# 3D Reconstruction Using Multiple View Stereo and a Brief Introduction to Kinect

Brojeshwar Bhowmick (IIT Delhi and Innovation Lab, Tata Consultancy Services, India)
DOI: 10.4018/978-1-4666-4558-5.ch002
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## Abstract

This chapter deals with the methodology of 3D reconstruction, both sparse and dense. The basic properties of the projective geometry and the camera models are introduced to understand the preliminaries about the subject. A more detail can be found in the book (Hartley & Zisserman, 2000). The sparse reconstruction deals with reconstructing 3D points for few image points. There are gaps in the reconstructed 3D points. Dense reconstruction tries to fill up gaps and make the density of the reconstruction higher. Estimation of correspondences is an integral part of multiview reconstruction and the author will discuss the point correspondences among images here. Finally the author will introduce the Microsoft Kinect, a divice which directly capture 3D information in realtime, and will show how to enhance the Kinect point cloud using vision framework.
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## Fundamentals Of Projective Geometry And Projective Camera Models

### Why Projective Geometry?

Image formation is a perspective transformation from 3D world scene to 2D plane and most of the Euclidean geometric property is lost due to this transformation. One of the most familiar properties is that parallel lines which never meet, or some fancy way of saying they meets at infinity in Euclidean space, doesn’t hold true after perspective transformation in image as shown in Figure 1. This figure shows two parallel rail lines meet at a point called vanishing point. This phenomenon distinguishes projective geometry from Euclidean geometry. The notion of distance and parallelism is destroyed in projective transformation. When the notion of distance is removed from Euclidean geometry keeping only parallelism, the structure becomes affine. Further, removing the preservation of parallelism property gives rise to projective structure. A more comprehensive detail can be found in (Hartley & Zisserman, 2000).

Figure 1.

(a) Parallel lines meet at vanishing point, (b) construction of image point in perspective drawing and vanishing point (image courtesy: geometric invariance in computer vision by Zisserman and Mundy), (c) sequence of two or more perspective projections (image courtesy: geometric invariance in computer vision by Zisserman and Mundy), (d) projective model (image courtesy: geometric invariance in computer vision by Zisserman and Mundy)

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