3-D Reconstruction of Three Views Based on Manifold Study - Advances in Image and Graphics Technologies - page 182

of epipolar geometry, even the novel methods[8,9,10]relied on optimized model of
matching points' residuals. When there exist mismatches, those methods could not
remove them absolutely, getting a better inliers set in the case of possible greater
probability. The trifocal tensor is a multiple view object in three views, which could be
described by the geometry of a point-point-point .So it can behave precise constraint
between matching points. With the constraint of three views, paper[11]excludes more
mismatches between adjacent view during the process of 3-D reconstruction and
achieve better results. In the same way, this article gets more accurate matching points
to build inliers set without solution of trifocal tensor. Then fundamental matrix is
calculated precisely with the optimal inliers set.
The projection matrix could be obtained through the decomposition of fundamental
matrix. Building and solving equations between the matching points and its
corresponding projection matrix, the reconstruction of 3-D point cloud is completed.
To acquire matching points, SIFT algorithm is adopted. As a result, point cloud mainly
represent the steady feature in the view. But, its are sparse and uneven distributed.
Considering the characteristics of the reconstructed 3-D point cloud, a new method to
reestablish the geometric surface model is also proposed in this article.
Nowadays, how to quickly and accurately reconstruct objects' geometric surface is
also a heated question by discrete 3-D points in many fields. Because of the excellent
performance in descripting object model, TIN(Triangulated Irregular Network) has
attracted lots of researches and wide application. The main methods of it could be
classified into Delaunay triangulation method and implicit surface fitting method.
On account of the obtaining point cloud is steady, sparse and uneven distributed,
methods have its own advantages and disadvantages in 3-D TIN reconstruction.
Sculpture algorithm[12] and incremental surface growing algorithm based on Delaunay
triangulation could gain high-quality triangular mesh surface. But its complexity of
time and space relies on points number. When the 3-D points set is large, its efficiency
becomes low. Its also couldn't deal with noisy and uneven distributed data. What's
more, it's sensitive to sampling density. Local triangulation method[13]has higher
efficiency in recovering TIN, but the topological relation between points is easily to be
changed. Making smaller differentiation between reconstructed TIN and object surface,
manifold study algorithm[14]guarantees the essential relationship between points.
However, it also requires a certain degree of sampling density. Implicit surface fitting
method[15,16]could describe shape of complicated object, and it rebuilds watertight
surface, being robust to tiny noise. Limits of it is that the reconstructed TIN doesn't
through the original 3-D points. So implicit surface fitting method with manifold study
method are combined in this article. Firstly, uniform 3-D point cloud is obtained by
RBF interpolation and resampling. Then the reconstruction of TIN is achieved by
manifold study, which guarantees the correctness of points topological relationship and
TIN via original points at the same time. Finally, 3-D reconstruction is completed after
texture mapping.
The main contributions of the method proposed in this article are listed as follow:
(1) Considering the weakness constraint of epipolar geometry, this article gets more
accurate matching points inliers set instead of using three views constraint, with no