Solving the Best Subset Selection Problem via Suboptimal Algorithms

Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the global optimal solution via an exact optimization method for a problem with dimensions of 1000s may take an impractical amount of CPU time. This suggests the importance of finding suboptimal procedures that can provide good approximate solutions using much less computational effort than exact methods. In this work, we introduce a new procedure and compare it with other popular suboptimal algorithms to solve the best subset selection problem. Extensive computational experiments using synthetic and real data have been performed. The results provide insights into the performance of these methods in different data settings. The new procedure is observed to be a competitive suboptimal algorithm for solving the best subset selection problem for high-dimensional data.

uLayout: Unified Room Layout Estimation for Perspective and Panoramic Images

We present uLayout, a unified model for estimating room layout geometries from both perspective and panoramic images, whereas traditional solutions require different model designs for each image type. The key idea of our solution is to unify both domains into the equirectangular projection, particularly, allocating perspective images into the most suitable latitude coordinate to effectively exploit both domains seamlessly. To address the Field-of-View (FoV) difference between the input domains, we design uLayout with a shared feature extractor with an extra 1D-Convolution layer to condition each domain input differently. This conditioning allows us to efficiently formulate a column-wise feature regression problem regardless of the FoV input. This simple yet effective approach achieves competitive performance with current state-of-the-art solutions and shows for the first time a single end-to-end model for both domains. Extensive experiments in the real-world datasets, LSUN, Matterport3D, PanoContext, and Stanford 2D-3D evidence the contribution of our approach. Code is available at https://github.com/JonathanLee112/uLayout.

POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality

In this paper, we present a novel algorithm for quantifying uncertainty and information gained within 3D Gaussian Splatting (3D-GS) through P-Optimality. While 3D-GS has proven to be a useful world model with high-quality rasterizations, it does not natively quantify uncertainty. Quantifying uncertainty in parameters of 3D-GS is necessary to understand the information gained from acquiring new images as in active perception, or identify redundant images which can be removed from memory due to resource constraints in online 3D-GS SLAM. We propose to quantify uncertainty and information gain in 3D-GS by reformulating the problem through the lens of optimal experimental design, which is a classical solution to measuring information gain. By restructuring information quantification of 3D-GS through optimal experimental design, we arrive at multiple solutions, of which T-Optimality and D-Optimality perform the best quantitatively and qualitatively as measured on two popular datasets. Additionally, we propose a block diagonal approximation of the 3D-GS uncertainty, which provides a measure of correlation for computing more accurate information gain, at the expense of a greater computation cost.

GAC-Net_Geometric and attention-based Network for Depth Completion

Depth completion is a key task in autonomous driving, aiming to complete sparse LiDAR depth measurements into high-quality dense depth maps through image guidance. However, existing methods usually treat depth maps as an additional channel of color images, or directly perform convolution on sparse data, failing to fully exploit the 3D geometric information in depth maps, especially with limited performance in complex boundaries and sparse areas. To address these issues, this paper proposes a depth completion network combining channel attention mechanism and 3D global feature perception (CGA-Net). The main innovations include: 1) Utilizing PointNet++ to extract global 3D geometric features from sparse depth maps, enhancing the scene perception ability of low-line LiDAR data; 2) Designing a channel-attention-based multimodal feature fusion module to efficiently integrate sparse depth, RGB images, and 3D geometric features; 3) Combining residual learning with CSPN++ to optimize the depth refinement stage, further improving the completion quality in edge areas and complex scenes. Experiments on the KITTI depth completion dataset show that CGA-Net can significantly improve the prediction accuracy of dense depth maps, achieving a new state-of-the-art (SOTA), and demonstrating strong robustness to sparse and complex scenes.

V-MIND: Building Versatile Monocular Indoor 3D Detector with Diverse 2D Annotations

The field of indoor monocular 3D object detection is gaining significant attention, fueled by the increasing demand in VR/AR and robotic applications. However, its advancement is impeded by the limited availability and diversity of 3D training data, owing to the labor-intensive nature of 3D data collection and annotation processes. In this paper, we present V-MIND (Versatile Monocular INdoor Detector), which enhances the performance of indoor 3D detectors across a diverse set of object classes by harnessing publicly available large-scale 2D datasets. By leveraging well-established monocular depth estimation techniques and camera intrinsic predictors, we can generate 3D training data by converting large-scale 2D images into 3D point clouds and subsequently deriving pseudo 3D bounding boxes. To mitigate distance errors inherent in the converted point clouds, we introduce a novel 3D self-calibration loss for refining the pseudo 3D bounding boxes during training. Additionally, we propose a novel ambiguity loss to address the ambiguity that arises when introducing new classes from 2D datasets. Finally, through joint training with existing 3D datasets and pseudo 3D bounding boxes derived from 2D datasets, V-MIND achieves state-of-the-art object detection performance across a wide range of classes on the Omni3D indoor dataset.

Modeling Uncertainty in 3D Gaussian Splatting through Continuous Semantic Splatting

In this paper, we present a novel algorithm for probabilistically updating and rasterizing semantic maps within 3D Gaussian Splatting (3D-GS). Although previous methods have introduced algorithms which learn to rasterize features in 3D-GS for enhanced scene understanding, 3D-GS can fail without warning which presents a challenge for safety-critical robotic applications. To address this gap, we propose a method which advances the literature of continuous semantic mapping from voxels to ellipsoids, combining the precise structure of 3D-GS with the ability to quantify uncertainty of probabilistic robotic maps. Given a set of images, our algorithm performs a probabilistic semantic update directly on the 3D ellipsoids to obtain an expectation and variance through the use of conjugate priors. We also propose a probabilistic rasterization which returns per-pixel segmentation predictions with quantifiable uncertainty. We compare our method with similar probabilistic voxel-based methods to verify our extension to 3D ellipsoids, and perform ablation studies on uncertainty quantification and temporal smoothing.

Configurable Embodied Data Generation for Class-Agnostic RGB-D Video Segmentation

This paper presents a method for generating large-scale datasets to improve class-agnostic video segmentation across robots with different form factors. Specifically, we consider the question of whether video segmentation models trained on generic segmentation data could be more effective for particular robot platforms if robot embodiment is factored into the data generation process. To answer this question, a pipeline is formulated for using 3D reconstructions (e.g. from HM3DSem) to generate segmented videos that are configurable based on a robot's embodiment (e.g. sensor type, sensor placement, and illumination source). A resulting massive RGB-D video panoptic segmentation dataset (MVPd) is introduced for extensive benchmarking with foundation and video segmentation models, as well as to support embodiment-focused research in video segmentation. Our experimental findings demonstrate that using MVPd for finetuning can lead to performance improvements when transferring foundation models to certain robot embodiments, such as specific camera placements. These experiments also show that using 3D modalities (depth images and camera pose) can lead to improvements in video segmentation accuracy and consistency. The project webpage is available at https://topipari.com/projects/MVPd

ET-Former: Efficient Triplane Deformable Attention for 3D Semantic Scene Completion From Monocular Camera

We introduce ET-Former, a novel end-to-end algorithm for semantic scene completion using a single monocular camera. Our approach generates a semantic occupancy map from single RGB observation while simultaneously providing uncertainty estimates for semantic predictions. By designing a triplane-based deformable attention mechanism, our approach improves geometric understanding of the scene than other SOTA approaches and reduces noise in semantic predictions. Additionally, through the use of a Conditional Variational AutoEncoder (CVAE), we estimate the uncertainties of these predictions. The generated semantic and uncertainty maps will aid in the formulation of navigation strategies that facilitate safe and permissible decision-making in the future. Evaluated on the Semantic-KITTI dataset, ET-Former achieves the highest IoU and mIoU, surpassing other methods by 15.16% in IoU and 24.24% in mIoU, while reducing GPU memory usage of existing methods by 25%-50.5%.

Enhancing Single Image to 3D Generation using Gaussian Splatting and Hybrid Diffusion Priors

3D object generation from a single image involves estimating the full 3D geometry and texture of unseen views from an unposed RGB image captured in the wild. Accurately reconstructing an object's complete 3D structure and texture has numerous applications in real-world scenarios, including robotic manipulation, grasping, 3D scene understanding, and AR/VR. Recent advancements in 3D object generation have introduced techniques that reconstruct an object's 3D shape and texture by optimizing the efficient representation of Gaussian Splatting, guided by pre-trained 2D or 3D diffusion models. However, a notable disparity exists between the training datasets of these models, leading to distinct differences in their outputs. While 2D models generate highly detailed visuals, they lack cross-view consistency in geometry and texture. In contrast, 3D models ensure consistency across different views but often result in overly smooth textures. We propose bridging the gap between 2D and 3D diffusion models to address this limitation by integrating a two-stage frequency-based distillation loss with Gaussian Splatting. Specifically, we leverage geometric priors in the low-frequency spectrum from a 3D diffusion model to maintain consistent geometry and use a 2D diffusion model to refine the fidelity and texture in the high-frequency spectrum of the generated 3D structure, resulting in more detailed and fine-grained outcomes. Our approach enhances geometric consistency and visual quality, outperforming the current SOTA. Additionally, we demonstrate the easy adaptability of our method for efficient object pose estimation and tracking.

Context-Aware Replanning with Pre-explored Semantic Map for Object Navigation

Pre-explored Semantic Maps, constructed through prior exploration using visual language models (VLMs), have proven effective as foundational elements for training-free robotic applications. However, existing approaches assume the map's accuracy and do not provide effective mechanisms for revising decisions based on incorrect maps. To address this, we introduce Context-Aware Replanning (CARe), which estimates map uncertainty through confidence scores and multi-view consistency, enabling the agent to revise erroneous decisions stemming from inaccurate maps without requiring additional labels. We demonstrate the effectiveness of our proposed method by integrating it with two modern mapping backbones, VLMaps and OpenMask3D, and observe significant performance improvements in object navigation tasks. More details can be found on the project page: https://carmaps.github.io/supplements/.