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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.

Typology: Lecture notes

2011/2012

Uploaded on 03/12/2012

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Intro to Computer Vision
Lecture 16
Greg Shakhnarovich
May 25, 2010
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Download Image-Based Volumetric Modeling: Visual Hull and Space Carving and more Lecture notes Computer Vision in PDF only on Docsity!

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