Line Primitives and Their Applications in Geometric Computer Vision

Zhang, Lilian

Line primitives are widely found in structured scenes which provide a higher level of structure information about the scenes than point primitives. Furthermore, line primitives in space are closely related to Euclidean transformations, because the dual vector (also known as Pluecker coordinates) representation of 3D lines is the counterpart of the dual quaternion which depicts an Euclidean transformation. These geometric properties of line primitives motivate the work in this thesis with the following contributions: Firstly, by combining local appearances of lines and geometric constraints between line pairs in images, a line segment matching algorithm is developed which constructs a novel line band descriptor to depict the local appearance of a line and builds a relational graph to measure the pair-wise consistency between line correspondences. Experiments show that the matching algorithm is robust to various image transformations and more efficient than conventional graph based line matching algorithms. Secondly, by investigating the symmetric property of line directions in space, this thesis presents a complete analysis about the solutions of the Perspective-3-Line (P3L) problem which estimates the camera pose from three reference lines in space and their 2D projections. For three spatial lines in general configurations, a P3L polynomial is derived which is employed to develop a solution of the Perspective-n-Line problem. The proposed robust PnL algorithm can efficiently and accurately estimate the camera pose for both small numbers and large numbers of line correspondences. For three spatial lines in special configurations (e.g., in a Manhattan world which consists of three mutually orthogonal dominant directions), the solution of the P3L problem is employed to solve the vanishing point estimation and line classification problem. The proposed vanishing point estimation algorithm achieves high accuracy and efficiency by thoroughly utilizing the Manhattan world characteristic. Another advantage of the proposed framework is that it can be easily generalized to images taken by central catadioptric cameras or uncalibrated cameras. The third major contribution of this thesis is about structure-from-motion using line primitives. To circumvent the Pluecker constraints on the Pluecker coordinates of lines, the Cayley representation of lines is developed which is inspired by the geometric property of the Pluecker coordinates of lines. To build the line observation model, two derivations of line projection functions are presented: one is based on the dual relationship between points and lines; and the other is based on the relationship between Pluecker coordinates and the Pluecker matrix. Then the motion and structure parameters are initialized by an incremental approach and optimized by sparse bundle adjustment. Quantitative validations show the increase in performance when compared to conventional line reconstruction algorithms.

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Zhang, Lilian: Line Primitives and Their Applications in Geometric Computer Vision. 2013.

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