Intro to Computer Vision
Lecture 16
Greg Shakhnarovich
May 25, 2010
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Image-Based Volumetric Modeling: Visual Hull and Space Carving, Lecture notes of Computer Vision
Image-based volumetric modeling, a technique used to build a 3d model of a scene using multiple views. The method involves calculating the visual hull and performing space carving to obtain a tight bound on the true scene. The document also covers the concept of photo consistency and the use of multiple view geometry for structure, motion, and correspondence. Additionally, it explains the process of camera calibration and the challenges of dealing with ambiguity in affine structure from motion.
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Intro to Computer Vision
Lecture 16
Greg Shakhnarovich
May 25, 2010
Image-based volumetric modeling
Basic idea: use multiple views to build a 3D model of the scene
Figures from Vogiatzis et al. 2005
Photo consistency
Suppose we have a scene, a set of calibrated cameras, and previously obtained images from each of the cameras
If we take another set of images, and they are exactly identical to the ones we had, the scene is photo-consistent with the cameras and previous images.
If only use silhouettes: visual hull
true scene visual hull
Photo hull
Union of all photo-consistent scenes in the volume
Tightest bound on the true scene!
true scene visual hull photo hull
Space carving: example
Visual hull and recognition
Shakhnarovich et al, 2001
Multiple view geometry questions
Correspondence: given a 2D point in one image, establish constraints on the location of the corresponding points in other images
Structure: given corresponding 2D points in multiple images, recover 3D position of the corresponding 3D point in the scene (relative to the cameras)
Motion: estimate the relative motion of camera viewpoints between views from sets of corresponding 2D points.
Structure from motion
Given: n images of fixed (static) 3D points X 1 ,... , Xn taken with m cameras xij is the image of Xi in camera j
Each camera is described by a projection matrix Pj
Calibration matrix
We can write projection matrix as
P =
f 0 0 0 0 f 0 0 0 0 1 0
= K [I 3 | 03 ]
where K is the calibration matrix
K =
f 0 0 0 f 0 0 0 1
Camera calibration: coordinates
Calibration: setup
Take an image of a set of points with known 3D coordinates Xi
Find corresponding 2D points xi
Recover P
Calibration: constraints
Calibration: solution
P has 11 degrees of freedom
Calibration: solution
P has 11 degrees of freedom
one correspondence = two (linearly independent) constraints
homogeneous least squares: need at least six correspondences