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Reconstruction of the relative coordinates of image using projective geometry

Augustynowicz M., Sawicki D.

Przegląd Elektrotechniczny

2016

R. 92, nr 1

208--211

Problem of determining the relative position often occurs in the process of image recognition. In general form, it can be described as quadrilateral to rectangle transformation. This paper describes and compares methods of simple relative coordinates calculation on the flat surface. The surface position can be set at any angle to the camera and in any rotation as well. The problem can be solved in efficient way using projective geometry, the new reconstruction method is introduced.

Problem określenia względnego położenia obiektów często występuje w procesie rozpoznawania obrazu. W ogólnej postaci, może to być opisane przekształceniem dowolnego czworokąta w prostokąt. W artykule przeanalizowano proste przekształcenia tego typu dla dowolnego ustawienia płaskiej powierzchni względem kamery. Został zaproponowany nowy algorytm, który rozwiązuje problem w prosty sposób z wykorzystaniem geometrii rzutowej.

Scatter matrix based iterative structure and pose estimation from a single image

Rodrigues M. A., Liu Y., Wei Q.

Machine Graphics and Vision

2000

Vol. 9, No. 1/2

525-538

It has been demonstranted that the constraint least squeres (CLS) method yields accurate and robust motion parameter estimation from range images ([16,20]) assuming that the image data are corrupted by noise only without outliers. Also, it has been shown that scatter matrix based correspondenceless motion estimation from range images ([4]) is mathematically well defined. In this paper, we propose a new accurate and robust method for pose and strycture estimation from perspective images that draws on the good features of scatter matrix and constraint least squares methods. For reasons of parciticality and efficiency, the method first iteratively estimates the depth of some control points based on the constraints induced from the scatter matrix based correspondenceless motion estimation algorithm and then provides a closed from estimation of the depths of the other points based on rigid constraints. Finally, the method estimates pose parameters by the constraint least squares. For a comparative study of performance, we also omplemented a linear algorithm for pose estimation and a motion estimation algorithm based on epipolar geometry, [2, 24]. Experimental results based on both synthetic data and real images shown the relative superior performance of the proposed algoithm.