This paper presents an end-to-end framework for reconstructing 3D parametric curves directly from multi-view edge maps. Contrasting with existing two-stage methods that follow a sequential ``edge point cloud reconstruction and parametric curve fitting'' pipeline, our one-stage approach optimizes 3D parametric curves directly from 2D edge maps, eliminating error accumulation caused by the inherent optimization gap between disconnected stages. However, parametric curves inherently lack suitability for rendering-based multi-view optimization, necessitating a complementary representation that preserves their geometric properties while enabling differentiable rendering. We propose a novel bi-directional coupling mechanism between parametric curves and edge-oriented Gaussian components. This tight correspondence formulates a curve-aware Gaussian representation, \textbf{CurveGaussian}, that enables differentiable rendering of 3D curves, allowing direct optimization guided by multi-view evidence. Furthermore, we introduce a dynamically adaptive topology optimization framework during training to refine curve structures through linearization, merging, splitting, and pruning operations. Comprehensive evaluations on the ABC dataset and real-world benchmarks demonstrate our one-stage method's superiority over two-stage alternatives, particularly in producing cleaner and more robust reconstructions. Additionally, by directly optimizing parametric curves, our method significantly reduces the parameter count during training, achieving both higher efficiency and superior performance compared to existing approaches.

Is there really much more to say about sparse autoencoders (SAEs)? Autoencoders in general, and SAEs in particular, represent deep architectures that are capable of modeling low-dimensional latent structure in data. Such structure could reflect, among other things, correlation patterns in large language model activations, or complex natural image manifolds. And yet despite the wide-ranging applicability, there have been relatively few changes to SAEs beyond the original recipe from decades ago, namely, standard deep encoder/decoder layers trained with a classical/deterministic sparse regularizer applied within the latent space. One possible exception is the variational autoencoder (VAE), which adopts a stochastic encoder module capable of producing sparse representations when applied to manifold data. In this work we formalize underappreciated weaknesses with both canonical SAEs, as well as analogous VAEs applied to similar tasks, and propose a hybrid alternative model that circumvents these prior limitations. In terms of theoretical support, we prove that global minima of our proposed model recover certain forms of structured data spread across a union of manifolds. Meanwhile, empirical evaluations on synthetic and real-world datasets substantiate the efficacy of our approach in accurately estimating underlying manifold dimensions and producing sparser latent representations without compromising reconstruction error. In general, we are able to exceed the performance of equivalent-capacity SAEs and VAEs, as well as recent diffusion models where applicable, within domains such as images and language model activation patterns.

Inserting objects into scenes and performing realistic relighting are common applications in augmented reality (AR). Previous methods focused on inserting virtual objects using CAD models or real objects from single-view images, resulting in highly limited AR application scenarios. We introduce a novel pipeline based on Neural Radiance Fields (NeRFs) for seamlessly integrating objects into scenes, from two sets of images depicting the object and scene. This approach enables novel view synthesis, realistic relighting, and supports physical interactions such as shadow casting between objects. The lighting environment is in a hybrid representation of Spherical Harmonics and Spherical Gaussians, representing both high- and low-frequency lighting components very well, and supporting non-Lambertian surfaces. Specifically, we leverage the benefits of volume rendering and introduce an innovative approach for efficient shadow rendering by comparing the depth maps between the camera view and the light source view and generating vivid soft shadows. The proposed method achieves realistic relighting effects in extensive experimental evaluations.

The emergence of massive data in recent years brings challenges to automatic statistical inference. This is particularly true if the data are too numerous to be read into memory as a whole. Accordingly, new sampling techniques are needed to sample data from a hard drive. In this paper, we propose a sequential addressing subsampling (SAS) method that can sample data directly from the hard drive. The newly proposed SAS method is time saving in terms of addressing cost compared to that of the random addressing subsampling (RAS) method. Estimators (e.g., the sample mean) based on the SAS subsamples are constructed, and their properties are studied. We conduct a series of simulation studies to verify the finite sample performance of the proposed SAS estimators. The time cost is also compared between the SAS and RAS methods. An analysis of the airline data is presented for illustration purpose.