combiningdepthfusion and photometricstero for fine-detailed3d models … · 2019. 6. 13. ·...

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Combining Depth Fusion and Photometric Sterofor Fine-Detailed 3D Models

Erik Bylow+,*, Robert Maier+, Fredrik Kahl⟡, Carl Olsson*,⟡+Technical University of Munich, *Lund University,

⟡Chalmers University of Technology Technische Universität München

• Input: TSDF, depth- and intensity-images and camera positions• Reflectance Model: Lambertian model and spherical harmonics

• Optimiziation: Optimize over normals, albedo and light sources• Output: 3D model with more details

RGB-D Data

Varying Illumina�on

depth

TSDF Fusion

→ Coarse 3D Model

Photometric Stereo

on TSDF

→ Re"ned 3D Model

depth + intensity

TSDF

System Overview

EL(d,⇢, s1, . . . , sK) =

KX

k=1

X

V 2Vk

X

x2V \S(Ik(⇡(x))� ⇢(x,⇢V )n(x,dV )

T sk)2 (1)

Edepth(d) =KX

k=1

X

v2Vk

(Dk(xv)� dv)2 (2)

Ealbedo(⇢) =X

V 2V

X

vi 6=vj2V

(⇢vi � ⇢vj )2 (3)

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Three error terms are used to improve the 3D model• Penalize deviation between rendered intensity and

observed intensity (1).• Favor surfaces that are close the observed one in

the depth images (2).• Favor solutions where neighboring voxels have

similar albedo (3).

Results

Shading - Hörmander

IntensityImages

Fused depthimages

Our Result Intrinsic3DMaier et. al.

Quantitative Result

IntensityImages Fused depth images Our Result

Compare to groundtruth – 3D printed model

Motivation

Problem: 3D models obtained from fusion of depth images lack details due to:• Noise in depth images• Low resolution• Smoothing in the fusion process.

Goal: Enhance the quality of the 3D models.

Method: • Capture richer data with varying illumination. • Combining techniques from Photometric Stereo and Truncated

Signed Distance Functions (TSDF).

Notation and Details

Shading - Shirt

3D Renderings

Our result

Intrinsic3DMaier et. al.

Intensity Images

• The Lambertian reflectance modelestimates the observed intensity in a projected point as

• The normal of a surface point in a TSDF can be computed as

• is the tri-linear interpolation functionwhich gives the distance to the surface at point .

Idea: • Refine the distance values to change the normals in the voxels to

better fit the intensity images. • Captured data with varying illumination contain information about

detailed geometry.

Notation• and are eight distance- and albedo-estimates for a voxel .

• are the spherical harmonics.

• Surface points are extracted in all voxels that has a zero-crossing,

denotes the set of all such surface points.

• denotes the set of voxels observed in frame .

n(x,dV ) =rgV (x,dV )

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gV : R3 ⇥ R8 ! R<latexit sha1_base64="FFF1OmfExLnjk1pzIs2GVMGeNSo=">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</latexit><latexit sha1_base64="FFF1OmfExLnjk1pzIs2GVMGeNSo=">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</latexit><latexit sha1_base64="FFF1OmfExLnjk1pzIs2GVMGeNSo=">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</latexit><latexit sha1_base64="FFF1OmfExLnjk1pzIs2GVMGeNSo=">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</latexit>

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