Geometric Approximation Method And Its Application In The Field Of Digital Image Processing

The function approximation problem has wide applications in digital image processing and communication engineering.In this thesis,several algorithms based on approximation and their applications in digital image processing are studied.The main contents include the following three points:(1)Exponential inequalities approximating trigonometric functions and their application in the field of digital signals.An exponential inequality approximation method is proposed for improving some famous triangular inequalities,including Jordan inequality,Cusa–Huygens inequality,Becker-Stark inequality,etc.,and provide them with simple proofs.Numerical examples show that the proposed method can obtain better approximation results compared with prevailing methods,and the obtained results can be applied to the field of digital image processing and communication.(2)Padé approximant to trigonometric bounding box method and its applications of digital image processing.A method based on two-point Padé approximation is proposed.For well-known trigonometric functions such as Wilker,this method has better approximation effect and provides new proofs as well.Numerical results show that the proposed method has smaller approximation errors than prevailing methods.The obtained results can also be applied to accelerate bilateral filtering algorithms.(3)Image noise location algorithm based on approximation.A noise location algorithm based on approximation is proposed.Experiments show that the algorithm has a certain effect on the noise contained in the image.It is expected to be used in images that require noise determination,such as defect detection,etc.,and can also be used in some noise-sensitive image algorithms such as Snake operators and Laplacian operators to avoid noise interference.Based on the noise location algorithm,the concept of discrimination is further proposed based on the energy function.It is expected that the prior probability of pixel point classification can be provided by the algorithm.