Zolly: Zoom Focal Length Correctly for Perspective-Distorted Human Mesh Reconstruction

As it is hard to calibrate single-view RGB images in the wild, existing 3D human mesh reconstruction (3DHMR) methods either use a constant large focal length or estimate one based on the background environment context, which can not tackle the problem of the torso, limb, hand or face distortion caused by perspective camera projection when the camera is close to the human body. The naive focal length assumptions can harm this task with the incorrectly formulated projection matrices. To solve this, we propose Zolly, the first 3DHMR method focusing on perspective-distorted images. Our approach begins with analysing the reason for perspective distortion, which we find is mainly caused by the relative location of the human body to the camera center. We propose a new camera model and a novel 2D representation, termed distortion image, which describes the 2D dense distortion scale of the human body. We then estimate the distance from distortion scale features rather than environment context features. Afterwards, we integrate the distortion feature with image features to reconstruct the body mesh. To formulate the correct projection matrix and locate the human body position, we simultaneously use perspective and weak-perspective projection loss. Since existing datasets could not handle this task, we propose the first synthetic dataset PDHuman and extend two real-world datasets tailored for this task, all containing perspective-distorted human images. Extensive experiments show that Zolly outperforms existing state-of-the-art methods on both perspective-distorted datasets and the standard benchmark (3DPW)

Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity

We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations, from time-dependent backscattering experimental radar data associated with a single source of electric pulses. The refractive index is$n\left(\mathbf{x}\right) =\sqrt{\varepsilon_{r}\left(\mathbf{x}\right)}.$The coefficient$\varepsilon_{r}\left(\mathbf{x}\right) $ is reconstructed using a two-stage reconstruction procedure. In the first stage an approximately globally convergent method proposed is applied to get a good first approximation of the exact solution. In the second stage a locally convergent adaptive finite element method is applied, taking the solution of the first stage as the starting point of the minimization of the Tikhonov functional. This functional is minimized on a sequence of locally refined meshes. It is shown here that all three components of interest of targets can be simultaneously accurately imaged: refractive indices, shapes and locations