Md. Ashiqur Rahman

Hrishikesh Viswanath, Md Ashiqur Rahman, Rashmi Bhaskara et al.

We present, AdaFNIO - Adaptive Fourier Neural Interpolation Operator, a neural operator-based architecture to perform video frame interpolation. Current deep learning based methods rely on local convolutions for feature learning and suffer from not being scale-invariant, thus requiring training data to be augmented through random flipping and re-scaling. On the other hand, AdaFNIO, learns the features in the frames, independent of input resolution, through token mixing and global convolution in the Fourier space or the spectral domain by using Fast Fourier Transform (FFT). We show that AdaFNIO can produce visually smooth and accurate results. To evaluate the visual quality of our interpolated frames, we calculate the structural similarity index (SSIM) and Peak Signal to Noise Ratio (PSNR) between the generated frame and the ground truth frame. We provide the quantitative performance of our model on Vimeo-90K dataset, DAVIS, UCF101 and DISFA+ dataset.

Hrishikesh Viswanath, Md Ashiqur Rahman, Chi Lin et al.

Accurate and efficient 3D mapping of large-scale outdoor environments from LiDAR measurements is a fundamental challenge in robotics, particularly towards ensuring smooth and artifact-free surface reconstructions. Although the state-of-the-art methods focus on memory-efficient neural representations for high-fidelity surface generation, they often fail to produce artifact-free manifolds, with artifacts arising due to noisy and sparse inputs. To address this issue, we frame surface mapping as a physics-informed energy optimization problem, enforcing surface smoothness by optimizing an energy functional that penalizes sharp surface ridges. Specifically, we propose a deep learning based approach that learns the signed distance field (SDF) of the surface manifold from raw LiDAR point clouds using a physics-informed loss function that optimizes the $L_2$-Hessian energy of the surface. Our learning framework includes a hierarchical octree based input feature encoding and a multi-scale neural network to iteratively refine the signed distance field at different scales of resolution. Lastly, we introduce a test-time refinement strategy to correct topological inconsistencies and edge distortions that can arise in the generated mesh. We propose a \texttt{CUDA}-accelerated least-squares optimization that locally adjusts vertex positions to enforce feature-preserving smoothing. We evaluate our approach on large-scale outdoor datasets and demonstrate that our approach outperforms current state-of-the-art methods in terms of improved accuracy and smoothness. Our code is available at \href{https://github.com/HrishikeshVish/HessianForge/}{https://github.com/HrishikeshVish/HessianForge/}