Multi-Class Boundary Extraction from Implicit Representations

Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. However, existing methods often struggle to balance training efficiency, rendering speed, and noise robustness: single-MLP approaches are expensive at inference, grid-based representations are fast but can limit surface smoothness and overfit input noise, and previous multiscale approaches frequently capture noise and produce artifacts due to hard spectral truncation. To address these limitations, we propose M-plicits, a multiscale framework that models surfaces as a residual sum of MLPs trained via a sequence of nested neighborhoods. Unlike existing residual approaches that rely on standard domain-wide sampling and require costly mesh extraction for visualization, our method strictly localizes supervision to narrow bands around the previous zero-level sets. This nested design naturally provides robustness against noisy input data: the coarse network acts as a low-pass filter that establishes a clean geometric prior, while subsequent residuals progressively refine the geometry without fitting to high-frequency artifacts. We further introduce a multiscale sphere-tracing algorithm and a GEMM-based analytical normal computation that bypasses auto-differentiation entirely, yielding high-fidelity real-time rendering. On Stanford and Thingi32, M-plicits achieves the best mean Chamfer distance in the coarse configuration and the best median Chamfer distance and IoU in the fine configuration, with substantially better noise robustness than iNGP, BACON, and IDF, while using an order of magnitude fewer parameters than grid-based baselines. Code, models, and data are available at https://github.com/dsilvavinicius/m-plicits.

We introduce two new methods for boundary detection in high-dimensional point cloud data, intended to work in situations with non-uniform density, high ambient dimension, and substantial noise. Our first method fits a separating hyperplane on local neighborhoods after doing local dimension reduction---this method works best when one can reliably estimate the intrinsic dimension of the data. Our second method measures the directional uniformity of local neighborhoods, and has the best overall performance on synthetic data. In addition to pointwise numerical boundary scores, our algorithms yield an estimated normal vector at each boundary point. We validate our methodology on synthetic data as well as two real examples: we analyze spatial transcriptomics data, where we show that we can detect the boundary of a tumor, and we also study LLM activation geometry.

Most Gaussian Splatting techniques that provide a 3D semantic representation of the scene do not optimize the underlying 3D geometry, making object-level editing or asset extraction challenging. Recent methods, such as COBGS, Trace3D, ObjectGS, acknowledge this limitation and propose approaches that modify the scene's geometry to represent the underlying semantics. We advance this concept further by proposing a novel solution that provides near perfect boundaries in object extraction. We do so by introducing two new losses in the optimization that take care of: 1) a loss that modifies the geometry of visible Gaussians to respect semantic boundaries, and 2) a loss that adjusts the geometry of non-visible Gaussians that appear once the object is extracted. Our first loss propagates gradients directly through the rasterization, allowing for seamless integration within the optimization of the Gaussian parameters. The second loss also propagates gradients to Gaussian parameters but does so without passing through the rasterization, enabling modification of the scene's geometry even when little transmittance reaches a Gaussian (partial or non-visible). Exhaustive comparisons with 12 state of the art methods across 4 datasets, using six metrics, demonstrate that our approach produces overall the best boundary segmentation to date.