The Chinese Center for Resources Satellite Data and Application (CRESDA) has released wide-swath optical imagery from GF-1, GF-6, and HJ-2A/B satellites for free, forming a virtual constellation capable of near-daily coverage of the national land surface. However, their geolocation accuracy typically exhibits errors of 2~3 pixels, which is insufficient for generating high-quality Analysis Ready Data (ARD). This study proposed a universal and efficient method, referred to as UniFast, for the accurate geometric correction of these wide-swath optical imagery. The UniFast has three key innovations: (1) integrated modeling and correction of internal nonlinear distortions and external attitude errors, (2) use of globally available Landsat imagery as reference data instead of geometric calibration field and (3) generalized applicability to GF-1/6 and HJ-2A/B satellite imagery. Experiments are carried out at two test sites, including a mountainous area in southeastern China and a texture less desert in western China. This study involves 26 scenes images downloaded from CRESDA, which shows that initial RMSEs reach up to 5.64 pixels. After applying the UniFast, all sensors achieve sub-pixel geolocation accuracy, with absolute errors consistently below one pixel. Specifically, the relative RMSEs among multi-satellites are reduced from a maximum of 3.53 pixels to below 0.3 pixels in the mountainous site, and from 4.99 pixels to below 0.5 pixels in the desert site. These results demonstrate the effectiveness and versatility of the UniFast, which overcomes a critical bottleneck in global change studies utilizing remote sensing images from the Chinese virtual constellation.

Algebraic boundaries of convex semi-algebraic sets are closely related to polynomial optimization problems. Building upon Rainer Sinn’s work, we refine the stratification of iterated singular loci to a Whitney (a) stratification, which gives a list of candidates of varieties whose dual is an irreducible component of the algebraic boundary of the dual convex body. We also present an algorithm based on Teissier’s criterion to compute Whitney (a) stratifications, which employs conormal spaces and prime decomposition.

The kinematic analysis of redundant serial manipulators with$2n+1$revolute joints (integer$n \geq 3$), which we call circular manipulators, is presented in this article. The structure of the kinematic chain of circular manipulators has special properties that can be seen in the Denavit–Hartenberg parameters: all orthogonal distances are zero, all even-numbered offsets are zeros, but odd-numbered offsets are not. Typical manipulators that fulfill these properties are redundant 7R serial chains ($n=3$) that mimic the human arm, e.g., the lightweight robot arm KUKA LBR iiwa. This 7R circular manipulator has self-motion as rotation around an axis that goes through two fixed points for a fixed pose. First, radical reparametrization is presented based on the swivel angle of the closed-form inverse kinematics solution for the 7R circular manipulator. Second, for a six-dimensional task, the inverse kinematics solution for redundant serial manipulators with$2n+1$revolute joints ($n\geq 3$) is reparametrized by the swivel angle and other$2n-6$rotation parameters. From a geometric point of view, for a circular manipulator with$2n+1$revolute joints, one can have${n(n-1)}/{2}$choices of such circular rotations. Third, we conjecture numerical kinematic singularities for circular manipulators in a recursive formula, confirming$n=5,6,7$.

We consider the problem of acquiring mechanical knowledge through visual cues to help robots use objects in new situations. In this work, we propose a novel deep learning approach that allows a robot to acquire mechanical knowledge from 3D point clouds. This presents two main challenges. The first challenge is that a robot needs to infer novel objects' functions from its experience. Secondly, the robot should also need to know how to manipulate these novel objects. To solve these problems, we present a two-branch deep neural network. The first branch detects function parts from the point clouds while the second branch predicts offset poses. Fusing the results from these two branches, our approach can not only detect what functions the novel objects may have but also generate key object states which can be used to guide a robot to manipulate these objects. We show that even though most of the training samples are synthetic data, our model still learns useful features and outputs proper results. Finally, we evaluate our approach on a real robot to run a series of tasks. The experimental results show that our approach has the capability to transfer mechanical knowledge in new situations.

Abstract We present an interactive tool compatible with existing software (Rhino/Grasshopper) to design ring structures with a paradoxic mobility, which are self‐collision‐free over the complete motion cycle. Our computational approach allows non‐expert users to create these invertible paradoxic loops with six rotational joints by providing several interactions that facilitate design exploration. In a first step, a rational cubic motion is shaped either by means of a four pose interpolation procedure or a motion evolution algorithm. By using the representation of spatial displacements in terms of dual‐quaternions, the associated motion polynomial of the resulting motion can be factored in several ways, each corresponding to a composition of three rotations. By combining two suitable factorizations, an arrangement of six rotary axes is achieved, which possesses a 1‐parametric mobility. In the next step, these axes are connected by links in a way that the resulting linkage is collision‐free over the complete motion cycle. Based on an algorithmic solution for this problem, collision‐free design spaces of the individual links are generated in a post‐processing step. The functionality of the developed design tool is demonstrated in the context of an architectural and artistic application studied in a master‐level studio course. Two results of the performed design experiments were fabricated by the use of computer‐controlled machines to achieve the necessary accuracy ensuring the mobility of the models.

This paper presents a novel coprime blurred pair (CBP) model to improve data security in camera surveillance. While most previous approaches have focused on completely encrypting the video stream, we introduce a spatial encryption scheme by strategically blurring the image/video contents. Specifically, we form a public stream and a private stream by blurring the original video data using two different kernels. Each blurred stream will provide the user who has lower clearance less access to personally identifiable details while still allowing behavior to be monitored. If the behavior is recognized as suspicious, a supervisor can use both streams to deblur the contents. Our approach is based on a new CBP theory where the two kernels are coprime when mapped to bivariate polynomials in the $(z)$ domain. We show that coprimality can be derived in terms of the rank of Bézout matrix formed by sampled polynomials, and we present an efficient algorithm to factor the Bézout matrix for recovering the latent image. To make our solution practical, we implement our decryption scheme on a graphics processing unit (GPU) to achieve real-time performance. Extensive experiments demonstrate that our new scheme can effectively protect sensitive identity information in surveillance videos and faithfully reconstruct the unblurred video stream when both CBP sequences are available.

We present a new Coprime Blurred Pair (CBP) theory that may benefit a number of computer vision applications. A CBP is constructed by blurring the same latent image with two unknown kernels, where the two kernels are co-prime when mapped to bivariate polynomials under the z-transform. We first show that the blurred contents in a CBP are difficult to restore using conventional blind deconvolution methods based on sparsity priors. We therefore introduce a new coprime prior for recovering the latent image in a CBP. Our solution maps the CBP to bivariate polynomials and sample them on the unit circle in both dimension. We show that coprimality can be derived in terms of the rank of the Bézout Matrix [2] formed by the sampled polynomials and we present an efficient algorithm to factor the Bézout Matrix for recovering the latent image. Finally, we discuss applications of the CBP theory in privacy-preserving surveillance and motion deblurring, as well as physical implementations of CBPs using flutter shutter cameras.

The problem of blind image deconvolution can be solved by computing approximate greatest common divisors (GCD) of polynomials. The bivariate polynomials corresponding to the z-transforms of several blurred images have an approximate GCD corresponding to the z-transform of the original image. Since blurring functions as cofactors have very low degree in general, this GCD will be of high degree. On the other hand, if we only have one blurred image and want to identify the original scene, the blurred image can be partitioned such that each part completely contains the blurring function, hence the blurring function becomes the GCD which is of low degree. Therefore, we design a specialized algorithm for computing GCDs of polynomials to recover true images in two different cases. The new algorithm is based on the fast GCD algorithm for univariate polynomials and the Fast Fourier Transform (FFT) algorithm. The complexity of our specialized algorithm for identifying both the true image and the blurring functions from blurred images of size n x n is O(n2 log(n)) in the case of blurring functions of very low degree. The algorithm has been implemented in Maple and can extract true images of hundreds by hundreds pixel images from blurred images in a few seconds.