3D Surface Reconstruction from 2D Images (Survey) 2006. 11. 3 (Fri) Young Ki Baik, Computer Vision Lab.

3D Surface Reconstruction from 2D Images References A Comparison and Evaluation of Multi-View Stereo Reconstruction Algorithms Steven M. Seitz, Richard Szeliski et. al. (CVPR 2006) A Survey of Methods for Volumetric Scene Reconstruction Greg Slabaugh et. al. (VG 2001) : Volume Graphics

3D Surface Reconstruction from 2D Images Contents Introduction Camera calibration Shape from 2D images, techniques Conclusion

3D Surface Reconstruction from 2D Images Introduction Volumetric data representations Gaining importance since their introduction in the early 70’s → 3D medical imaging [Greenleaf 70]

3D Surface Reconstruction from 2D Images Introduction Volumetric data representation The exponential growth of computational storage and processing → practical alternatives to surface based geometrical representation for many applications in computer graphics and scientific visualization

3D Surface Reconstruction from 2D Images Application Reverse engineering Augmented reality Human computer interaction Animation, Game Etc.

3D Surface Reconstruction from 2D Images Methods for volumetric reconstruction By hand 3D tool (3DMAX, MAYA, …) Limitation Too much time, tedious

3D Surface Reconstruction from 2D Images Methods for volumetric reconstruction Laser scanner (Range data) Advantage High quality and accuracy Limitation Too much money Specific configuration

3D Surface Reconstruction from 2D Images Methods for volumetric reconstruction CCD camera (Images) Advantage Cheap price Usefulness

3D Surface Reconstruction from 2D Images Condition of 3D reconstruction 3D point 3D object mapping Image plane Camera Camera Camera system for obtaining images

3D Surface Reconstruction from 2D Images Condition of 3D reconstruction Point correspondence Camera parameter and motion 3D point 3D object Camera Camera 3D reconstruction system to make 3D object

3D Surface Reconstruction from 2D Images Camera Calibration Camera parameters: Extrinsic: Translation T, Rotation R. Intrinsic: Focal Length f, image center (ox ,oy), effective pixel size (sx ,sy), radial distortion k. Recover parameters from 3D points and their projections. Object View9 View1 View6 Camera Motion

3D Surface Reconstruction from 2D Images Camera Calibration Simple overall flow Camera is set fixed location. Obtaining camera parameters using projected 2D image and world 3D data with Known plane or 3D rig. We can acquire 3D volumetric representation by applying various reconstruction algorithm.

3D Surface Reconstruction from 2D Images Camera Calibration Calibration with pattern: Tsai’s method [Tsai87] Zhang’s method [Zhang00] Self-calibration [Maybank92] Bundle adjustment [Triggs], evenly distribute errors.

3D Surface Reconstruction from 2D Images Shape from 2D Images Shape from silhouette Shape from structured light Shape from Illumination Shape from shading Photometric stereo Shape from Color(or intensity) Voxel coloring Stereo vision Fusion method

3D Surface Reconstruction from 2D Images Shape from Silhouette(SFS) Early works of vision Effective method Sculpturing a statue

3D Surface Reconstruction from 2D Images Shape from Silhouette(SFS) - Calibrated cameras and object - Set initial 3D volumetric region including object - Obtain 3D volumetric data from intersecting back-projected volume - Back-project each silhouette along the ray O1 O2 O3

3D Surface Reconstruction from 2D Images Shape from Silhouette(SFS) Advantages: Simple to implement and fairly robust Fast execution complete closed surface → commonly used as the effective initial boundary Limitations: only produced line hull can’t detect non-convex region sensitive to segmentation result → specific color is used as the background

3D Surface Reconstruction from 2D Images Shape from Structured Light Rays coming out of light source hit the object surface and captured by image sensor (usually a camera) in a different angle. [Levoy00, Allen03] Problem - Optically uncooperative materials - Scanning in the presence of occlusion - Filling holes in dense polygon models

3D Surface Reconstruction from 2D Images Shape from Illumination Shape from Shading Assume distance point light source, orthographic projection, local shading and Lambertian surface Given image intensity, determine depth by solving reflectance map in the fields of Radiometry. Lambertian A surface point is equally bright from all directions. Limitation - Do not provide qualified results

3D Surface Reconstruction from 2D Images Shape from Illumination Photometric stereo Advanced version of shape from shading Method to determine surface shape using multiple images taken by varying illumination direction, while fixed camera position Advantage - Provide good results relative to shape from shading Limitation - Have to know the location of light sources

3D Surface Reconstruction from 2D Images Shape from Color Voxel Coloring Images can be constraints on 3D scene: a valid 3D scene model projected must produce synthetic images same as the corresponding real input images. SFS+color consistency Opaque or not Sees blue Sees red Sees green

3D Surface Reconstruction from 2D Images Shape from Color Voxel Coloring (overall flow) - Set up voxel region covering object. - Set the camera on the fixed location. - Place the object to the fixed location.

3D Surface Reconstruction from 2D Images Shape from Color Voxel Coloring (overall flow) - Iterate this algorithm about all voxel in the region. - Judge opaqueness by thresholding variance of colors. - Select a voxel and project onto the each image.

3D Surface Reconstruction from 2D Images Voxel Coloring Advantages: simple to implement and fairly robust Limitations: performance depends on voxel and image resolution. → reconstruct object in small area → high computational cost occlusion and illumination problem

3D Surface Reconstruction from 2D Images Voxel coloring More advanced algorithm Space carving Generalized voxel coloring Multi-hypothesis voxel coloring

3D Surface Reconstruction from 2D Images Shape from color Stereo vision Features popular method pixel based method mimics the behavior of human vision apply feature matching criterion at all pixels simultaneously search only over epipolar lines (fewer candidate positions) Scene object point Left Camera Optical axes Epipolar lines Epipolar plane Image plane

3D Surface Reconstruction from 2D Images Shape from color Stereo vision Matching cost Squared Intensity Differences (SD,SSD). Absolutely Intensity Differences (AD,MSE). Normalized Cross-correlation, normalized SSD.

3D Surface Reconstruction from 2D Images Stereo vision Advantages gives detailed surface estimates covering wide area object Building, topography Fast execution multi-view aggregation improves accuracy

3D Surface Reconstruction from 2D Images Stereo vision Limitation narrow baseline give rise to noisy estimates fails in ~ textureless and occlusion areas sparse, in complete surface sensitive to non-Lambertian effects. Other effective methods http://cat.middlebury.edu/stereo/

3D Surface Reconstruction from 2D Images Fusion methods Silhouette and Stereo Fusion for 3D Object Modeling - Carlos Hernandez Esteban and Francis Schmitt (CVIU 2004) # SFS +multi +stereo correlation voting +Gradient vector flow +Snake High-Fidelity Image-Based Modeling - Yasutaka Furukawa, Jean Ponce (CVR-TR-2006) # SFS + wide baseline matching + propagation + Energy minimization Multi-View Stereo Revisited - Michael Goesele et. al. (CVPR2006) # SFS +Stereo matching + volumetric method (range data + Level Set) MultiView Geometry for Texture mapping 2D Images Onto 3D Range Data - Lingyoun Liu et. Al. (CVPR2006) # SFS +Stereo matching + volumetric method (range data)

3D Surface Reconstruction from 2D Images Trend of 3D reconstruction method ~1995 Simple algorithm ~1999 VC and variants (treating occlusion), LevelSet, optimization ~2001 Probabilistic formulation ~2003 Non-Lambatian surface, specular surface, textureless regions ~2006 PGM, Fusion method (SFS + Stereo + Level set + …)

3D Surface Reconstruction from 2D Images Conclusion Survey of methods for volumetric scene reconstruction from photographs. States of the arts shows very good reconstruction results. All algorithm do not solve problems yet. occlusion ,illumination changes non-Lambatian surface Real data (no silhouette) There is room for improvement