CN103871107A - Quantitative measurement method for iso-surface extraction precision - Google Patents
Quantitative measurement method for iso-surface extraction precision Download PDFInfo
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- CN103871107A CN103871107A CN201410067145.3A CN201410067145A CN103871107A CN 103871107 A CN103871107 A CN 103871107A CN 201410067145 A CN201410067145 A CN 201410067145A CN 103871107 A CN103871107 A CN 103871107A
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Abstract
The invention discloses a quantitative measurement method for iso-surface extraction precision. The quantitative measurement method comprises the steps of selecting a plurality of sampling points on a triangular patch, and calculating the Euclidean distances from the sampling points to corresponding points in a real curve; then accurately measuring from multiple angles to obtain the iso-surface extraction precision by taking the maximum value of the Euclidean distances from all the sampling points in the triangular patch to the corresponding points as the maximum degree, the average value as the average deviation degree and the mean square error as the deviation fluctuating margin respectively according to the distances between the sampling points and the corresponding points. The quantitative measurement method effectively solves the problem of measurement for the deviation of an iso-surface extraction result, and realizes quantitative measurement through qualitative analysis. A user can conveniently select a suitable iso-surface extraction method according to the application occasions. Both the quantitative measurement method and the iso-surface extraction method are realized, so that the application range is wide, and the extraction precision of all the iso-surface extraction methods can be quantitatively measured.
Description
Technical field
The present invention relates to computer graphics contour surface and extract field, be specifically related to a kind of method for quantitative measuring of contour surface extraction accuracy.
Background technology
For three-dimensional scalar field volume data or implicit function, contour surface refers to the set of the point that its scalar value or functional value are a certain constant.By selecting different scalar value or functional value, can obtain different contour surfaces, thereby contribute to visual volume data and the implicit surface relevant with analysis.Therefore, contour surface extraction is the underlying issue in the application such as three-dimensional scalar field data visualization, implicit surface demonstration, three-dimension curved surface reconstruction.The main thought of contour surface extraction algorithm is: for three-dimensional scalar field volume data, normally described by discrete voxel unit set; Implicit function is carried out to spatial sampling, generate basic voxel cell; Then in basic voxel cell, approach contour surface with Linear Triangular dough sheet.Marching tetrahedra algorithm (mobile tetrahedron, mt algorithm) and marching cubes algorithm (marching cubes algorithm, mc algorithm) are two typical contour surface extraction algorithms.
In mc algorithm, basic processing unit is cube.The basic thought of algorithm is all voxels in traversal volume mesh, judge successively the position relationship between 8 angle points and the true curved surface of each voxel, then institute's find intersection is connected into tri patch according to the connected mode in advance given look-up table, in this voxel, approach expression thereby obtain contour surface.Look-up table has 256 (=2
8) the respectively corresponding 256 kinds of situations of individual entry.The treatment scheme of mt algorithm and mc algorithm flow are similar, first judge the position relationship of 4 angle points and true curved surface, utilize linear interpolation or high-order approach method to obtain the intersection point on contour surface and voxel limit, then according to the look-up table of mt algorithm, tried to achieve intersection point is connected into tri patch.The entry of the look-up table of mt algorithm has 16 (=2
4).
It is the underlying issue in the application such as three-dimensional scalar field data visualization, implicit surface demonstration, three-dimension curved surface reconstruction that contour surface extracts.In essence, discrete cube volume data is that three linear proximity of initial body data or implicit function are represented, now the contour surface in each three linear cube is cubic algebra curved surface, and mc algorithm acquired results is the linear proximity for this cubic algebra curved surface, therefore in mc algorithm, there is twice approximate process; Discrete tetrahedron volume data is the linear proximity to initial body data or implicit function, and under the supposed premise of linear proximity, mt algorithm acquired results is accurate, therefore in mt algorithm, exists and once approaches.Obviously, in mc and mt algorithm, the sampling density of volume data or implicit function is larger, and the approximation accuracy of contour surface is higher, but the triangular plate number producing is also more, and the space of algorithm and time loss also can correspondingly increase; Vice versa.Therefore, the approximation accuracy of these two kinds of representative algorithms of quantitative measurment has important reference value for relevant Science and engineering application.
In sum, all there is deviation in the extraction result of contour surface extraction algorithm, and deviation is mainly from two aspects: (1) linear or three linear hypothesis to voxel cell; (2) in voxel cell, use tri patch to approach contour surface.At present, contour surface extraction algorithm is of a great variety, little but the achievement of result precision is extracted in judge.And only a small amount of extraction accuracy judgment criteria research all concentrate on difference situation processing, extract the difference of result on subjective vision etc. qualitative aspect.Therefore, industry lack one can quantitative measurment contour surface extraction accuracy judgment criteria and corresponding computing method.
Summary of the invention
For the deficiencies in the prior art, the present invention proposes a kind of method for quantitative measuring of contour surface extraction accuracy.
A method for quantitative measuring for contour surface extraction accuracy, described contour surface extraction accuracy comprises average departure degree, the fluctuating range of deviation and maximum deviation degree, described method for quantitative measuring comprises:
(1) extracting on each tri patch obtaining and evenly getting several sampled points by contour surface extraction algorithm;
(2) determine the corresponding point of all sampled points in true curved surface, and each sampled point is to the Euclidean distance of corresponding point;
(3) relatively each sampled point obtains maximum Euclidean distance to the size of the Euclidean distance of corresponding corresponding point, calculate mean value and the mean square deviation of all sampled points of all tri patchs and the Euclidean distance of corresponding corresponding point, and using described mean value as average departure degree, using described mean square deviation as deviation fluctuating range, using maximum Euclidean distance as maximum deviation degree.
The distance of the tri patch that the result of utilizing contour surface to extract in the method for quantitative measuring of contour surface extraction accuracy of the present invention obtains and true curved surface is quantitative to contour surface extraction accuracy.When calculating contour surface and extracting the distance of the tri patch that obtains and true curved surface, by choose several sampled point on tri patch, calculating sampling is put the distance of corresponding point in true curved surface, then the Euclidean distance with corresponding corresponding point according to sampled point, by relatively obtaining maximum Euclidean distance (this distance is all result dough sheets that obtain of extraction to the forward direction Hausdorff distance of true curved surface) as maximum deviation degree, and calculate mean value and the mean square deviation of all Euclidean distances, respectively as maximum deviation degree, average departure degree and deviation fluctuating range, thereby accurately and multi-angle measure contour surface extraction accuracy, efficiently solve the metric question that contour surface extracts the deviation of result, realize quantitative measurment from qualitative analysis, person easy to use selects suitable contour surface extracting method according to described application scenario.And method for quantitative measuring realization itself and the contour surface extracting method adopting, applied widely, can there is the extraction accuracy of all contour surface extracting method of effective quantitative measurment.
Hausdorff distance is described distance between two compact subsets in metric space, is widely used in as the field such as Geometric Modeling, Model Matching.Hausdorff distance has directivity, comprises forward direction Hausdorff distance and backward Hausdorff distance.In prior art, extract result (set that adopts contour surface extraction algorithm to extract all tri patchs that obtain) in the forward direction Hausdorff distance of true curved surface according to formula:
Calculate, wherein S is for extracting result, and D is true curved surface, and p is the point in S,
represent points all in S to the maximal value in the Euclidean distance of true curved surface.These computing method need to travel through extracts in result institute a little, and each point needs to travel through in D institute a little, therefore calculated amount is very large, and efficiency is low.In the present invention, directly utilize the approximate forward direction Hausdorff distance that arrives true curved surface as three extraction results of maximal value in Euclidean distance between sampled point and true curved surface, greatly reduce calculated amount, be conducive to improve measurement efficiency.
In described step (2) corresponding point of each sampled point be in true curved surface with the point of the Euclidean distance minimum of this sampled point.
Described step (2) is many to be realized by optimized algorithm.
As preferably, in described step (2), adopt interior point method to determine the corresponding point of each sampled point in true curved surface, and each sampled point is to the Euclidean distance of corresponding point.Compared with other optimization methods such as positive collection method, interior point method is polynomial time algorithm, and solution efficiency is higher.
The sampled point number of getting on each tri patch is identical.Three summits that the sampled point of getting in described step (1) is tri patch and be parallel to the intersection point between the mean line on three bases of tri patch.
In sampled point, have 3 three summits that are tri patch, in addition, a part of intersection point is the intersection point of 2 mean lines, and part is the intersection point of 3 mean lines, and wherein the intersection point of 2 mean lines is positioned on the limit of tri patch, and the intersection point of 3 mean lines drops in tri patch.
Described mean line is n mean line, and wherein n is non-vanishing natural number, selects according to actual conditions, and when n=1 represents not decile, direct three summits take tri patch are as sampled point.In fact sampled point number depends on the value of n.The sampled point number of getting on each tri patch is (n+1) × (n+2)/2.
The isodisperse of described mean line is 2～6.Isodisperse is higher, and the number of sampled point is more.Conventionally the more result of calculation of sampled point is more accurate, but calculated amount is larger, and efficiency is low, considers and is generally 2～6.
As preferably, the isodisperse of described mean line is 4.Consider the accuracy of efficiency and result of calculation, conventionally triangle, in the time that sampled point is the intersection point being parallel between 4 mean lines on three bases of tri patch, is enough to meet accuracy computation requirement when a tri patch is got 15 sampled points.
The distance of utilizing contour surface to extract result and true curved surface in the method for quantitative measuring of contour surface extraction accuracy of the present invention is measured the precision of contour surface extraction algorithm quantitatively, with multi-angle, efficiently solve the metric question that contour surface extracts the deviation of result, realize quantitative measurment from qualitative analysis, person easy to use selects suitable contour surface extracting method according to described application scenario.And method for quantitative measuring realization itself and the contour surface extracting method adopting, applied widely, can there is the extraction accuracy of all contour surface extracting method of effective quantitative measurment.
Embodiment
Below in conjunction with embodiment, the method for quantitative measuring of contour surface extraction accuracy of the present invention is elaborated.
In the present embodiment, utilize the method for quantitative measuring measurement of this contour surface extraction accuracy to utilize the extraction accuracy of the result that contour surface that marching cubes algorithm (mc algorithm) completes extracts, the number of extracting the tri patch obtaining is 2752.
The method for quantitative measuring medium value face extraction accuracy of the contour surface extraction accuracy of the present embodiment comprises average departure degree, the fluctuating range of deviation and maximum deviation degree.
The method for quantitative measuring of the contour surface extraction accuracy of the present embodiment comprises:
A kind of method for quantitative measuring of contour surface extraction accuracy comprises:
(1) extracting on each tri patch obtaining and evenly getting several sampled points by contour surface extraction algorithm, specific as follows:
Using three summits of tri patch be parallel to intersection point between the n mean line on three bases of the tri patch sampled point as this tri patch, the sampled point number obtaining is (n+1) × (n+2)/2, and wherein n is non-vanishing natural number.
N=4 in the present embodiment, using three summits of tri patch be parallel to intersection point between the quarterline on three bases of the tri patch sampled point as this tri patch.Obtain altogether 15 sampled points, wherein 3 three summits that are tri patch, 9 is the intersection point (being positioned on the limit of tri patch) of two four mean lines, 3 is the intersection point (being positioned at tri patch) of three mean lines.
(2) determine the corresponding point of all sampled points in true curved surface, and each sampled point is to the Euclidean distance of corresponding point.
In the present embodiment, utilize interior point method to determine respectively this sampled point unique corresponding point in true curved surface, then calculate Euclidean distance between the two.This step is the nonlinear optimal problem of a belt restraining in fact, its solve relevant arrange as follows:
Majorized function is the Euclidean distance formula between sample point and corresponding point, constraint condition is the toroidal function of true curved surface, initial point is sample point, the span of optimum solution is centered by sample point and the cubic space equal size of voxel, and the iterations in exit criteria is 100, function numerical value corresponding to optimum solution is 10
-8, iteration stop step-length be 10
-8.
(3) relatively each sampled point obtains maximum Euclidean distance to the size of the Euclidean distance of corresponding corresponding point, calculate mean value and the mean square deviation of all sampled points of all tri patchs and the Euclidean distance of corresponding corresponding point, and using described mean value as average departure degree, using described mean square deviation as deviation fluctuating range, using maximum Euclidean distance as maximum deviation degree.
In the present embodiment, k tri patch is to the forward direction Hausdorff distance of true curved surface
according to formula:
Calculate, wherein:
N is the number of the sampled point on each tri patch, N=15 in the present embodiment,
be the i(i=1 of k triangle on unilateral, 2 ... N) individual sampled point, S is the set of extracting all tri patchs that obtain, D is true curved surface, k=1,2 ... m, the number (m=2752 in the present embodiment) that m is tri patch,
The method is with all sampled points to the corresponding forward direction Hausdorff distance that arrives true curved surface as tri patch of the maximal value in the distance of true curved surface D, and the forward direction Hausdorff distance obtaining is approximate value.
Utilize formula:
Calculate the mean value of the Euclidean distance of each sampled point and corresponding corresponding point, n
sfor the sum of sampled point in all tri patchs,
represent that traversal i and k are to all
summation.In the time that contour surface extraction algorithm result dough sheet number is m, each tri patch is got 15 sample points, therefore one has 15 × m sampled point, i.e. n
s=15 × m.
Utilize formula:
Calculate the mean square deviation of the Euclidean distance of each sampled point and corresponding corresponding point,
represent traversal i and k couple
summation.
The above; be only the specific embodiment of the present invention, but protection scope of the present invention is not limited to this, any be familiar with those skilled in the art the present invention disclose technical scope in; the variation that can expect easily or replacement, within all should being encompassed in protection scope of the present invention.
Claims (7)
1. a method for quantitative measuring for contour surface extraction accuracy, is characterized in that, described contour surface extraction accuracy comprises average departure degree, the fluctuating range of deviation and maximum deviation degree, and described method for quantitative measuring comprises:
(1) extracting on each tri patch obtaining and evenly getting several sampled points by contour surface extraction algorithm;
(2) determine the corresponding point of all sampled points in true curved surface, and each sampled point is to the Euclidean distance of corresponding point;
(3) relatively each sampled point obtains maximum Euclidean distance to the size of the Euclidean distance of corresponding corresponding point, calculate mean value and the mean square deviation of all sampled points of all tri patchs and the Euclidean distance of corresponding corresponding point, and using described mean value as average departure degree, using described mean square deviation as deviation fluctuating range, using maximum Euclidean distance as maximum deviation degree.
2. the method for quantitative measuring of contour surface extraction accuracy as claimed in claim 1, is characterized in that, in described step (2) corresponding point of each sampled point be in true curved surface with the point of the Euclidean distance minimum of this sampled point.
3. the method for quantitative measuring of contour surface extraction accuracy as claimed in claim 2, is characterized in that, adopt interior point method to determine the corresponding point of each sampled point in true curved surface, and each sampled point is to the Euclidean distance of corresponding point in described step (2).
4. the method for quantitative measuring of contour surface extraction accuracy as claimed in claim 3, is characterized in that, the sampled point number of getting on each tri patch is identical.
5. the method for quantitative measuring of contour surface extraction accuracy as claimed in claim 4, is characterized in that, three summits that the sampled point of getting in described step (1) is tri patch and be parallel to the intersection point between the mean line on three bases of tri patch.
6. the method for quantitative measuring of contour surface extraction accuracy as claimed in claim 5, is characterized in that, the isodisperse of described mean line is 2～6.
7. the method for quantitative measuring of contour surface extraction accuracy as claimed in claim 6, is characterized in that, the isodisperse of described mean line is 4.
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| CN111323148A (en) * | 2020-03-06 | 2020-06-23 | 江苏省农业科学院 | Greenhouse sensor arrangement method and system based on three-dimensional space |
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| CN111323148A (en) * | 2020-03-06 | 2020-06-23 | 江苏省农业科学院 | Greenhouse sensor arrangement method and system based on three-dimensional space |
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