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The Coherent Point Drift (CPD) algorithm which based on Gauss Mixture Model is a robust point set registration algorithm. However, the selection of robustness weight which used to describe the noise may directly affect the point set registration efficiency. For resolving the problem, this paper presents a CPD registration algorithm which based on distance threshold constraint. Before the point set registration, the inaccurate template point set by resampling become the initial point set of point set matching, in order to eliminate some points that the distance to target point set is too close and too far in the inaccurate template point set, and set the weights of robustness as . In the simulation experiments, we make two group experiments: the first group is the registration of the inaccurate template point set and the accurate target point set, while the second group is the registration of the accurate template point set and the accurate target point set. The results of comparison show that our method can solve the problem of selection for the weight. And it improves the speed and precision of the original CPD registration.

The point set registration technology is widely used in image registration, target recognition, computer vision, image retrieval and classification, the mobile robot and so on. The registration usually falls into two categories: rigid or non-rigid. The goal of point set registration is to find the corresponding relationship between two sets of points and to solve the transform relationship. However, two sets of points were obtained from different imaging equipment, different perspectives, different time or different conditions (weather, illumination), so the relationship between two sets of points is not sure, and also due to deformation, noise and outliers, the point set matching is a very difficult problem.

Currently, point set registration algorithm is roughly divided into two categories: the one is based on the transformation parameter estimation algorithm, such as Coherent Point Drift [

Compared with other point set registration algorithms, CPD has higher registration precision, not only to the rigid registration, also to the non-rigid. However, it finds the corresponding relationship between the two point sets by EM iteration minimizing the expectation of the negative log-likelihood function, there are two major defects: the one is that the selection of the weight parameters which is used to account for the noise and outliers directly affects the precision and efficiency of registration. Another is that the selection of initial registration parameters has important influence to the whole, may be trapped in local optimal solution. For the problem, this paper simply introduces the process of original CPD algorithm, and then presents a CPD registration algorithm based on distance threshold constraint. Before the point set registration, the inaccurate template point set by resampling becomes the initial point set of point set matching, in order to eliminate some points that the distance to target point set is too close and too far in the inaccurate template point set. And the experiment proves that it can improve the speed and precision of the original CPD registration.

In fact, the CPD can be seen as a kind of probability density parameter estimation problem, where one point set represents the Gaussian mixture model centroids, and the other one represents the data points, the problem changes into maximum likelihood estimation by establishing the logarithmic likelihood function of the data points, We define the correspondence probability between two points sets as the posterior probability of the GMM centroids given the data point, the optimal registration place is likely to be the largest posterior probability.

Set up two sets of points: we define the template point set as

where

try transformation,

CPD algorithm finds parameters

where

where

Although the EM [

For the template point set Y and the target point set X, for a point

We have found

Fist-step: For the template point set Y and the target point set X, we search for five points which ordered from small to large according to the distance of

Second-step: As same as One-step, we search for five points which ordered from large to small according to the distance of

Third-step: Firstly, we compute the average distance between the adjacent point of Point set X by Equation (5). Assume that the coordinates of the five points are

Fourth-step: Computing the coordinates

where

Fifth-step: We get the distance threshold value interval of the target point set to the template point set. We weed out the noise points which are away from the template point set with

Sixth-step: If

We use Windows XP system, Intel Pentium Dual, the memory of 1.81 GHz, 2 GB and the development environment is Matlab 2011b. We prepare Two groups of non-rigid images from different light, different perspective shooting as our experimental data. Converting the color images to the grayscale by Matlab, and extracting the image edge by canny method. In the process of extracting edges, in order to ensure the integrity and continuity of the image edge, there may be some noise points in extracted images.

In order to verify the algorithm in this paper,

This experiment uses two critical condition of iteration as registration accuracy standard, namely covariance and standard tolerance. Refer to (8):

where

time and the previous logarithmic likelihood function values.

In the

The original CPD | This algorithm | |
---|---|---|

E_R | 1.0587 | 0.7461 |

E_s | 0.3118 | 0.0508 |

tol | 9.2427 ´ 10^{−6} | 9.0064 ´ 10^{−6} |

Sigma2 | 0.0020126 | 0.0010464 |

achieve a smaller value on the registration accuracy, this algorithm is better than the original algorithm on the accuracy.

The Coherent Point Drift is a kind of efficient point set registration algorithm, and obtains better effect, but the selection of robustness weight may directly affect the point set registration efficiency. So this paper presents a CPD registration algorithm which based on distance threshold constraint. The experiment proves that these point sets which resampling by this algorithm are involved in CPD registration algorithm, the weight of robustness is

Wei Guang Liu,Tian Wang, (2015) Image Registration Technique Based on a Fast CPD Algorithm. Journal of Computer and Communications,03,182-188. doi: 10.4236/jcc.2015.35023