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This research presents a novel depth estimation algorithm based on a Transformer-encoder architecture, tailored for the NYU and KITTI Depth Dataset. This research adopts a transformer model, initially renowned for its success in natural…
Robotic insertion is a highly challenging task that requires exceptional precision in cluttered environments. Existing methods often have poor generalization capabilities. They typically function in restricted and structured environments,…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
Sparse depth measurements are widely available in many applications such as augmented reality, visual inertial odometry and robots equipped with low cost depth sensors. Although such sparse depth samples work well for certain applications…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
We propose a novel plug-and-play (PnP) module for improving depth prediction with taking arbitrary patterns of sparse depths as input. Given any pre-trained depth prediction model, our PnP module updates the intermediate feature map such…
Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal…
Depth perception is essential for a robot's spatial and geometric understanding of its environment, with many tasks traditionally relying on hardware-based depth sensors like RGB-D or stereo cameras. However, these sensors face practical…
Modern cameras are equipped with a wide array of sensors that enable recording the geospatial context of an image. Taking advantage of this, we explore depth estimation under the assumption that the camera is geocalibrated, a problem we…
Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…
State-of-the-art monocular depth estimation (MDE) models often struggle in challenging environments, primarily because they overlook robust physical information. To demonstrate this, we first conduct an empirical study by computing the…
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we proposed an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD) of a set of…
Omnidirectional depth estimation presents a significant challenge due to the inherent distortions in panoramic images. Despite notable advancements, the impact of projection methods remains underexplored. We introduce Multi-Cylindrical…
Depth estimation is a core problem in robotic perception and vision tasks, but 3D reconstruction from a single image presents inherent uncertainties. Current depth estimation models primarily rely on inter-image relationships for supervised…
The main contribution of this paper is the proof of the convexity of the omni-directional tethered robot workspace (namely, the set of all tether-length-admissible robot configurations), as well as a set of distance-optimal tethered path…