Aiming at the problem of missing data after point cloud data filtering, this paper proposes a point cloud repair method based on the principle of Linear Maximum Entropy, which converts the Maximum Entropy Model into a linear model, and then uses linear programming to solve the model. The mathematical expectation and variance in the elevation value is used to establish linear constraints, and the weight coefficient of the sampling point is solved by the maximum entropy value to determine the elevation value of the fixed point, so as to complete the point cloud repair. By comparing with Maximum Entropy Method and Inverse Distance Weight method, the feasibility of Linear Maximum Entropy Model in point cloud data repairs is discussed. The results show that the point cloud data repaired by the Linear Maximum Entropy Model is more accurate, and a high-quality model can be established.
There is negative-weight in traditional interpolation of gridding DEM, in the article, the principle of Maximum
Entropy is utilized to analyze the model system which depends on modulus of space weight. Negative-weight
problem of the DEM interpolation is researched via building Maximum Entropy model, and adding nonnegative,
first and second order’s Moment constraints, the negative-weight problem is solved. The correctness and accuracy
of the method was validated with genetic algorithm in matlab program. The method is compared with the method
of Yang Chizhong interpolation and quadratic program. Comparison shows that the volume and scaling of
Maximum Entropy’s weight is fit to relations of space and the accuracy is superior to the latter two.
In the geospatial data processing, a large number of mathematical models are nonlinear models. The observation equations are of strong nonlinearity and sensitivity to the initial value point of the series expansion. This paper proposes a regularization homotopy improved algorithm which is base on regularization method and homotopy continuation idea. This algorithm constructs regularization homotopy function by adding a stable functional to make nonlinear least square ill-posed problem into optimization problem. The iterative formula is derived by adopting the strategy of f (x) linearization, linking least square principle and introducing step size factor λ in the paper. Finally the calculation results of classical nonlinear least square problem show that regularization homotopy improved algorithm not only low dependence on initial value, but also make small fluctuation in the iterative process, and the solution is stable relatively. The method is correctly and applicable.
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