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3D Imaging of Complex Specular Surfaces by Fusing Polarimetric and Deflectometric Information

Jiazhang Wang, Oliver Cossairt, Florian Willomitzer

TL;DR

The paper tackles the challenge of robust 3D imaging of specular surfaces, where traditional PMD suffers from normal-depth ambiguity and SfP suffers from polarization ambiguities and an orthographic assumption. It introduces a fusion method that jointly leverages PMD geometry and shape-from-polarization cues to recover absolute surface normals and depth without the orthographic constraint, usable in single-shot or multi-shot configurations. The key contributions include an analytic framework to resolve all normal and depth ambiguities, a practical polarization-camera–based setup, and quantitative validation achieving a normal error below $ $0.6^\circ$ and accurate surface radii on a bearing ball, plus qualitative results on complex free-form shapes. The approach promises significant impact for high-precision surface metrology with applications in industrial inspection, medical imaging, AR/VR, cultural heritage, and robotics, by enabling fast, accurate 3D reconstructions of challenging specular objects.

Abstract

Accurate and fast 3D imaging of specular surfaces still poses major challenges for state-of-the-art optical measurement principles. Frequently used methods, such as phase-measuring deflectometry (PMD) or shape-from-polarization (SfP), rely on strong assumptions about the measured objects, limiting their generalizability in broader application areas like medical imaging, industrial inspection, virtual reality, or cultural heritage analysis. In this paper, we introduce a measurement principle that utilizes a novel technique to effectively encode and decode the information contained in a light field reflected off a specular surface. We combine polarization cues from SfP with geometric information obtained from PMD to resolve all arising ambiguities in the 3D measurement. Moreover, our approach removes the unrealistic orthographic imaging assumption for SfP, which significantly improves the respective results. We showcase our new technique by demonstrating single-shot and multi-shot measurements on complex-shaped specular surfaces, displaying an evaluated accuracy of surface normals below $0.6^\circ$.

3D Imaging of Complex Specular Surfaces by Fusing Polarimetric and Deflectometric Information

TL;DR

The paper tackles the challenge of robust 3D imaging of specular surfaces, where traditional PMD suffers from normal-depth ambiguity and SfP suffers from polarization ambiguities and an orthographic assumption. It introduces a fusion method that jointly leverages PMD geometry and shape-from-polarization cues to recover absolute surface normals and depth without the orthographic constraint, usable in single-shot or multi-shot configurations. The key contributions include an analytic framework to resolve all normal and depth ambiguities, a practical polarization-camera–based setup, and quantitative validation achieving a normal error below 0.6^\circ$ and accurate surface radii on a bearing ball, plus qualitative results on complex free-form shapes. The approach promises significant impact for high-precision surface metrology with applications in industrial inspection, medical imaging, AR/VR, cultural heritage, and robotics, by enabling fast, accurate 3D reconstructions of challenging specular objects.

Abstract

Accurate and fast 3D imaging of specular surfaces still poses major challenges for state-of-the-art optical measurement principles. Frequently used methods, such as phase-measuring deflectometry (PMD) or shape-from-polarization (SfP), rely on strong assumptions about the measured objects, limiting their generalizability in broader application areas like medical imaging, industrial inspection, virtual reality, or cultural heritage analysis. In this paper, we introduce a measurement principle that utilizes a novel technique to effectively encode and decode the information contained in a light field reflected off a specular surface. We combine polarization cues from SfP with geometric information obtained from PMD to resolve all arising ambiguities in the 3D measurement. Moreover, our approach removes the unrealistic orthographic imaging assumption for SfP, which significantly improves the respective results. We showcase our new technique by demonstrating single-shot and multi-shot measurements on complex-shaped specular surfaces, displaying an evaluated accuracy of surface normals below .
Paper Structure (4 sections, 8 equations, 2 figures)

This paper contains 4 sections, 8 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Mathematical framework
  3. Our solution
  4. Summary and Discussion

Figures (2)

  • Figure 1: 3D imaging of specular surfaces: Shortcomings of current methods and our solution: a) Normal-depth ambiguity in phase-measuring deflectometry (PMD): Without knowing the position $S$ of each object surface point along the camera ray, the respective surface normal can not be retrieved. b) In shape from polarization (SfP), the ambiguity in two potential zenith angles and two potential azimuth angles leads to four candidates for each surface normal. Moreover, the unrealistic orthographic assumption leads to high normal errors in off-center image regions. c) Our proposed solution combines geometric information from PMD and polarization information from SfP, to calculate the shape and normal map of the specular object surface in single-shot with high accuracy, free from any ambiguity.
  • Figure 2: Quantitative and Qualitative measurements. (a) Experimental setup: Quantitative measurement of a bearing ball with known size. (b) Sample polarization camera image. (c) Retrieved normal map (RMSE normal error: $0.6^\circ$). (d) 3D surface shape. (e)-(l) Qualitative measurements of two objects (horse and bird) with complex shapes (high surface frequencies). Columns from left to right: object pictures, captured sample camera images, evaluated surface normal map, evaluated 3D shape.