**1. Overview**

In the field of computer vision, one of the main issues is how exactly we
recover 3D shape of a target object from its perspective images. Several
methods for estimating camera motion and reconstructing 3D shape have been
proposed such as shape from X(X:shading,texture,contour and motion). These
methods have been useful in many fields such as virtual reality, shape
recognition, navigation for a moving robot, virtual city space and
commercial advertisements on web sites. However those methods have
difficulties of being highly sensitive to noise. To overcome these problems,
we propose a fusion method of 3D shape obtained from multiple view points.
First, 2D point correspondence is supplied to make the 3D shape. We propose
an automatic point correspondence method based on the
Kanade-Lucas feature point tracking method. Second, deciding the 2D point
correspondence, we recover 3D shapes in the same view point set by using
Mukai's method. The same view point set means that there is no self
occlusion among the shapes in the same view point set. Then, we fuse 3D
shapes which are the same shapes but in the different coordinate system due
to camera movement. We regard this part as the partial shape fusion
process. Finally, we consider the self occlusion. By integrating 3D partial
shapes obtained from the partial shape fusion process and selecting the high
accuracy points in each partial shape, the whole shape can be obtained
with high accuracy.

**2. Improving the Point Correspondence Accuracy of Kanade-Lucas Method by
Affine Transformation and Correlation**

The Kanade-Lucas(KL) feature tracker is one of the good matching methods.
However it fails to find corresponded points of two images when image motion
is large. We propose a feature point matching method by using affine
transformation and correlation so that KL method works well for large image
motion. First, KL method is used to match points. Some points are matched
well, other points are mismatched or failed to be matched.
Second, correlation of two matched points between the first and the second
images obtained by KL method is used to discriminate well matched point and
badly matched point. If correlation coefficient is lower than a specified
threshold, it is regarded as an outlier. Third, all the points to be matched
in the first image are transformed on the second image by affine
transformation obtained by using well matched points alone. However, all the
transformed points from the first image to the second image are not matched
well due to the approximation of camera movement by affine transformation.
The role of affine transformation is to reduce the
computation time and the number of mismatching points by designating only
the small searching area around the transformed point. Finally, correlation
is used to find the best matching point around the transformed point. Real
image has been used to test the proposed method, and excellent results have
been obtained with the error of 0.811 pixels in average(Fig.1).

**Fig.1 Experimental images. (a) is the first
image. (b) is the second image. 28 reference
points(white dots) in the first image are
required to be tracked in the second image**.

**3. Fusion of 3D Shapes in Multiple View Points to Obtain More Accurate
Shape**

The aim of this section is to obtain an exact 3D model using multiple images
captured by a camera in the same viewpoint set. The reconstruction of 3D
shape using two images has problems such as being weak at noise. Therefore
we present a method to reduce noise and to improve the accuracy of 3D shape
with multiple images. The method consists of three stages: firstly,
reconstruction of 3D shapes at different camera positions,
secondly fusing the 3D shapes to obtain a para-ideal shape, and thirdly
removing the outlier shapes and feature points by evaluation function, and
fusing the rest of shapes. Even though the corruption of image data by noise
is one of the unavoidable problems in any system, noise is removed
effectively by the proposed method in multiple view points. Experimental
results show that our system performs well to remove noise with
robustness. The maximum noise reduction rate is 82% in the real image
experiment(Fig.2).

**Fig.2 Left shape: reconstructed shape without
fusion method. Right shape: fused shape. There are lost three points in the
shapes as outliers.**

**4. Recovery of 3D Whole Shape and Accuracy Improvement by Fusing Partial
Shapes**

In this section, we describe a novel approach for recovering an exact 3D
whole model using image sequences. To recover a whole shape, more than two
shapes in the different view point sets should be used, which is convenient
to avoid problems such as inclusion of noise and self occlusion. We present
a method of **fusion** and **integration** of 3D shapes. The fusion
process indicates that 3D partial shapes in the same viewpoint set
are fused sequentially to improve accuracy. The integration process
indicates that refined partial shapes by the fusion process in each
viewpoint set are integrated to construct the whole shape with high
accuracy. A novel iterative orthonormal fitting transform method(IOFTM)
is proposed to transform the shapes' coordinate system to the standard one.
IOFTM is compared with the steepest descent method. We fuse
shapes by the point-weighted fusion method. The whole shape is constructed
by the integration of partial shapes' points which are at lower
noise level between corresponding feature points. The method consists of
five stages: first, reconstruction of partial shapes at different camera
positions, second, fusion of the partial shapes to obtain a para-ideal
shape by the uniform-weighted fusion method, third, detection of the outlier
shapes and feature points based on an evaluation function, fourth, fusion of
shapes by the point-weighted fusion method, and fifth, integration of
accurate partial shapes to construct the refined whole shape. Experimental
results indicate that our system performs well in removing noise with
robustness. The noise reduction rates are 85.8% - 97.4% in the simulation
and real image experiments, respectively(Fig.3).

**Fig.3 Reconstructed whole shape. Comparing a shape
before and after fusion.**