting and ending points based on the surface geometry. We then utilize the detected landmarks and quasi-conformal theory for achieving the surface registration. Specifically, we develop a coefficient prediction network (CP-Net) for predicting the Beltrami coefficients associated with the desired landmark-based registration and a mapping network called the disk Beltrami solver network (DBS-Net) for generating quasi-conformal mappings from the predicted Beltrami coefficients, with the bijectivity guaranteed by quasi-conformal theory. Experimental results are presented to demonstrate the effectiveness of our proposed framework. Altogether, our work paves a new way for surface-based morphometry and medical shape analysis.

cs.CV↗
arXiv2022

A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging

Many imaging problems can be formulated as mapping problems. A general mapping problem aims to obtain an optimal mapping that minimizes an energy functional subject to the given constraints. Existing methods to solve the mapping problems are often inefficient and can sometimes get trapped in local minima. An extra challenge arises when the optimal mapping is required to be diffeomorphic. In this work, we address the problem by proposing a deep-learning framework based on the Quasiconformal (QC) Teichmuller theories. The main strategy is to learn the Beltrami coefficient (BC) that represents a mapping as the latent feature vector in the deep neural network. The BC measures the local geometric distortion under the mapping, with which the interpretability of the deep neural network can be enhanced. Under this framework, the diffeomorphic property of the mapping can be controlled via a simple activation function within the network. The optimal mapping can also be easily regularized by integrating the BC into the loss function. A crucial advantage of the proposed framework is that once the network is successfully trained, the optimized mapping corresponding to each input data information can be obtained in real time. To examine the efficacy of the proposed framework, we apply the method to the diffeomorphic image registration problem. Experimental results outperform other state-of-the-art registration algorithms in both efficiency and accuracy, which demonstrate the effectiveness of our proposed framework to solve the mapping problem.

cs.CV↗
arXiv2022

A unifying framework for $n$-dimensional quasi-conformal mappings

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal theory can be utilized for ensuring the bijectivity of the mappings. In addition, it is often desirable for the mappings to satisfy certain prescribed geometric constraints and possess low distortion in conformality or volume. In this work, we develop a unifying framework for computing $n$-dimensional quasi-conformal mappings. More specifically, we propose a variational model that integrates quasi-conformal distortion, volumetric distortion, landmark correspondence, intensity mismatch and volume prior information to handle a large variety of deformation problems. We further prove the existence of a minimizer for the proposed model and devise efficient numerical methods to solve the optimization problem. We demonstrate the effectiveness of the proposed framework using various experiments in two- and three-dimensions, with applications to medical image registration, adaptive remeshing and shape modeling.

cs.CG↗
arXiv2022

Topology-Preserving Segmentation Network: A Deep Learning Segmentation Framework for Connected Component

Medical image segmentation, which aims to automatically extract anatomical or pathological structures, plays a key role in computer-aided diagnosis and disease analysis. Despite the problem has been widely studied, existing methods are prone to topological errors. In medical imaging, the topology of the structure, such as the kidney or lung, is usually known. Preserving the topology of the structure in the segmentation process is of utmost importance for accurate image analysis. In this work, a novel learning-based segmentation model is proposed. A {\it topology-preserving segmentation network (TPSN)} is trained to give an accurate segmentation result of an input image that preserves the prescribed topology. TPSN is a deformation-based model that yields a deformation map through a UNet, which takes the medical image and a template mask as inputs. The main idea is to deform a template mask describing the prescribed topology by a diffeomorphism to segment the object in the image. The topology of the shape in the template mask is well preserved under the diffeomorphic map. The diffeomorphic property of the map is controlled by introducing a regularization term related to the Jacobian in the loss function. As such, a topology-preserving segmentation result can be guaranteed. Furthermore, a multi-scale TPSN is developed in this paper that incorporates multi-level information of images to produce more precise segmentation results. To evaluate our method, we applied the 2D TPSN on Ham10000 and 3D TPSN on KiTS21. Experimental results illustrate our method outperforms the baseline UNet segmentation model with/without connected-component analysis (CCA) by both the dice score and IoU score. Besides, results show that our method can produce reliable results even in challenging cases, where pixel-wise segmentation models by UNet and CCA fail to obtain accurate results.

eess.IV↗
arXiv2021

Parallelizable global quasi-conformal parameterization of multiply-connected surfaces via partial welding

Conformal and quasi-conformal mappings have widespread applications in imaging science, computer vision and computer graphics, such as surface registration, segmentation, remeshing, and texture map compression. While various conformal and quasi-conformal parameterization methods for simply-connected surfaces have been proposed, efficient parameterization methods for multiply-connected surfaces are less explored. In this paper, we propose a novel parallelizable algorithm for computing the global conformal and quasi-conformal parameterization of multiply-connected surfaces onto a 2D circular domain using variants of the partial welding algorithm and the Koebe's iteration. The main idea is to partition a multiply-connected surface into several subdomains and compute the free-boundary conformal or quasi-conformal parameterizations of them respectively, and then apply a variant of the partial welding algorithm to reconstruct the global mapping. We apply the Koebe's iteration together with the geodesic algorithm to the boundary points and welding paths before and after the global welding to transform all the boundaries to circles conformally. After getting all the updated boundary conditions, we obtain the global parameterization of the multiply-connected surface by solving the Laplace equation for each subdomain. Using this divide-and-conquer approach, the parameterization of surfaces with very high resolution can be efficiently computed. Experimental results are presented to demonstrate the effectiveness of our proposed algorithms.

math.NA↗
arXiv2021

Harmonic Beltrami Signature: A Novel 2D Shape Representation for Object Classification

There is a growing interest in shape analysis in recent years. We present a novel shape signature for 2D bounded simply-connected domains, named the Harmonic Beltrami signature (HBS). The proposed signature is based on the harmonic extension of the conformal welding map of a unit circle and its Beltrami coefficient. We show that there is a one-to-one correspondence between the quotient space of HBS and the space of 2D simply-connected shapes up to a translation, rotation and scaling. With a suitable normalization, each equivalence class in the quotient space of HBS is associated to a unique representative. It gets rid of the conformal ambiguity. As such, each shape is associated to a unique HBS. Conversely, the associated shape of a HBS can be reconstructed based on quasiconformal Teichmuller theories, which is uniquely determined up to a translation, rotation and scaling. The HBS is thus an effective fingerprint to represent a 2D shape. The robustness of HBS is studied both theoretically and experimentally. With the HBS, simple metric, such as L2, can be used to measure geometric dissimilarity between shapes. Experiments have been carried out to classify shapes in different classes using HBS. Results show good classification performance, which demonstrate the efficacy of our proposed shape signature.

cs.CV↗
arXiv2021

Quasiconformal model with CNN features for large deformation image registration

Image registration has been widely studied over the past several decades, with numerous applications in science, engineering and medicine. Most of the conventional mathematical models for large deformation image registration rely on prescribed landmarks, which usually require tedious manual labeling and are prone to error. In recent years, there has been a surge of interest in the use of machine learning for image registration. In this paper, we develop a novel method for large deformation image registration by a fusion of quasiconformal theory and convolutional neural network (CNN). More specifically, we propose a quasiconformal energy model with a novel fidelity term that incorporates the features extracted using a pre-trained CNN, thereby allowing us to obtain meaningful registration results without any guidance of prescribed landmarks. Moreover, unlike many prior image registration methods, the bijectivity of our method is guaranteed by quasiconformal theory. Experimental results are presented to demonstrate the effectiveness of the proposed method. More broadly, our work sheds light on how rigorous mathematical theories and practical machine learning approaches can be integrated for developing computational methods with improved performance.

cs.CV↗