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Surgical 3D reconstruction is a critical area of research in robotic surgery, with recent works adopting variants of dynamic radiance fields to achieve success in 3D reconstruction of deformable tissues from single-viewpoint videos. However, these methods often suffer from time-consuming optimization or inferior quality, limiting their adoption in downstream tasks. Inspired by 3D Gaussian Splatting, a recent trending 3D representation, we present EndoGS, applying Gaussian Splatting for deformable endoscopic tissue reconstruction. Specifically, our approach incorporates deformation fields to handle dynamic scenes, depth-guided supervision with spatial-temporal weight masks to optimize 3D targets with tool occlusion from a single viewpoint, and surface-aligned regularization terms to capture the much better geometry. As a result, EndoGS reconstructs and renders high-quality deformable endoscopic tissues from a single-viewpoint video, estimated depth maps, and labeled tool masks. Experiments on DaVinci robotic surgery videos demonstrate that EndoGS achieves superior rendering quality. Code is available at https://github.com/HKU-MedAI/EndoGS., Comment: Accepted by Embodied AI and Robotics for HealTHcare of International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI EARTH 2024). 11 pages, 4 figures

Neural implicit fields, such as the neural signed distance field (SDF) of a shape, have emerged as a powerful representation for many applications, e.g., encoding a 3D shape and performing collision detection. Typically, implicit fields are encoded by Multi-layer Perceptrons (MLP) with positional encoding (PE) to capture high-frequency geometric details. However, a notable side effect of such PE-equipped MLPs is the noisy artifacts present in the learned implicit fields. While increasing the sampling rate could in general mitigate these artifacts, in this paper we aim to explain this adverse phenomenon through the lens of Fourier analysis. We devise a tool to determine the appropriate sampling rate for learning an accurate neural implicit field without undesirable side effects. Specifically, we propose a simple yet effective method to estimate the intrinsic frequency of a given network with randomized weights based on the Fourier analysis of the network's responses. It is observed that a PE-equipped MLP has an intrinsic frequency much higher than the highest frequency component in the PE layer. Sampling against this intrinsic frequency following the Nyquist-Sannon sampling theorem allows us to determine an appropriate training sampling rate. We empirically show in the setting of SDF fitting that this recommended sampling rate is sufficient to secure accurate fitting results, while further increasing the sampling rate would not further noticeably reduce the fitting error. Training PE-equipped MLPs simply with our sampling strategy leads to performances superior to the existing methods.

The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the capabilities of parametric surfaces, which are the prevalent surface representations in product design, CAD/CAM, and computer animation. We present Neural Parametric Surfaces, the first piecewise neural surface representation that allows coarse patch layouts of arbitrary $n$-sided surface patches to model complex surface geometries with high precision, offering greater flexibility over traditional parametric surfaces. By construction, this new surface representation guarantees $G^0$ continuity between adjacent patches and empirically achieves $G^1$ continuity, which cannot be attained by existing neural patch-based methods. The key ingredient of our neural parametric surface is a learnable feature complex $\mathcal{C}$ that is embedded in a high-dimensional space $\mathbb{R}^D$ and topologically equivalent to the patch layout of the surface; each face cell of the complex is defined by interpolating feature vectors at its vertices. The learned feature complex is mapped by an MLP-encoded function $f:\mathcal{C} \rightarrow \mathcal{S}$ to produce the neural parametric surface $\mathcal{S}$. We present a surface fitting algorithm that optimizes the feature complex $\mathcal{C}$ and trains the neural mapping $f$ to reconstruct given target shapes with high accuracy. We further show that the proposed representation along with a compact-size neural net can learn a plausible shape space from a shape collection, which can be used for shape interpolation or shape completion from noisy and incomplete input data. Extensive experiments show that neural parametric surfaces offer greater modeling capabilities than traditional parametric surfaces., Comment: 17 pages, 16 figures

We propose a method, named DualMesh-UDF, to extract a surface from unsigned distance functions (UDFs), encoded by neural networks, or neural UDFs. Neural UDFs are becoming increasingly popular for surface representation because of their versatility in presenting surfaces with arbitrary topologies, as opposed to the signed distance function that is limited to representing a closed surface. However, the applications of neural UDFs are hindered by the notorious difficulty in extracting the target surfaces they represent. Recent methods for surface extraction from a neural UDF suffer from significant geometric errors or topological artifacts due to two main difficulties: (1) A UDF does not exhibit sign changes; and (2) A neural UDF typically has substantial approximation errors. DualMesh-UDF addresses these two difficulties. Specifically, given a neural UDF encoding a target surface $\bar{S}$ to be recovered, we first estimate the tangent planes of $\bar{S}$ at a set of sample points close to $\bar{S}$. Next, we organize these sample points into local clusters, and for each local cluster, solve a linear least squares problem to determine a final surface point. These surface points are then connected to create the output mesh surface, which approximates the target surface. The robust estimation of the tangent planes of the target surface and the subsequent minimization problem constitute our core strategy, which contributes to the favorable performance of DualMesh-UDF over other competing methods. To efficiently implement this strategy, we employ an adaptive Octree. Within this framework, we estimate the location of a surface point in each of the octree cells identified as containing part of the target surface. Extensive experiments show that our method outperforms existing methods in terms of surface reconstruction quality while maintaining comparable computational efficiency., Comment: ICCV 2023

Neural implicit representations are known to be more compact for depicting 3D shapes than traditional discrete representations. However, the neural representations tend to round sharp corners or edges and struggle to represent surfaces with open boundaries. Moreover, they are slow to train. We present a unified neural implicit representation, called Patch-Grid, that fits to complex shapes efficiently, preserves sharp features, and effectively models surfaces with open boundaries and thin geometric features. Our superior efficiency comes from embedding each surface patch into a local latent volume and decoding it using a shared MLP decoder, which is pretrained on various local surface geometries. With this pretrained decoder fixed, fitting novel shapes and local shape updates can be done efficiently. The faithful preservation of sharp features is enabled by adopting a novel merge grid to perform local constructive solid geometry (CSG) combinations of surface patches in the cells of an adaptive Octree, yielding better robustness than using a global CSG construction as proposed in the literature. Experiments show that our Patch-Grid method faithfully captures shapes with complex sharp features, open boundaries and thin structures, and outperforms existing learning-based methods in both efficiency and quality for surface fitting and local shape updates.

This paper presents a Progressively-connected Light Field network (ProLiF), for the novel view synthesis of complex forward-facing scenes. ProLiF encodes a 4D light field, which allows rendering a large batch of rays in one training step for image- or patch-level losses. Directly learning a neural light field from images has difficulty in rendering multi-view consistent images due to its unawareness of the underlying 3D geometry. To address this problem, we propose a progressive training scheme and regularization losses to infer the underlying geometry during training, both of which enforce the multi-view consistency and thus greatly improves the rendering quality. Experiments demonstrate that our method is able to achieve significantly better rendering quality than the vanilla neural light fields and comparable results to NeRF-like rendering methods on the challenging LLFF dataset and Shiny Object dataset. Moreover, we demonstrate better compatibility with LPIPS loss to achieve robustness to varying light conditions and CLIP loss to control the rendering style of the scene. Project page: https://totoro97.github.io/projects/prolif., Comment: Project page: https://totoro97.github.io/projects/prolif