Accurate geometrical optics model for single-lens stereovision system using a prism

Area of Science:

• Optics
• Computer Vision
• Geometric Modeling

Background:

• Analyzing image formation in optical systems like prisms is crucial for 3D reconstruction.
• Existing methods may lack accuracy or efficiency in complex optical setups.
• Prism-based systems offer unique advantages for stereovision and depth perception.

Purpose of the Study:

• To propose a novel method for analyzing prism image formation based on optical geometry.
• To derive a transformation matrix representing object-image relationships through prism refraction.
• To demonstrate the application of this matrix in epipolar geometry and 3D point reconstruction.

Main Methods:

• The prism is modeled as a system of individual planes.
• Each plane's optical transformation is analyzed and combined.
• A comprehensive transformation matrix is derived for the entire prism system.

Main Results:

• The derived transformation matrix accurately describes image formation by prism refraction.
• The method enables accurate 3D point reconstruction and epipolar geometry analysis.
• Experimental results show superior accuracy compared to previous methods and comparability with multicamera systems.

Conclusions:

• The proposed optical geometry method provides an accurate and efficient way to analyze prism image formation.
• This technique is suitable for multiocular prism systems and 3D reconstruction applications.
• The derived transformation matrix offers a valuable tool for optical system design and analysis.