人眼立体视觉空间与虚拟三维空间的几何映射关系理论分析

J4 ›› 2014, Vol. 36 ›› Issue (06): 1120-1126.

人眼立体视觉空间与虚拟三维空间的几何映射关系理论分析

廖明1,2,周良辰1,闾国年1,盛业华1,潘轶2,曹燕2

(1.南京师范大学地理科学学院,江苏南京 220078;2.解放军理工大学，江苏南京 210007)

收稿日期:2013-01-03 修回日期:2013-04-28 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家科技支撑计划课题资助（2012BAH35B02）；国家自然科学青年基金资助项目(2011105GZ30030)；校内预先研究基金资助项目（KYGYZLXY1309,KYGYZLYY1304)

Theoretical analysis of the geometric relations between
human stereo visional space and virtual 3D space

LIAO Ming1,2,ZHOU Liangchen1,L Guonian1,SHENG Yehua1,PAN Yi2，CAO Yan2

（1.School of Geography Science,Nanjing Normal University,Nanjing 220078;
2.PLA University of Science & Technology,Nanjing 210007,China）

Received:2013-01-03 Revised:2013-04-28 Online:2014-06-25 Published:2014-06-25

摘要/Abstract

摘要：

虚拟三维空间是现实世界的数字化三维空间，而人眼立体视觉空间则是人眼视觉系统对于现实世界或虚拟世界所形成的三维立体构象。传统上人眼直接观察现实世界，确立了人眼立体视觉空间与现实世界之间的几何对应关系。而人眼立体视觉空间与虚拟三维空间是否也存在对应的几何关系？以人眼立体视觉和虚拟三维场景为研究对象，根据双目视差原理，论述了人眼立体视觉的几何模型及视觉三维模型的表示形式。通过分析虚拟空间三维点元、屏幕视差及网膜视差等三者之间的内在几何关系，利用矩阵代数建立了虚拟空间与视觉空间之间的几何映射关系。这一映射关系表明视觉三维模型与虚拟三维模型之间存在一一对应关系，也反映了人眼视觉系统在虚拟空间中的可测量性质。本文创新性之处在于得到了视觉三维模型的完整表示，突破了传统上立体显示的定性感知，提供了定量分析的基础。这一工作对于在虚拟空间中的立体体验、虚拟交互以及立体测量等实践活动具有一定理论参考价值。

关键词: 立体视觉, 双目视差, 视模型, 立体像对, 同名像点, 虚拟三维空间

Abstract:

The virtual 3D space is a digital one of real world and the human stereo visional space is a 3D reconstruction of the real world or virtual scene through human visional system. Traditionally, human views the environment around himself directly and the geometric relationship between the human stereo visional space and the real world exists undoubtedly. How about the relations of stereo visional space to the virtual 3D space are? According to the principle of binocular disparity, a geometric model of stereo vision is established for the virtual 3D scene and the corresponding visional 3D model is constructed too. And the screen disparity and retina disparity are analyzed with respect to an arbitrary spatial point. As a result, the geometric mapping between the point of virtual space and the one in visional space is established with matrix algebra, indicating that the 3D visional model can be mapped to a virtual 3D model unambiguously and the metric capability of human visional system is intrinsic. The main contribution of this paper is that a wholesome visional 3D model is proposed, which lays down a quantitative analysis foundation for the traditional stereo vision. The results are useful theory explorations for the stereo presence, the virtual interaction and the metric applications.

Key words: stereo vision;binocular disparity;3D visional model;stereo image pair;conjugated points;virtual 3D space

廖明1,2,周良辰1,闾国年1,盛业华1,潘轶2,曹燕2. 人眼立体视觉空间与虚拟三维空间的几何映射关系理论分析[J]. J4, 2014, 36(06): 1120-1126.

LIAO Ming1,2,ZHOU Liangchen1,L Guonian1,SHENG Yehua1,PAN Yi2，CAO Yan2. Theoretical analysis of the geometric relations between
human stereo visional space and virtual 3D space [J]. J4, 2014, 36(06): 1120-1126.

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