Shape Recovery from Differential Motion with Unknown Reflectance
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Solution Overview
Problem
Existing shape determination methods from optical flow rely on incorrect assumptions such as brightness constancy and diffuse reflection, failing to accurately account for real-world objects' reflectance behavior, particularly under unknown bidirectional reflectance distribution functions (BRDF).
Innovation Solution
A computer-implemented method that determines shape from differential motion by relating image intensities to arbitrary BRDF, using various camera and illumination conditions, including orthographic and perspective projections, colocated lighting, area lighting, and RGB+Depth sensors, to eliminate BRDF terms and recover depth and surface normal.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If brightness constancy assumption is used, then shape determination is simplified, but accuracy deteriorates due to incorrect physical model
Solution Approach 1:
The patent changes the fundamental parameter of reflectance modeling from simplified assumptions (brightness constancy or diffuse reflection) to the general BRDF function. This allows the system to accurately model real-world reflectance behavior while maintaining computational feasibility through differential motion analysis that eliminates BRDF terms.
2Device complexity
If diffuse reflection model is used, then computation is simplified, but accuracy deteriorates for most real-world objects
Solution Approach 1:
The patent extracts and eliminates the BRDF terms from the imaging equations through differential motion analysis. By taking the time derivative of the imaging equation and eliminating BRDF dependencies, the system obtains a simplified relation between image intensities, motion, and shape that is accurate for general reflectance models without requiring complex computations.
3Measurement precision
If unknown BRDF is modeled, then reflectance accuracy is improved, but problem complexity increases
Solution Approach 1:
The patent uses differential motion (time derivatives) to transform the static imaging problem into a dynamic one. By analyzing changes in image intensity over time during object motion, the system can eliminate BRDF terms and recover shape information that would otherwise be inaccessible with static images and unknown reflectance.
Data Source
AI summary
A computer implemented method for determining shape from differential motion with unknown reflectance includes deriving a general relation that relates spatial and temporal image derivatives to bidirectional reflectance distribution function BRDF derivatives, responsive to 3D points and relative camera poses from images and feature tracks of an object in motion under colocated and unknown directional light conditions, employing a rank deficiency in image sequences from the deriving for shape determinations, under predetermined multiple camera and lighting conditions, to eliminate BDRF terms; and recovering a surface depth for determining a shape of the object.