Interval Type-2 (IT2) fuzzy systems have gained significant attention due to their strong capability in handling system uncertainties. This paper investigates the robust stability analysis of conventional Takagi–Sugeno (TS) IT2 fuzzy systems under an observer-based control framework. A non-uniform piecewise linear approximation method is introduced to more accurately capture the boundary characteristics of IT2 membership functions (MFs), allowing key variation information of MFs to be effectively exploited. Subsequently, an error model transformation strategy is proposed to reconstruct approximation-induced errors into an auxiliary fuzzy model, enabling richer error-related and MF information to be explicitly incorporated into the stability conditions and thereby reducing conservatism. By leveraging Lyapunov stability theory and a scaling approach, sufficient stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be efficiently solved using standard convex optimization tools. Simulation results and comparative studies demonstrate that the proposed method achieves less conservative stability conditions and enhanced robustness compared with existing approaches.

In structured light systems, the accuracy of measurement notably diminishes when assessing complex texture objects, especially encountering boundaries between various colors. To address this challenge, this paper meticulously analyzes and establishes an error model, elaborating the correlation between phase errors and the gradients of phase and gray-scale. Based on this analysis, a novel high-precision method is proposed for measuring complex texture objects via bidirectional fringe projection. This approach firstly leverages horizontal and vertical fringe projections to derive bidirectional phase information and calculates the angles between the tangent of the texture edges and the phase gradient. Subsequently, a refined temporal phase correction algorithm is formulated based on the epipolar matching algorithm and the devised error model, effectively mitigating numerical instability issues within the algorithm and significantly reducing errors of bidirectional phases. Ultimately, corrected point clouds are calculated based on bidirectional phases, and the obtained point clouds are merged to further diminish phase errors. Comparison experiments indicate that this method can reduce Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) by 65.74% and 67.75%, respectively. Compared to existing methods, it improves performance by 27.29% and 33.74%, respectively, demonstrating superior performance.

To address the problem of robust stability analysis for interval type-2 fuzzy systems (IT2FSs), this paper proposes an innovative analysis approach based on model transformation. Firstly, a classical piecewise linear approximation method is utilized to process the upper boundary membership functions (UMFs) and lower boundary membership functions (LMFs) of the footprint of uncertainty (FOU) in IT2FSs, resulting in linear boundary membership functions (MFs) that are more convenient for analysis, along with the corresponding approximation error functions. Subsequently, a novel error model transformation method is introduced to handle these error terms. By constructing new fuzzy rules and MFs, the boundary error terms are converted into a new fuzzy model, thereby incorporating more information about the error functions into the stability analysis. Based on this model, a robust stability condition in the form of linear matrix inequalities (LMIs) are derived, achieving improved robustness. Finally, the effectiveness of the proposed method is validated through simulations on real-world systems, and its superiority is demonstrated by comparison with existing methods.

3D pose transfer over unorganized point clouds is a challenging generation task, which transfers a source’s pose to a target shape and keeps the target’s identity. Recent deep models have learned deformations and used the target’s identity as a style to modulate the combined features of two shapes or the aligned vertices of the source shape. However, all operations in these models are point-wise and independent and ignore the geometric information on the surface and structure of the input shapes. This disadvantage severely limits the generation and generalization capabilities. In this study, we propose a geometry-aware method based on a novel transformer autoencoder to solve this problem. An efficient self-attention mechanism, that is, cross-covariance attention, was utilized across our framework to perceive the correlations between points at different distances. Specifically, the transformer encoder extracts the target shape’s local geometry details for identity attributes and the source shape’s global geometry structure for pose information. Our transformer decoder efficiently learns deformations and recovers identity properties by fusing and decoding the extracted features in a geometry attentional manner, which does not require corresponding information or modulation steps. The experiments demonstrated that the geometry-aware method achieved state-of-the-art performance in a 3D pose transfer task. The implementation code and data are available at https://github.com/SEULSH/Geometry-Aware-3D-Pose-Transfer-Using-Transformer-Autoencoder .

3D reconstruction is a fundamental task in robotics and AI, providing a prerequisite for many related applications. Fringe projection profilometry is an efficient and non-contact method for generating 3D point clouds out of 2D images. However, during the actual measurement, it is inevitable to experiment with translucent objects, such as skin, marble, and fruit. Indirect illumination from these objects has substantially compromised the precision of 3D reconstruction via the contamination of 2D images. This paper presents a fast and accurate approach to correct for indirect illumination. The essential idea is to design a highly suitable network architecture founded on a precise error model that facilitates accurate error rectification. Initially, our method transforms the error generated by indirect illumination into a sine series. Based on this error model, the multilayer perceptron is more effective in error correction than traditional methods and convolutional neural networks. Our network was trained solely on simulated data but was tested on authentic images. Three sets of experiments, including two sets of comparison experiments, indicate that the designed network can efficiently rectify the error induced by indirect illumination.

Fringe projection profilometry is a widely used technique for 3D measurement due to its high accuracy and speed. However, the accuracy significantly decreases when measuring complex texture objects, especially in the junction of different colors. This paper analyzes the causes of errors resulting from complex textures and proposes a height compensation method to revise the error by employing a dual-projector structure. Moreover, the dual-projector is capable of acquiring a pair of errors with opposite signs, which can be utilized to calculate the accurate 3D information after determining the ratio of this pair of errors. Experiments provide significant improvement in measuring complex texture objects, demonstrating the proposed method's ability.