Breast cancer is one of the most prevalent forms of cancer in the world today. The search for effective treatment and screening methods is a highly active area of research. The Digital Image-based ElastoTomography (DIET) project is a new breast cancer screening system under development, where surface motion from the mechanically actuated breast is measured in 3D, and used as input to an inverse problem solving for breast elasticity. Cancerous lesions appear as high contrast features, being an order of magnitude stiffer than healthy tissue. The 3D motion capture is measured by an array of digital cameras using computer vision techniques. This thesis presents a complete imaging system and algorithms for the capture of 3D breast surface motion. The main components of the 3D motion capture system are the hardware and software image capture system, camera calibration, intra-image feature tracking, and 3D surface and motion reconstruction. Accurate algorithms for each of these components are developed, with a view to future development and potential modifications needed for a clinically-appropriate system. A number of the algorithms developed have potential applications outside of the DIET system. Proof of concept studies demonstrate the viability of the system, with full motion reconstruction being performed on silicone gel phantoms, designed to approximate human soft tissue, in a number of laboratory experiments.