Zhiping Shi

Formal Kinematic Analysis of a General 6R Manipulator Using the Screw Theory

Kinematic analysis is a significant method when planning the trajectory of robotic manipulators. The main idea behind kinematic analysis is to study the motion of the robot based on the geometrical relationship of the robotic links and their joints, such as the Denavit-Hartenberg parameters. Given the continuous nature of kinematic analysis and the shortcoming of the traditional verification methods, we propose to use high-order-logic theorem proving for conducting formal kinematic analysis. Based on the screw theory in HOL4, which is newly developed by our research institute, we utilize the geometrical theory of HOL4 to develop formal reasoning support for the kinematic analysis of a robotic manipulator. To illustrate the usefulness of our fundamental formalization, we present the formal kinematic analysis of a general 6R manipulator.

The Retrieval of Shoeprint Images Based on the Integral Histogram of the Gabor Transform Domain

Shoeprint images which are extracted at the scene of cases are a kind of important modern forensic clue and evidence. Retrieving the images of the same or the similar shoeprint images from the database quickly and accurately is very important to criminal investigation. To deal with the fragmental shoeprint images, we propose a shoeprint images matching and retrieval algorithm which computing the integral histogram in the Gabor transform domain. First, through the integral histogram find out the most similar position of the fragmental image in the intact image. Then, extract the features of the region found in the first step. At last, compute the similarity of the two components. Experiment results prove that this algorithm leads an increase of 4.82% in the retrieval precision, compared with computing the global features of two images directly.

Formal analysis of the kinematic Jacobian in screw theory

As robotic systems flourish, reliability has become a topic of paramount importance in the human–robot relationship. The Jacobian matrix in screw theory underpins the design and optimization of robotic manipulators. Kernel properties of robotic manipulators, including dexterity and singularity, are characterized with the Jacobian matrix. The accurate specification and the rigorous analysis of the Jacobian matrix are indispensable in guaranteeing correct evaluation of the kinematics performance of manipulators. In this paper, a formal method for analyzing the Jacobian matrix in screw theory is presented using the higher-order logic theorem prover HOL4. Formalizations of twists and the forward kinematics are performed using the product of exponentials formula and the theory of functional matrices. To the best of our knowledge, this work is the first to formally analyze the kinematic Jacobian using theorem proving. The formal modeling and analysis of the Stanford manipulator demonstrate the effectiveness and applicability of the proposed approach to the formal verification of the kinematic properties of robotic manipulators.

Robust Principal Component Analysis via Symmetric Alternating Direction for Moving Object Detection

Robust Principal Component Analysis (RPCA) has been proved to be effective for the moving object detection with background variation. Alternating Direction Method (ADM) based RPCA takes full advantages of the separable structure of the objective function to achieve better results than traditional RPCA methods. But it suffers from the heavy computing burden and low efficiency. In this paper, a Symmetric Alternating Direction Method (SADM) is proposed to solve above problems. SADM optimizes the iterative strategy of ADM by updating the multiplier of the linear constraint twice every iteration which speeds up the convergence, thus reduces the execution times of Singular Value Decomposition (SVD). Besides, the new equilibrium parameter and interrupt mechanism are introduced to guarantee the object detection accuracy and avoid the unnecessary iterations. Compared with ADM, the experimental results show that not only the detection accuracy of proposed method is improved by 46.8%, but also the time consumption is reduced by 97.5%.

A Confidence Weighted Real-Time Depth Filter for 3D Reconstruction

3D reconstruction is an important technique in the environmental perception and rehabilitation process. With the help of active depth-aware sensors, such as Kinect from Microsoft and SwissRanger, the depth map can be captured at the video frame rate together with color information to enable the real-time reconstruction. Particularly, it features prominently in the activity recognition and remote rehabilitation. Unfortunately, the coarseness of the depth map make it difficult to extract the detailed information in 3D reconstruction of the scene and tracking of thin objects. Especially, geometric distortions occur around the edge of an object. Therefore, this paper presents a confidence weighted real-time depth filter for the edge recovery to reduce the extra artifacts due to the uncertainty of each depth measurement. Also the intensity of depth map is taken into account to optimize the weighting term in the algorithm. Moreover, the GPU implementation guarantees the high computational efficiency for the real-time applications. Experimental results are shown to illustrate the performance of the proposed method by the comparisons with the traditional methods.

The Formalization of Discrete Fourier Transform in HOL

Traditionally, Discrete Fourier Transform (DFT) is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT) and cosine frequency shift.

Formalizing the Matrix Inversion Based on the Adjugate Matrix in HOL4

This paper presents the formalization of the matrix inversion based on the adjugate matrix in the HOL4 system. It is very complex and difficult to formalize the adjugate matrix, which is composed of matrix cofactors. Because HOL4 is based on a simple type theory, it is difficult to formally express the sub-matrices and cofactors of an n-by-n matrix. In this paper, special n-by-n matrices are constructed to replace the (n − 1)-by-(n − 1) sub-matrices, in order to compute the cofactors, thereby, making it possible to formally construct aadjugate matrices. The Laplace’s formula is proven and the matrix inversion based on the adjugate matrix is then inferred in HOL4. The paper also presents formal proofs of properties of the invertible matrix.

Multipath Convolutional-Recursive Neural Networks for Object Recognition

Extracting good representations from images is essential for many computer vision tasks. While progress in deep learning shows the importance of learning hierarchical features, it is also important to learn features through multiple paths. This paper presents Multipath Convolutional-Recursive Neural Networks(M-CRNNs), a novel scheme which aims to learn image features from multiple paths using models based on combination of convolutional and recursive neural networks (CNNs and RNNs). CNNs learn low-level features, and RNNs, whose inputs are the outputs of the CNNs, learn the efficient high-level features. The final features of an image are the combination of the features from all the paths. The result shows that the features learned from M-CRNNs are a highly discriminative image representation that increases the precision in object recognition.

Automatic Image Annotation and Retrieval Using Hybrid Approach

We firstly propose continuous probabilistic latent semantic analysis (PLSA) to model continuous quantity. In addition, corresponding Expectation-Maximization (EM) algorithm is derived to determine the model parameters. Furthermore, we present a hybrid framework which employs continuous PLSA to model visual features of images in generative learning stage and uses ensembles of classifier chains to classify the multi-label data in discriminative learning stage. Since the framework combines the advantages of generative and discriminative learning, it can predict semantic annotation precisely for unseen images. Finally, we conduct a series of experiments on a standard Corel dataset. The experiment results show that our approach outperforms many state-of-the-art approaches.

A Novel Model for Semantic Learning and Retrieval of Images

In this paper, we firstly propose an extended probabilistic latent semantic analysis (PLSA) to model continuous quantity. In addition, corresponding EM algorithm is derived to determine the parameters. Then, we apply this model in automatic image annotation. In order to deal with the data of different modalities according to their characteristics, we present a semantic annotation model which employs continuous PLSA and traditional PLSA to model visual features and textual words respectively. These two models are linked with the same distribution over all aspects. Furthermore, an asymmetric learning approach is adopted to estimate the model parameters. This model can predict semantic annotation well for an unseen image because it associates visual and textual modalities more precisely and effectively. We evaluate our approach on the Corel5k and Corel30k dataset. The experiment results show that our approach outperforms several state-of-the-art approaches.