In order to improve the performance of estimating the fundamental matrix, a key problem arising in stereo vision, a novel method based on stripe constraints is presented. In contrast to traditional methods based on algebraic least-square algorithms, the proposed approach aims to minimize a cost function that is derived from the minimum radius of the Hough transform. In a structured-light system with a particular stripe code pattern, there are linear constraints that the points with the same code are on the same surface. Using the Hough transform, the pixels with the same code map to the Hough space, and the radius of the intersections can be defined as the evaluation function in the optimization progress. The global optimum solution of the fundamental matrix can be estimated using a Levenberg- Marquardt optimization iterative process based on the Hough transform radius. Results illustrate the validity of this algorithm, and prove that this method can obtain good performance with high efficiency.
To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.
