Neural implicit representations have emerged as a powerful paradigm for 3D
reconstruction. However, despite their success, existing methods fail to
capture fine geometric details and thin structures, especially in scenarios
where only sparse RGB views of the objects of interest are available. We
hypothesize that current methods for learning neural implicit representations
from RGB or RGBD images produce 3D surfaces with missing parts and details
because they only rely on 0-order differential properties, i.e. the 3D surface
points and their projections, as supervisory signals. Such properties, however,
do not capture the local 3D geometry around the points and also ignore the
interactions between points. This paper demonstrates that training neural
representations with first-order differential properties, i.e. surface normals,
leads to highly accurate 3D surface reconstruction even in situations where
only as few as two RGB (front and back) images are available. Given multiview
RGB images of an object of interest, we first compute the approximate surface
normals in the image space using the gradient of the depth maps produced using
an off-the-shelf monocular depth estimator such as Depth Anything model. An
implicit surface regressor is then trained using a loss function that enforces
the first-order differential properties of the regressed surface to match those
estimated from Depth Anything. Our extensive experiments on a wide range of
real and synthetic datasets show that the proposed method achieves an
unprecedented level of reconstruction accuracy even when using as few as two
RGB views. The detailed ablation study also demonstrates that normal-based
supervision plays a key role in this significant improvement in performance,
enabling the 3D reconstruction of intricate geometric details and thin
structures that were previously challenging to capture.

通过使用一阶微分特性 (即，表面法线)，本文展示了训练神经表示形成高准确度的 3D 表面重建，即使只有两个 RGB 视图可用，极大地改善了以前难以捕捉的复杂几何细节和薄结构。

基于法向引导的高保真三维曲面重建的神经隐式函数

Normal-guided Detail-Preserving Neural Implicit Functions for  High-Fidelity 3D Surface Reconstruction

Many applications in vision require estimation of thin structures such as
boundary edges, surfaces, roads, blood vessels, neurons, etc. Unlike most
previous approaches, we simultaneously detect and delineate thin structures
with sub-pixel localization and real-valued orientation estimation. This is an
ill-posed problem that requires regularization. We propose an objective
function combining detection likelihoods with a prior minimizing curvature of
the center-lines or surfaces. Unlike simple block-coordinate descent, we
develop a novel algorithm that is able to perform joint optimization of
location and detection variables more effectively. Our lower bound optimization
algorithm applies to quadratic or absolute curvature. The proposed early vision
framework is sufficiently general and it can be used in many higher-level
applications. We illustrate the advantage of our approach on a range of 2D and
3D examples.

提出了一个目标函数，其中结合了检测似然和先验条件，最小化中心线或表面的曲率，用于同时检测和描绘细结构，具有亚像素定位和实值方向估计。