Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model

We study the existence and uniqueness of the positive solution for the fractional differential system involving the Riemann-Stieltjes integral boundary conditions , , , , , and , where , , and and are the standard Riemann-Liouville derivatives, and are functions of bounded variation, and and denote the Riemann-Stieltjes integral. Our results are based on a generalized fixed point theorem for weakly contractive mappings in partially ordered sets

Deep Planar Parallax for Monocular Depth Estimation

Recent research has highlighted the utility of Planar Parallax Geometry in monocular depth estimation. However, its potential has yet to be fully realized because networks rely heavily on appearance for depth prediction. Our in-depth analysis reveals that utilizing flow-pretrain can optimize the network's usage of consecutive frame modeling, leading to substantial performance enhancement. Additionally, we propose Planar Position Embedding (PPE) to handle dynamic objects that defy static scene assumptions and to tackle slope variations that are challenging to differentiate. Comprehensive experiments on autonomous driving datasets, namely KITTI and the Waymo Open Dataset (WOD), prove that our Planar Parallax Network (PPNet) significantly surpasses existing learning-based methods in performance

One-Stage 3D Whole-Body Mesh Recovery with Component Aware Transformer

Whole-body mesh recovery aims to estimate the 3D human body, face, and hands parameters from a single image. It is challenging to perform this task with a single network due to resolution issues, i.e., the face and hands are usually located in extremely small regions. Existing works usually detect hands and faces, enlarge their resolution to feed in a specific network to predict the parameter, and finally fuse the results. While this copy-paste pipeline can capture the fine-grained details of the face and hands, the connections between different parts cannot be easily recovered in late fusion, leading to implausible 3D rotation and unnatural pose. In this work, we propose a one-stage pipeline for expressive whole-body mesh recovery, named OSX, without separate networks for each part. Specifically, we design a Component Aware Transformer (CAT) composed of a global body encoder and a local face/hand decoder. The encoder predicts the body parameters and provides a high-quality feature map for the decoder, which performs a feature-level upsample-crop scheme to extract high-resolution part-specific features and adopt keypoint-guided deformable attention to estimate hand and face precisely. The whole pipeline is simple yet effective without any manual post-processing and naturally avoids implausible prediction. Comprehensive experiments demonstrate the effectiveness of OSX. Lastly, we build a large-scale Upper-Body dataset (UBody) with high-quality 2D and 3D whole-body annotations. It contains persons with partially visible bodies in diverse real-life scenarios to bridge the gap between the basic task and downstream applications.Comment: Accepted to CVPR2023; Top-1 on AGORA SMPLX benchmark; Project Page: https://osx-ubody.github.io

NeFII: Inverse Rendering for Reflectance Decomposition with Near-Field Indirect Illumination

Inverse rendering methods aim to estimate geometry, materials and illumination from multi-view RGB images. In order to achieve better decomposition, recent approaches attempt to model indirect illuminations reflected from different materials via Spherical Gaussians (SG), which, however, tends to blur the high-frequency reflection details. In this paper, we propose an end-to-end inverse rendering pipeline that decomposes materials and illumination from multi-view images, while considering near-field indirect illumination. In a nutshell, we introduce the Monte Carlo sampling based path tracing and cache the indirect illumination as neural radiance, enabling a physics-faithful and easy-to-optimize inverse rendering method. To enhance efficiency and practicality, we leverage SG to represent the smooth environment illuminations and apply importance sampling techniques. To supervise indirect illuminations from unobserved directions, we develop a novel radiance consistency constraint between implicit neural radiance and path tracing results of unobserved rays along with the joint optimization of materials and illuminations, thus significantly improving the decomposition performance. Extensive experiments demonstrate that our method outperforms the state-of-the-art on multiple synthetic and real datasets, especially in terms of inter-reflection decomposition.Comment: Accepted in CVPR 202