CN107403468A - A kind of robust registration algorithm between similarity transformation three-dimensional body - Google Patents
A kind of robust registration algorithm between similarity transformation three-dimensional body Download PDFInfo
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- CN107403468A CN107403468A CN201710622440.4A CN201710622440A CN107403468A CN 107403468 A CN107403468 A CN 107403468A CN 201710622440 A CN201710622440 A CN 201710622440A CN 107403468 A CN107403468 A CN 107403468A
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Abstract
The invention discloses the robust registration algorithm between a kind of similarity transformation three-dimensional body, comprise the following steps：First, using the registration law of point-to-point, user is firstly the need of at least 3 pairs of corresponding points are provided, and then algorithm can go out rotation, zooming and panning parameter according to the Euclidean distance iterative between corresponding points pair；After preliminary convergence, we arrive the registration law of plane using point, if random selection is done, using the distance of point of the iteration closest approach method optimization point between to plane, so as to obtain final similarity transformation.The present invention uses two step registration laws, with reference to point-to-point and point to the advantage and disadvantage of Plat algorithm, is compensated mutually, adds robustness；Introduce amount of zoom, it is proposed that a new iterative algorithm for similarity transformation, so as to improve the accuracy of algorithm.
Description
Technical field
The present invention relates to computer graphical and image processing field, and in particular to the Shandong between a kind of similarity transformation three-dimensional body
Rod registration algorithm.
Background technology
Two or more three-dimensional bodies or point cloud are registered, is one and finds geometric transformation between them
Process.People only consider rigid body translation as a rule, that is, assume do not have deformation between two objects.But actually should
In, generally can all there is different degrees of scaling between object, this brings trouble to registration.It is this at the same find rotation, contracting
The process put and translated also is called 3D Procrustes analyses, very common in the industrial flow of non real-time system, such as three
Tie up among the post-processing of scan data and the data acquisition of film game special.The most frequently used method of industrial quarters at present
It is singular value decomposition (SVD, Singular Value Decomposition) method that Horn et al. is proposed, this method calculates first
Scaling, then utilizes polar decomghtion (Polar Decomposition) analytical Calculation based on SVD to go out spin matrix.This method speed
Degree is fast, but must manually select more point, is not so good as iterative algorithm in terms of accuracy and robustness.It is most popular at present to open
Source point cloud storehouse (PCL) realizes similar method, but as described in document, approximate matrix is not under Frobenius norms
It is optimal.
The content of the invention
To solve the above problems, the invention provides the robust between a general similarity transformation object and accurate registration
Method, this method is widely portable between tri patch, the registration between point cloud and between tri patch and point cloud, in number
In the case of having defect, still can effectively it be registered.
To achieve the above object, the technical scheme taken of the present invention is：
A kind of robust registration algorithm between similarity transformation three-dimensional body, comprises the following steps：First, using point-to-point
(Point-to-Point) registration law, user need first to provide at least 3 pairs of corresponding points, and then algorithm can be according to corresponding points to it
Between Euclidean distance iterative go out rotation, zooming and panning parameter；After preliminary convergence, we arrive plane using point
(Point-to-Plane) registration law, if random selection is done, using iteration closest approach (ICP, Iterative Closest
Point) method optimizes point of the point between to the distance of plane, so as to obtain final similarity transformation (Similarity
Transformation)。
Preferably, specifically comprise the following steps：
S1, the registration law first by point-to-point (Point-to-Point), user need first to provide at least 3 pairs of correspondences
Point, these corresponding points are preferably located at the diverse location of object；It is assumed that selection m (m ＞ 2) individual corresponding points pair so that these points are to it
Between it is minimum apart from sum, so as to similitude transformation matrix T and translation t corresponding to solving, be shown below：
Formula (2) is substituted intoAnd by value to be solved be classified as a vectorial r=[s, α, beta, gamma,
tx, ty, tz]T, then can obtain：
The iterative formula is until convergence, and at this moment two models tentatively align；
S2, point of use to plane registration law, object function are changed into：
Wherein,It is the point p of destination objectjThe normal vector at place；Formula (2) is substituted into above formula, obtained：
Wherein,a2=[- yj, xj, 0]T·nj, a3=[zj, 0 ,-xj]T·nj, a4=[0 ,-zj, yj]T·nj；
Here we take n point (n ＞ m), can by around corresponding points stochastical sampling realize.
The invention has the advantages that：
Using two step registration laws, the advantage and disadvantage of Plat algorithm are arrived with reference to point-to-point and point, is compensated mutually, both avoided
Algorithm is absorbed in local minimum, reduces the manually input of user again, while also add robustness；With rigid registration algorithm phase
Than we introduce amount of zoom, it is proposed that a new iterative algorithm for similarity transformation, improve the accuracy of algorithm.
Brief description of the drawings
The different scan data for having defect of 3D models and a yardstick in Fig. 1 embodiment of the present invention.
Fig. 2 is two models of gross alignment of the embodiment of the present invention.
Fig. 3 is two models of Accurate align in the embodiment of the present invention.
Embodiment
In order that objects and advantages of the present invention are more clearly understood, the present invention is carried out with reference to embodiments further
Describe in detail.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to limit this hair
It is bright.
The rigid transformation (rigid transformation) for only translating and rotating can be by a point p=[x, y, z]T
Transform to p '：
P '=Rp+t,
Wherein, R is 3 × 3 spin matrix, and t=[tx, ty, tz]TIt is translation in space；According to minimum rotation
(Infinitesimal Rotation) is theoretical, and a spin matrix can be approximated by：
Wherein, α, β and γ represent the anglec of rotation around z, y and x-axis respectively, the above formula only when these rotation amount all very littles
Just set up；If it is considered that the yardstick of model may change, we just need to introduce amount of zoom s, spatial alternation at this moment
Referred to as similarity transformation (Similarity Transformation), T is denoted as, its approximate representation is by we：
Identical with formula (1), the formula assumes that rotation amount is very small.
The embodiments of the invention provide the robust registration algorithm between a kind of similarity transformation three-dimensional body, comprise the following steps：
First by point-to-point (Point-to-Point) registration law, user needs first to provide at least 3 pairs of corresponding points, this
A little corresponding points are preferably located at the diverse location of object；It is assumed that selection m corresponding points pair so that these points to the distance between sum
Minimum, so as to solve corresponding similitude transformation matrix T and translation t, it is shown below：
Formula (2) is substituted into above formula by us, and value to be solved is classified as into vectorial r=[s, α, beta, gamma, a tx, ty, tz]T, then
It can obtain：
The iterative formula is until convergence, and at this moment two models tentatively align；
S2, point of use to plane registration law, the method similar to before, only this time we are used a little to flat
The distance in face, object function are changed into：
Wherein,It is the point p of destination objectjThe normal vector at place.As before, we are by formula (2)
Above formula is substituted into, is obtained：
Wherein,a2=[- yj, xj, 0]T·nj, a3=[zj, 0 ,-xj]T·nj, a4=[0 ,-zj, yj]T·
nj.Here we take n point (n ＞ m), can by around corresponding points stochastical sampling realize.P ' is nearest by iteration
Point method obtains, and we used space octree structure for this process to be accelerated.If model has defect, can crop
It is corresponding, realize that robust is registered.
Embodiment
In order to which the different scan data for having defect of a 3D model and a yardstick is alignd (Fig. 1), our two steps
Registration algorithm first uses two models (Fig. 2) of point-to-point registration technology gross alignment, then arrives plane registration algorithm using again
Two models (Fig. 3) of Accurate align.In this example, user only needs to provide 3 pairs of corresponding points.
Formula (3) and formula (4) can be by being expressed as matrix form：
Mr=b.
This is an overdetermined equation, and we can pass through normal equation M corresponding to itTMr=MTB solves its least square
Solution, Cholesky, which is decomposed, can effectively solve this very small linear system.It can be seen that in whole two steps registration process
In, we are optimizing zooming parameter s always, therefore can obtain optimal scaling.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (2)
1. the robust registration algorithm between a kind of similarity transformation three-dimensional body, it is characterised in that comprise the following steps：First, use
The registration law of point-to-point, user need first to provide at least 3 pairs of corresponding points, then algorithm can according to the Europe between corresponding points pair it is several in
Apart from iterative go out rotation, zooming and panning parameter；After preliminary convergence, we arrive the registration law of plane using point, with
It is final similar so as to obtain using the distance of iteration closest approach method optimization point of the point between to plane if machine selection is done
Conversion.
2. the robust registration algorithm between a kind of similarity transformation three-dimensional body as claimed in claim 1, it is characterised in that specific bag
Include following steps：
S1, the registration law first by point-to-point, user need first to provide at least 3 pairs of corresponding points：Point p on the object of sourcej=[xj,
yj, zj]TWith the point p on target objectj'=[xj', yj', zj'], j=1...m；Wherein m is the number of corresponding points pair so that this
A little points to the distance between sum it is minimum, so as to similitude transformation matrix T and translation t corresponding to solving, be shown below：
Formula (2) is substituted intoWherein, α, β and γ represent the anglec of rotation around z, y and x-axis, s respectively
To scale, if it is t to make the translation in three dimensionsx, tyAnd tz, and by value to be solved be classified as a vectorial r=[s, α, beta, gamma,
tx, ty, tz]T, then can obtain：
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S2, point of use to plane registration law, object function are changed into：
Wherein,It is the point p of destination objectjThe normal vector at place；Formula (2) is substituted into above formula, obtained：
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Application publication date: 20171128 |