A Global Optimization Algorithm For Reconstructing Height Field From Discrete Normals

With the rapid development of computer vision technology,3D reconstruction technology has become one of the highly regarded directions.There are multiple reconstruction methods in 3D reconstruction technology,which can be divided into two categories.One method is to directly obtain the 3D information of the target object or scene,such as laser scanning,Li DAR,structured light method,time-of-flight method,and triangulation method.The other method is to obtain the normal field information of the object,and the 3D height information of the object needs to be obtained through algorithmic calculation,including photometric stereo method,shape from shading method,and deflection measurement method.Due to many practical problems in calculating the height field from the normal field of the object,the algorithm reconstructing the height field of the object from the normal field has become a research direction with practical value.This work is focus on the problem of obtaining the height field of an object surface through calculation,from known normal field.Mathematically,reconstructing the height field of a scene or object from the normal field can be seen as an integration process.However,due to the influence of normal field noise,the integration process can easily lead to error accumulation and other problems.This paper proposes a method of reconstructing the height field of an object from its normal field using discrete geometry.First,each point of the obtained object normal field is adjusted as a face to obtain the best orientation.Then,the least squares method is used to optimize the connections between each point in each row of the normal field,the optimized height field of each row is also can obtained.The optimized calculation of each row can reduce the computational memory.Finally,because the optimized height fields of each row are separated from each other,the optimized height value of a single or multiple columns is used as the basic height value to each row,and the complete object surface height field are reassembled.This algorithm is based on the calculation of image rows or columns,which can comprehensively utilize global image information for optimization and can effectively reduce error accumulation in theory.In the experimental part,local iterative method and the algorithm proposed in this paper were implemented using C#programming and their precision and computation speed are compared and analyzed based on four conditions.Firstly,several ideal geometric models show that,the local iterative method’s integration process will lead to error accumulation in the process of obtaining object height field,while the discrete method is able to reduce the error accumulation.Secondly,noise-contaminated conical surfaces were processed,and it was found that the local iterative method was greatly affected by noise,while the discrete method could obtain a relatively accurate object surface height field with little noise impact.Then,the two methods were tested using simple geometric models and a rabbit model.Both methods could obtain a height field close to the true geometric model for the simple geometric models,while the local iterative method had edge calculation errors in the rabbit model,but the discrete method could obtain an accurate height field and retain object edge information.Finally,the height field of a real oil painting normal map was reconstructed.It was found that aligning multiple columns could obtain the optimal oil painting surface height field.In terms of algorithmic computational efficiency,the iterative method was approximately 10~2times more efficient than the global optimization algorithm,compared with performance improvements,the computational cost proposed in this paper is acceptable.In summary,this paper proposes a method for obtaining an object’s surface height field from its normal field,and compares it’s precision and computation efficiency the iterative method by four conditions.The experimental results show that the proposed algorithm can obtain accurate and reliable object surface height fields from digital normal images,object surface edge information can be preserved,and it’s precision is less affected by noise.However,the disadvantage of this method is that it needs more computational cost than the iterative method,and needs to improved in the future.