Surface reconstruction in gradient-field domain using compressed sensing

Area of Science:

• Computer Vision
• Image Processing
• Computational Geometry

Background:

• Surface reconstruction from spatial gradients is crucial for applications like photometric stereo and shape-from-shading.
• Complex surfaces with shadowing and transparency require dense gradient measurements for accurate reconstruction.
• Hardware limitations can lead to insufficient sampling density, hindering the recovery of surface details.

Purpose of the Study:

• To resolve the problem of insufficient gradient sampling density in surface reconstruction.
• To introduce and evaluate Derivative Compressed Sensing (DCS) as a solution for enhanced surface reconstruction.

Main Methods:

• Derivative Compressed Sensing (DCS), a modification of classical Compressed Sensing (CS).
• Augmenting the standard CS setting with constraints from intrinsic properties of potential vector fields.
• Conducting numerical experiments to validate the proposed method.

Main Results:

• DCS reduces the number of required gradient measurements compared to standard dense sampling.
• DCS yields surface estimates with higher accuracy than traditional CS-based methods.
• DCS demonstrates smaller variability in estimates compared to CS-based approaches.

Conclusions:

• Derivative Compressed Sensing effectively addresses limitations in surface reconstruction due to sparse gradient data.
• DCS offers a more efficient and accurate approach for recovering surface details from limited measurements.
• The proposed method shows significant improvements over existing CS techniques for gradient-based surface reconstruction.