arXiv subjects

Hao Pan

Publications and source records attributed to Hao Pan.

At least 73 records · Page 4Linked to original sources

arXiv2022

Discovering Design Concepts for CAD Sketches

Sketch design concepts are recurring patterns found in parametric CAD sketches. Though rarely explicitly formalized by the CAD designers, these concepts are implicitly used in design for modularity and regularity. In this paper, we propose a learning based approach that discovers the modular concepts by induction over raw sketches. We propose the dual implicit-explicit representation of concept structures that allows implicit detection and explicit generation, and the separation of structure generation and parameter instantiation for parameterized concept generation, to learn modular concepts by end-to-end training. We demonstrate the design concept learning on a large scale CAD sketch dataset and show its applications for design intent interpretation and auto-completion.

cs.LG↗

arXiv2022

A new theorem on quadratic residues modulo primes

Let $p>3$ be a prime, and let $(\frac{\cdot}p)$ be the Legendre symbol. Let $b\in\mathbb Z$ and $\varepsilon\in\{\pm 1\}$. We mainly prove that $$\left|\left\{N_p(a,b):\ 1 \{ax^2+b\}_p$, and $\{m\}_p$ with $m\in\mathbb{Z}$ is the least nonnegative residue of $m$ modulo $p$.

math.NT↗

arXiv2022

Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation

We present a novel implicit representation -- neural halfspace representation (NH-Rep), to convert manifold B-Rep solids to implicit representations. NH-Rep is a Boolean tree built on a set of implicit functions represented by the neural network, and the composite Boolean function is capable of representing solid geometry while preserving sharp features. We propose an efficient algorithm to extract the Boolean tree from a manifold B-Rep solid and devise a neural network-based optimization approach to compute the implicit functions. We demonstrate the high quality offered by our conversion algorithm on ten thousand manifold B-Rep CAD models that contain various curved patches including NURBS, and the superiority of our learning approach over other representative implicit conversion algorithms in terms of surface reconstruction, sharp feature preservation, signed distance field approximation, and robustness to various surface geometry, as well as a set of applications supported by NH-Rep.

cs.GR↗

arXiv2022

Partitions of nonnegative integers with identical representation functions

Let $\mathbb{N}$ be the set of all nonnegative integers. For any integer $r$ and $m$, let $r+m\mathbb{N}=\{r+mk: k\in\mathbb{N}\}$. For $S\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let $R_{S}(n)$ denote the number of solutions of the equation $n=s+s'$ with $s, s'\in S$ and $s<s'$. Let $r_{1}, r_{2}, m$ be integers with $0<r_{1}<r_{2}<m$ and $2\mid r_{1}$. In this paper, we prove that there exist two sets $C$ and $D$ with $C\cup D=\mathbb{N}$ and $C\cap D=(r_{1}+m\mathbb{N})\cup (r_{2}+m\mathbb{N})$ such that $R_{C}(n)=R_{D}(n)$ for all $n\in\mathbb{N}$ if and only if there exists a positive integer $l$ such that $r_{1}=2^{2l+1}-2, r_{2}=2^{2l+1}-1, m=2^{2l+2}-2$.

math.NT↗

arXiv2022

Partitions of finite nonnegative integer sets with identical representation functions

Let $\mathbb{N}$ be the set of all nonnegative integers. For $S\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let the representation function $R_{S}(n)$ denote the number of solutions of the equation $n=s+s'$ with $s, s'\in S$ and $s<s'$. In this paper, we determine the structure of $C, D\subseteq \mathbb{N}$ with $C\cup D=[0, m]$ and $|C\cap D|=2$ such that $R_{C}(n)=R_{D}(n)$ for any nonnegative integer $n$.

math.NT↗

arXiv2022

DISP6D: Disentangled Implicit Shape and Pose Learning for Scalable 6D Pose Estimation

Scalable 6D pose estimation for rigid objects from RGB images aims at handling multiple objects and generalizing to novel objects. Building on a well-known auto-encoding framework to cope with object symmetry and the lack of labeled training data, we achieve scalability by disentangling the latent representation of auto-encoder into shape and pose sub-spaces. The latent shape space models the similarity of different objects through contrastive metric learning, and the latent pose code is compared with canonical rotations for rotation retrieval. Because different object symmetries induce inconsistent latent pose spaces, we re-entangle the shape representation with canonical rotations to generate shape-dependent pose codebooks for rotation retrieval. We show state-of-the-art performance on two benchmarks containing textureless CAD objects without category and daily objects with categories respectively, and further demonstrate improved scalability by extending to a more challenging setting of daily objects across categories.

cs.CV↗

arXiv2022

ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation

We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. vertices, edges and surface patches, and the correspondence of primitives, which are holistically modeled as a chain complex, and show that by modeling such comprehensive structures more complete and regularized reconstructions can be achieved. We solve the complex generation problem in two steps. First, we propose a novel neural framework that consists of a sparse CNN encoder for input point cloud processing and a tri-path transformer decoder for generating geometric primitives and their mutual relationships with estimated probabilities. Second, given the probabilistic structure predicted by the neural network, we recover a definite B-Rep chain complex by solving a global optimization maximizing the likelihood under structural validness constraints and applying geometric refinements. Extensive tests on large scale CAD datasets demonstrate that the modeling of B-Rep chain complex structure enables more accurate detection for learning and more constrained reconstruction for optimization, leading to structurally more faithful and complete CAD B-Rep models than previous results.

cs.CV↗

arXiv2022

Safe, efficient and socially-compatible decision of automated vehicles: a case study of unsignalized intersection driving

Safe and smooth interacting with other vehicles is one of the ultimate goals of driving automation. However, recent reports of demonstrative deployments of automated vehicles (AVs) indicate that AVs are still difficult to meet the expectation of other interacting drivers, which leads to several AV accidents involving human-driven vehicles (HVs). This is most likely due to the lack of understanding about the dynamic interaction process, especially about the human drivers. By investigating the causes of 4,300 video clips of traffic accidents, we find that the limited dynamic visual field of drivers is one leading factor in inter-vehicle interaction accidents, especially in those involving trucks. A game-theoretic decision algorithm considering social compatibility is proposed to handle the interaction with a human-driven truck at an unsignalized intersection. Starting from a probabilistic model for the visual field characteristics of truck drivers, social fitness and reciprocal altruism in the decision are incorporated in the game payoff design. Human-in-the-loop experiments are carried out, in which 24 subjects are invited to drive and interact with AVs deployed with the proposed algorithm and two comparison algorithms. Totally 207 cases of intersection interactions are obtained and analyzed, which shows that the proposed decision-making algorithm can not only improve both safety and time efficiency, but also make AV decisions more in line with the expectation of interacting human drivers. These findings can help inform the design of automated driving decision algorithms, to ensure that AVs can be safely and efficiently integrated into the human-dominated traffic.

eess.SY↗

arXiv2022

Sketch2PQ: Freeform Planar Quadrilateral Mesh Design via a Single Sketch

The freeform architectural modeling process often involves two important stages: concept design and digital modeling. In the first stage, architects usually sketch the overall 3D shape and the panel layout on a physical or digital paper briefly. In the second stage, a digital 3D model is created using the sketch as a reference. The digital model needs to incorporate geometric requirements for its components, such as the planarity of panels due to consideration of construction costs, which can make the modeling process more challenging. In this work, we present a novel sketch-based system to bridge the concept design and digital modeling of freeform roof-like shapes represented as planar quadrilateral (PQ) meshes. Our system allows the user to sketch the surface boundary and contour lines under axonometric projection and supports the sketching of occluded regions. In addition, the user can sketch feature lines to provide directional guidance to the PQ mesh layout. Given the 2D sketch input, we propose a deep neural network to infer in real-time the underlying surface shape along with a dense conjugate direction field, both of which are used to extract the final PQ mesh. To train and validate our network, we generate a large synthetic dataset that mimics architect sketching of freeform quadrilateral patches. The effectiveness and usability of our system are demonstrated with quantitative and qualitative evaluation as well as user studies.

cs.GR↗

arXiv2022

Self-Supervised Image Representation Learning with Geometric Set Consistency

We propose a method for self-supervised image representation learning under the guidance of 3D geometric consistency. Our intuition is that 3D geometric consistency priors such as smooth regions and surface discontinuities may imply consistent semantics or object boundaries, and can act as strong cues to guide the learning of 2D image representations without semantic labels. Specifically, we introduce 3D geometric consistency into a contrastive learning framework to enforce the feature consistency within image views. We propose to use geometric consistency sets as constraints and adapt the InfoNCE loss accordingly. We show that our learned image representations are general. By fine-tuning our pre-trained representations for various 2D image-based downstream tasks, including semantic segmentation, object detection, and instance segmentation on real-world indoor scene datasets, we achieve superior performance compared with state-of-the-art methods.

cs.CV↗

arXiv2022

On the supercongruences involving harmonic numbers of order 2

We prove several supercongruences involving the harmonic number of order two $H_n^{(2)}:=\sum_{k=1}^n1/k^2$. For example, if $p>5$ is prime and $α$ is $p$-integral, then we can completely determine $$ \sum_{k=0}^{p-1}\frac{H_k^{(2)}}{k}\cdot\binomα{k}\binom{-1-α}{k}\quad\text{and}\quad \sum_{k=0}^{\frac{p-1}{2}}\frac{H_k^{(2)}}{k}\cdot\binomα{k}\binom{-1-α}{k} $$ modulo $p^3$. In particular, by setting $α=-1/2$, we confirm two conjectured congruences of Z.-W. Sun.

math.NT↗

arXiv2021

Paired Ru-O-Mo ensemble for efficient and stable alkaline hydrogen evolution reaction

Electrocatalytic hydrogen evolution reaction (HER) in alkaline media is a promising electrochemical energy conversion strategy. Ruthenium (Ru) is an efficient catalyst with a desirable cost for HER, however, the sluggish H2O dissociation process, due to the low H2O adsorption on its surface, currently hampers the performances of this catalyst in alkaline HER. Herein, we demonstrate that the H2O adsorption improves significantly by the construction of Ru-O-Mo sites. We prepared Ru/MoO2 catalysts with Ru-O-Mo sites through a facile thermal treatment process and assessed the creation of Ru-O-Mo interfaces by transmission electron microscope (TEM) and extended X-ray absorption fine structure (EXAFS). By using Fourier-transform infrared spectroscopy (FTIR) and H2O adsorption tests, we proved Ru-O-Mo sites have tenfold stronger H2O adsorption ability than that of Ru catalyst. The catalysts with Ru-O-Mo sites exhibited a state-of-the-art overpotential of 16 mV at 10 mA cm-2 in 1 M KOH electrolyte, demonstrating a threefold reduction than the previous bests of Ru (59 mV) and commercial Pt (31 mV) catalysts. We proved the stability of these performances over 40 hours without decline. These results could open a new path for designing efficient and stable catalysts.

physics.chem-ph↗

arXiv2021

Unsupervised Shape Completion via Deep Prior in the Neural Tangent Kernel Perspective

We present a novel approach for completing and reconstructing 3D shapes from incomplete scanned data by using deep neural networks. Rather than being trained on supervised completion tasks and applied on a testing shape, the network is optimized from scratch on the single testing shape, to fully adapt to the shape and complete the missing data using contextual guidance from the known regions. The ability to complete missing data by an untrained neural network is usually referred to as the deep prior. In this paper, we interpret the deep prior from a neural tangent kernel (NTK) perspective and show that the completed shape patches by the trained CNN are naturally similar to existing patches, as they are proximate in the kernel feature space induced by NTK. The interpretation allows us to design more efficient network structures and learning mechanisms for the shape completion and reconstruction task. Being more aware of structural regularities than both traditional and other unsupervised learning-based reconstruction methods, our approach completes large missing regions with plausible shapes and complements supervised learning-based methods that use database priors by requiring no extra training data set and showing flexible adaptation to a particular shape instance.

cs.CV↗

arXiv2021

Deep Implicit Moving Least-Squares Functions for 3D Reconstruction

Point set is a flexible and lightweight representation widely used for 3D deep learning. However, their discrete nature prevents them from representing continuous and fine geometry, posing a major issue for learning-based shape generation. In this work, we turn the discrete point sets into smooth surfaces by introducing the well-known implicit moving least-squares (IMLS) surface formulation, which naturally defines locally implicit functions on point sets. We incorporate IMLS surface generation into deep neural networks for inheriting both the flexibility of point sets and the high quality of implicit surfaces. Our IMLSNet predicts an octree structure as a scaffold for generating MLS points where needed and characterizes shape geometry with learned local priors. Furthermore, our implicit function evaluation is independent of the neural network once the MLS points are predicted, thus enabling fast runtime evaluation. Our experiments on 3D object reconstruction demonstrate that IMLSNets outperform state-of-the-art learning-based methods in terms of reconstruction quality and computational efficiency. Extensive ablation tests also validate our network design and loss functions.

cs.CV↗

arXiv2020

A local-global theorem for $p$-adic supercongruences

Let ${\mathbb Z}_p$ denote the ring of all $p$-adic integers and call $${\mathcal U}=\{(x_1,\ldots,x_n):\,a_1x_1+\ldots+a_nx_n+b=0\}$$ a hyperplane over ${\mathbb Z}_p^n$, where at least one of $a_1,\ldots,a_n$ is not divisible by $p$. We prove that if a sufficiently regular $n$-variable function is zero modulo $p^r$ over some suitable collection of $r$ hyperplanes, then it is zero modulo $p^r$ over the whole ${\mathbb Z}_p^n$. We provide various applications of this general criterion by establishing several $p$-adic analogues of hypergeometric identities.

math.NT↗

arXiv2020

Sketch2CAD: Sequential CAD Modeling by Sketching in Context

We present a sketch-based CAD modeling system, where users create objects incrementally by sketching the desired shape edits, which our system automatically translates to CAD operations. Our approach is motivated by the close similarities between the steps industrial designers follow to draw 3D shapes, and the operations CAD modeling systems offer to create similar shapes. To overcome the strong ambiguity with parsing 2D sketches, we observe that in a sketching sequence, each step makes sense and can be interpreted in the \emph{context} of what has been drawn before. In our system, this context corresponds to a partial CAD model, inferred in the previous steps, which we feed along with the input sketch to a deep neural network in charge of interpreting how the model should be modified by that sketch. Our deep network architecture then recognizes the intended CAD operation and segments the sketch accordingly, such that a subsequent optimization estimates the parameters of the operation that best fit the segmented sketch strokes. Since there exists no datasets of paired sketching and CAD modeling sequences, we train our system by generating synthetic sequences of CAD operations that we render as line drawings. We present a proof of concept realization of our algorithm supporting four frequently used CAD operations. Using our system, participants are able to quickly model a large and diverse set of objects, demonstrating Sketch2CAD to be an alternate way of interacting with current CAD modeling systems.

cs.GR↗

arXiv2020

PFCNN: Convolutional Neural Networks on 3D Surfaces Using Parallel Frames

Surface meshes are widely used shape representations and capture finer geometry data than point clouds or volumetric grids, but are challenging to apply CNNs directly due to their non-Euclidean structure. We use parallel frames on surface to define PFCNNs that enable effective feature learning on surface meshes by mimicking standard convolutions faithfully. In particular, the convolution of PFCNN not only maps local surface patches onto flat tangent planes, but also aligns the tangent planes such that they locally form a flat Euclidean structure, thus enabling recovery of standard convolutions. The alignment is achieved by the tool of locally flat connections borrowed from discrete differential geometry, which can be efficiently encoded and computed by parallel frame fields. In addition, the lack of canonical axis on surface is handled by sampling with the frame directions. Experiments show that for tasks including classification, segmentation and registration on deformable geometric domains, as well as semantic scene segmentation on rigid domains, PFCNNs achieve robust and superior performances without using sophisticated input features than state-of-the-art surface based CNNs.

cs.CV↗

arXiv2020

On a conjectural congruence of Guo

Let $p\equiv3\pmod{4}$ be a prime and $r$ a positive integer. We show that $$ \prod_{k=1}^{(p^{2r}-1)/2}\frac{4k-1}{4k+1}\equiv1\pmod{p^2}. $$ This confirms a recent conjecture of Guo.

math.NT↗