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Near-light Photometric Stereo with Symmetric Lights

Lilika Makabe, Heng Guo, Hiroaki Santo, Fumio Okura, Yasuyuki Matsushita

Abstract

This paper describes a linear solution method for near-light photometric stereo by exploiting symmetric light source arrangements. Unlike conventional non-convex optimization approaches, by arranging multiple sets of symmetric nearby light source pairs, our method derives a closed-form solution for surface normal and depth without requiring initialization. In addition, our method works as long as the light sources are symmetrically distributed about an arbitrary point even when the entire spatial offset is uncalibrated. Experiments showcase the accuracy of shape recovery accuracy of our method, achieving comparable results to the state-of-the-art calibrated near-light photometric stereo method while significantly reducing requirements of careful depth initialization and light calibration.

Near-light Photometric Stereo with Symmetric Lights

Abstract

This paper describes a linear solution method for near-light photometric stereo by exploiting symmetric light source arrangements. Unlike conventional non-convex optimization approaches, by arranging multiple sets of symmetric nearby light source pairs, our method derives a closed-form solution for surface normal and depth without requiring initialization. In addition, our method works as long as the light sources are symmetrically distributed about an arbitrary point even when the entire spatial offset is uncalibrated. Experiments showcase the accuracy of shape recovery accuracy of our method, achieving comparable results to the state-of-the-art calibrated near-light photometric stereo method while significantly reducing requirements of careful depth initialization and light calibration.
Paper Structure (19 sections, 1 theorem, 27 equations, 14 figures, 1 table)

This paper contains 19 sections, 1 theorem, 27 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related work
  3. Near-light photometric stereo
  4. Photometric stereo with specific light arrangement
  5. Problem statement
  6. Proposed method
  7. Symmetric-light constraints
  8. Linear constraints by light fall-off relaxation
  9. Surface normal and position estimation
  10. Optimality under relaxation
  11. Valid light arrangements
  12. Experiments
  13. Experimental settings
  14. Evaluation with synthetic scenes
  15. Effect of varying light-to-surface distance
  16. ...and 4 more sections

Key Result

Proposition 2

When the radii of the symmetric lights $r_*$ of all pairs are the same, all the possible Apollonius spheres are centered on a line, whose direction is $\left[-y',x',0\right]$.

Figures (14)

  • Figure 1: Examples of light source arrangement for our method. At least three pairs of symmetric point light sources are arranged to the image plane with a shared center. Our near-light photometric stereo achieves global minima in shape recovery using the proposed symmetric near-light configuration.
  • Figure 2: Overview of the proposed method. We consider the differences and summations of observations under the symmetric light pairs and construct a linear optimization system to estimate light-to-surface (scaled) distance $e_*$. From the scaled distance $e_*$, we compute the surface position (up to scale if radii are unknown) and normal.
  • Figure 3: Light coordinate system.
  • Figure 4: Relative vector relation.
  • Figure 5: Examples of valid/invalid light arrangements.
  • ...and 9 more figures

Theorems & Definitions (1)

  • Proposition 2