CN104376592A - Avalokitesvara hand-shaped historical relic lost part size prediction method - Google Patents

Abstract

The invention discloses an Avalokitesvara hand-shaped historical relic lost part size prediction method, and belongs to the field of historical relic repair engineering. The method comprises the steps of obtaining a plurality of sets of skeleton lines extracted from an Avalokitesvara hand-shaped historical relic prepared to be repaired, and building the proportional relation of the sizes of geometric structures in the historical relic by means of length information of the skeleton line among the geometric structures of the Avalokitesvara hand-shaped historical relic; using the formula specified in the specification as a prediction model for fitting to obtain the size of the lost part of the Avalokitesvara hand-shaped historical relic, wherein according to the prediction model, L feature 1 and L feature 2 are size parameters of the two geometric structures having the regression relation on the skeleton lines, and according to two formulas specified in the specifications, n is the number of samples, and Xi and Yi correspond to the ith data group. According to the Avalokitesvara hand-shaped historical relic lost part size prediction method, statistics and analysis are carried out on the length information of the skeleton lines of the historical relic, a historical relic lost part size prediction mathematic model is built, the restoration basis is provided for virtual repair of grouped or similar historical relics with certain geometric features with the implication relation, the virtual historical relic repair reliability can be improved, and assistance is provided for the historical relic preservation repair engineering.

Description

The Forecasting Methodology of kwan-yin hand shape historical relic disappearance size

Technical field

The present invention relates to historical relic recovery project field, particularly relating to a kind of Forecasting Methodology that kwan-yin hand shape historical relic disappearance size of auxiliary foundation is provided for repairing kwan-yin hand shape historical relic.

Background technology

At present, when repairing damaged historical relic, generally to find reparation foundation to the reparation of lack part, as by going through material, picture record and analyzing the style of historical relic, utilizing computer technology to restore historical relic, as reparation foundation.But the numerous historical relic of China, due to long history, has a lot of historical relic not to be handed down reliable data for reference.And processing in the more complicated virtual repairing research of damaged historical relic of geometrical construction, research institution is had to recombinate to terra cotta warriors and horses statue fragment impaired in earthquake in 2009, then the geometric shape of the sculpture right hand is passed through as a reference, the virtual left hand having repaired loss, also decorates to its faience the recovery carried out and is studied.The method that the people such as Min Lu utilize rigid surface to mate, with four faces of the same pinnacle in Cambodia Ba Yun temple, there is this reparation foundation of very high similarity, using mask as template, generate dense some cloud, matrix is recovered by building with damaged face points cloud unified coordinate system, and the original appearance of damaged historical relic that utilized this matrix to restore.Above two kinds of methods are when processing the virtual reparation of complex geometry historical relic, take into full account the problem of the virtual reparation foundation of historical relic, but faced by be difficult to find similar historical relic to carry out the mutual reference of geometric shape time, repair according to cannot simply determine, therefore these two kinds of methods to the disappearance size prediction of kwan-yin hand shape historical relic, cannot can not provide foundation for the reparation of kwan-yin hand shape historical relic.

Summary of the invention

Based on the problem existing for above-mentioned prior art, the invention provides one and can predict kwan-yin hand shape historical relic lack part size, the Forecasting Methodology of kwan-yin hand shape historical relic disappearance size of auxiliary foundation is provided for the reparation of kwan-yin hand shape historical relic.

For solving the problems of the technologies described above, the invention provides the Forecasting Methodology of a kind of kwan-yin hand shape historical relic disappearance size, comprising:

Obtain the some groups of skeleton lines extracted from kwan-yin hand shape historical relic preparing to repair;

Utilize the length information of skeleton line between each geometry structure of described kwan-yin hand shape historical relic, set up the proportionate relationship of size between each geometry structure in this historical relic;

With for forecast model matching obtains the size of described kwan-yin hand shape historical relic deleted areas, in described forecast model, L _{feature 1}with L _{feature 2}for the dimensional parameters that the geometry that on described skeleton line, two exist regression relation builds, $\hat{a}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i-\frac{\hat{b}}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i,\hat{b}=\frac{n{\mathrm{\Σ}}_{i=1}^n{x}_i{y}_i-\left({\mathrm{\Σ}}_{i=1}^n{x}_i\right)\left({\mathrm{\Σ}}_{i=1}^n{y}_i\right)}{n{\mathrm{\Σ}}_{i=1}^n{x}_i^2-{\left({\mathrm{\Σ}}_{i=1}^n{x}_i\right)}^2},$ In two groups of formula, n is sample size, the corresponding i-th group of data pair of Xi, Yi.

Beneficial effect of the present invention is: by carrying out statistics and analysis to the length information of historical relic skeleton line, establish historical relic lack part size prediction mathematical model, in groups or the virtual reparation of historical relic that there is implication relation in similar historical relic between some geometric properties provide recovery foundation.The method can improve historical relic and carry out empty paraprotehetic reliability, for historical relic's protection recovery project provides auxiliary.

Accompanying drawing explanation

In order to be illustrated more clearly in the technical scheme of the embodiment of the present invention, below the accompanying drawing used required in describing embodiment is briefly described, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawings can also be obtained according to these accompanying drawings.

The extracting method process flow diagram that Fig. 1 provides for the embodiment of the present invention;

Forecast model Establishing process figure in the extracting method that Fig. 2 provides for the embodiment of the present invention.

Embodiment

Be clearly and completely described the technical scheme in the embodiment of the present invention below, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiments.Based on embodiments of the invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to protection scope of the present invention.

Figure 1 shows that the Forecasting Methodology of a kind of kwan-yin hand shape historical relic disappearance size that the embodiment of the present invention provides, be used in historical relic recovery project, for the reparation of historical relic lack part provides foundation, the method comprises:

Obtain the some groups of skeleton lines extracted from kwan-yin hand shape historical relic preparing to repair;

Utilize the length information of skeleton line between each geometry structure of described kwan-yin hand shape historical relic, set up the proportionate relationship of size between each geometry structure in this historical relic;

With for forecast model matching obtains the size of described kwan-yin hand shape historical relic deleted areas, in described forecast model, L _{feature 1}with L _{feature 2}for the dimensional parameters that the geometry that on described skeleton line, two exist regression relation builds; $\hat{a}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i-\frac{\hat{b}}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i,\hat{b}=\frac{n{\mathrm{\Σ}}_{i=1}^n{x}_i{y}_i-\left({\mathrm{\Σ}}_{i=1}^n{x}_i\right)\left({\mathrm{\Σ}}_{i=1}^n{y}_i\right)}{n{\mathrm{\Σ}}_{i=1}^n{x}_i^2-{\left({\mathrm{\Σ}}_{i=1}^n{x}_i\right)}^2},$ In two groups of formula, n is sample size, the corresponding i-th group of data pair of Xi, Yi.

In above-mentioned Forecasting Methodology, from prepare repair kwan-yin hand shape historical relic extract some groups of skeleton lines in the following ways:

Adopt 3 D laser scanning to prepare kwan-yin hand shape historical relic repaired, obtain the cloud data of this kwan-yin hand shape historical relic;

The cloud data of the described kwan-yin hand shape historical relic obtained is utilized to obtain the triangle grid model of this kwan-yin hand shape historical relic through three-dimensional reconstruction;

The process of skeleton line extraction algorithm is adopted to extract the three dimensions skeleton line of described kwan-yin hand shape historical relic from described triangle grid model.

In above-mentioned Forecasting Methodology, skeleton line extraction algorithm comprises: the geometric contraction step to described triangle grid model of carrying out successively, skeleton simplify step and node trim step.

In above-mentioned Forecasting Methodology, with the size obtaining described kwan-yin hand shape historical relic deleted areas for forecast model matching comprises:

Delete residual sum Cook distance three parameters by leverage value, studentization and judge whether the dimensional data of matching is abnormity point, if, then give up this dimensional data, if not then this dimensional data of matching obtains the size of described kwan-yin hand shape historical relic deleted areas.

In above-mentioned Forecasting Methodology, leverage value ch _iiby following formulae discovery: wherein, x1 is average, and Xi1 is Xi value of data centering.

In above-mentioned Forecasting Methodology, studentization deletes residual error SRE _(i)by following formulae discovery: ${\mathrm{SRE}}_{\left(i\right)}={\mathrm{SRE}}_i{(\frac{n-p-1}{n-p-2}-\frac{{\mathrm{SRE}}_i^2}{n-p-2})}^{-\frac{1}{2}},$ Wherein, ${\mathrm{SRE}}_i=\frac{e_i}{\mathrm{MSE}\sqrt{1-h_{\mathrm{ii}}}},$ In this formula: e _ifor residual error, MSE is the square error of regression model, and n is sample total, and p is the number of parameters in model, lever value centered by h.

In above-mentioned Forecasting Methodology, Cook distance D _iby following formulae discovery: wherein, e _ifor residual error, MSE is the square error of regression model, and n is sample total, and p is the number of parameters in model, lever value centered by h.

Below in conjunction with specific embodiment, Forecasting Methodology of the present invention is described further.

First the dimension information that a certain class or a certain group of intact each geometry of historical relic build is carried out classify and added up in the virtual reparation of historical relic, then the regression relation of size between different geometry structure is found by regretional analysis, if this relation exists, the regression model between them so namely can be set up.This model is then as the forecast model of historical relic deleted areas size, when carrying out virtual reparation to incomplete historical relic, can according to dimension information intact in incomplete historical relic, estimate the dimension information at incomplete position, the dimension information obtained can be used as the foundation that damaged historical relic is repaired, and this forecast model can repair foundation reliably for the virtual reparation of historical relic provides.Forecasting Methodology of the present invention calculates the size of historical relic deleted areas by the forecast model set up, and this forecast model is the forecast model utilizing the thought of regretional analysis in mathematical statistics to set up, and this forecast model is specially: wherein, L _{feature 1}with L _{feature 2}it is the dimensional parameters that two geometry that there is regression relation builds; $\hat{a}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i-\frac{\hat{b}}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i,\hat{b}=\frac{n{\mathrm{\Σ}}_{i=1}^n{x}_i{y}_i-\left({\mathrm{\Σ}}_{i=1}^n{x}_i\right)\left({\mathrm{\Σ}}_{i=1}^n{y}_i\right)}{n{\mathrm{\Σ}}_{i=1}^n{x}_i^2-{\left({\mathrm{\Σ}}_{i=1}^n{x}_i\right)}^2},$ In two groups of formula, n is sample size, the corresponding i-th group of data pair of Xi, Yi.

Utilize the length information of skeleton line between each geometry structure of historical relic, set up the proportionate relationship of size between each geometry structure in this group historical relic, then can realize the mutual prediction of different geometric features size in damaged historical relic.Can finding out when carrying out virtual reparation to historical relic deleted areas by this formula, only needing the size knowing parts in damaged historical relic, then the damaged part size relevant to it can make estimation (see Fig. 2).

When the size prediction model of matching historical relic deleted areas, concrete data processing comprises following steps altogether:

(1) test of hypothesis;

(2) abnormity point is got rid of.

First step test of hypothesis of data processing whether there is linear relationship between the dimension information that two class geometry build, only have this linear relationship to deposit in case, could be for further processing to data, otherwise this forecast model does not exist for verifying.

It is get rid of the abnormity point existed in data that the second step abnormity point of data processing is got rid of, to ensure the precision of historical relic deleted areas size prediction model, although some abnormal data can be got rid of by subjective observation, subjective judgement cannot find all abnormal datas.

In the present invention, in order to the abnormity point of the historical relic dimension information to statistics judges, introduce three parameters as weighing the standard whether data are abnormity point, this parameter is respectively leverage value, studentization deletes residual error and Cook distance (Cook's Distance).Outlier detection needs above-mentioned three parametric synthesis to judge, effect and the computing method of each parameter are as follows:

(1) center lever value:

Leverage value is for checking the parameter of distance degree between i-th observed reading and independent variable mean value in mathematical statistics, be commonly used to the Highly Influential case detecting independent variable, because the observation station of big lever value is away from center of a sample, therefore, it is possible to regression model is pulled to oneself, so the larger point of lever value is also referred to as Highly Influential case.

In the present invention, this parameter is used to detect in a certain class geometric properties, and one of them observation data is away from the degree of average length, wherein ch _iibe center lever value, see formula (11):

${\mathrm{ch}}_{\mathrm{ii}}=\frac{{(X_{i1}-{\stackrel{\‾}{X}}_1)}^2}{\mathrm{SSX}}---\left(11\right)$

Wherein,

$\mathrm{SSX}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(X_{i1}-{\stackrel{\‾}{X}}_1)}^2$

(2) studentization deletion residual error:

Studentized residuals is the business of residual error and standard deviation, and the thought of deleting studentized residuals is then calculate removal i-th observed reading, utilizes all the other n-1 observation data fit regression model, calculates the match value after the i-th observed reading deletion.Therefore, it can reflect that i-th data is to the influence degree of predicted value, is used to detect whether dependent variable is Highly Influential case, and the computing method that studentization deletes residual error are shown in formula (12):

${\mathrm{SRE}}_{\left(i\right)}={\mathrm{SRE}}_i{(\frac{n-p-1}{n-p-2}-\frac{{\mathrm{SRE}}_i^2}{n-p-2})}^{-\frac{1}{2}}---\left(12\right)$

Wherein,

${\mathrm{SRE}}_i=\frac{e_i}{\mathrm{MSE}\sqrt{1-h_{\mathrm{ii}}}}$

In formula:

E _ifor residual error;

MSE is the square error of regression model;

N is sample total;

P is the number of parameters in model.

(3) Cook distance (Cook ' s Distance)

Cook distance is commonly used estimative figure strong point becomes regretional analysis impact on a most young waiter in a wineshop or an inn, this parameter measure result of the given observed reading of deletion, if data point has larger residual error or larger lever value, then may cause the result generation error of forecast model, the computing method of Cook ' s D are shown in formula (13):

$D_i=\frac{e_i^2}{\mathrm{pMSE}}\left[\frac{h_{\mathrm{ii}}}{{(1-h_{\mathrm{ii}})}^2}\right]---\left(13\right)$

(4) abnormity point analysis:

When analyzing the abnormity point in historical relic geometries characteristic, integrating center lever value, studentization to delete residual error and Cook distance three parameters to judge this abnormity point whether for the forecast model of matching historical relic deleted areas size.When leverage value be greater than 0.03 or studentization delete residual values be greater than positive 1 or be less than negative 1 time, still size prediction model can be met between this geometric properties, these data can't cause very large impact to the fitting precision of model, therefore can not be considered abnormity point and be excluded.But when Cook distance is greater than 0.01, then there is situation out of proportion between the size that two class geometric properties are described, then need to be taken as abnormity point and do not participate among the matching of forecast model.

Beneficial effect of the present invention is: utilize regression model to set up out the forecast model can estimating kwan-yin fingertip tracking spot size for theory, lacks the length of finger, as reparation foundation, improve the reliability of the virtual repairing effect of historical relic in estimation kwan-yin hand.Solve and reliably restore foundation because lack, the problem of defect kwan-yin hand geometric shape cannot be determined.

At present, first the virtual reparation of historical relic utilizes three-dimensional laser scanner to obtain historical relic cloud data, and constructs historical relic three-dimensional grid model by three-dimensional reconstruction.On this basis, in model preprocessing process, the leak that the dead angle that cannot be scanned due to the reflection strength in 3 D laser scanning process and historical relic geometry complexity causes is repaired, geometric deformation and noises such as removing the historical relic top layer disease that this article object model comprises simultaneously, such as goldleaf warps, blindage efflorescence and Rock Masses Fractures cause.Then by finding the reparation foundation of historical relic deleted areas, curved surface fusion and curve reestablishing technology is utilized to carry out Virtual restora-tion to historical relic deleted areas.Finally, utilize the three-dimensional historical relic model after virtual reparation, for historical relic repair provides aid decision making, such as, three-dimensional amount is calculated, is provided reference mark and plane, facade, sectional view etc.

The above; be only the present invention's preferably embodiment, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (7)

1. a Forecasting Methodology for kwan-yin hand shape historical relic disappearance size, is characterized in that, comprising:

Obtain the some groups of skeleton lines extracted from kwan-yin hand shape historical relic preparing to repair;

Utilize the length information of skeleton line between each geometry structure of described kwan-yin hand shape historical relic, set up the proportionate relationship of size between each geometry structure in this historical relic;

With for forecast model matching obtains the size of described kwan-yin hand shape historical relic deleted areas, in described forecast model, L _{feature 1}with L _{feature 2}for the dimensional parameters that the geometry that on described skeleton line, two exist regression relation builds, in two groups of formula, n is sample size, the corresponding i-th group of data pair of Xi, Yi.

2. the Forecasting Methodology of kwan-yin hand shape historical relic according to claim 1 disappearance size, is characterized in that, the described some groups of skeleton lines extracted from kwan-yin hand shape historical relic preparing to repair in the following ways:

Adopt 3 D laser scanning to prepare kwan-yin hand shape historical relic repaired, obtain the cloud data of this kwan-yin hand shape historical relic;

The cloud data of the described kwan-yin hand shape historical relic obtained is utilized to obtain the triangle grid model of this kwan-yin hand shape historical relic through three-dimensional reconstruction;

The process of skeleton line extraction algorithm is adopted to extract the three dimensions skeleton line of described kwan-yin hand shape historical relic from described triangle grid model.

3. the Forecasting Methodology of kwan-yin hand shape historical relic disappearance size according to claim 2, it is characterized in that, described skeleton line extraction algorithm comprises: the geometric contraction step to described triangle grid model of carrying out successively, skeleton simplify step and node trim step.

4. the Forecasting Methodology of kwan-yin hand shape historical relic according to claim 1 disappearance size, is characterized in that, described with the size obtaining described kwan-yin hand shape historical relic deleted areas for forecast model matching comprises:

Delete residual sum Cook distance three parameters by leverage value, studentization and judge whether the dimensional data of matching is abnormity point, if, then give up this dimensional data, if not then this dimensional data of matching obtains the size of described kwan-yin hand shape historical relic deleted areas.

5. the Forecasting Methodology of kwan-yin hand shape historical relic disappearance size according to claim 4, is characterized in that, described leverage value ch _iiby following formulae discovery: wherein, x1 is average, and Xi1 is Xi value of data centering.

6. the Forecasting Methodology of kwan-yin hand shape historical relic disappearance size according to claim 4, it is characterized in that, described studentization deletes residual error SRE _(i)by following formulae discovery: wherein, in this formula: e _ifor residual error, MSE is the square error of regression model, and n is sample total, and p is the number of parameters in model, lever value centered by h.

7. the Forecasting Methodology of kwan-yin hand shape historical relic disappearance size according to claim 4, is characterized in that, described Cook distance D _iby following formulae discovery: wherein, e _ifor residual error, MSE is the square error of regression model, and n is sample total, and p is the number of parameters in model, lever value centered by h.