CN111429467B - Level set three-dimensional surface feature segmentation method for improved Lee-Seo model - Google Patents
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Abstract
The invention provides a level set three-dimensional surface feature segmentation method for an improved Lee-Seo model, which mainly comprises the following steps: acquiring and processing to obtain target image information, constructing an energy general function, obtaining a level set function and an evolution equation, and executing evolution to finish three-dimensional surface feature segmentation; the method has the advantages that the convex energy functional is reconstructed, the problem that the traditional model energy functional is lack of evidence in non-convexity is solved, an implicit Euler method can be applied when the minimum value position is solved, iteration step length limitation is removed, the convergence process can be greatly accelerated, meanwhile, the energy functional parameters can gradually approach to a certain value along with the fixation of a segmentation area, the solving process of the algorithm is further simplified through the preset parameters, and the operation speed is improved.
Description
Technical Field
The invention belongs to the field of workpiece surface appearance feature extraction, and particularly relates to a level set three-dimensional surface feature segmentation method for an improved Lee-Seo model.
Background
The microscopic topography of the workpiece surface has a direct effect on the workpiece function, and in order to be able to perform feature evaluation on the workpiece surface and to link the feature evaluation with the functional features of the surface and the processing parameters, a segmentation algorithm for effectively extracting different features of the surface is required. Because the surface appearance characteristics of the workpiece have the characteristics of various and complex shapes and fuzzy boundary information, most of the algorithms based on the boundary gradient cannot well extract the surface characteristics.
The level set algorithm solves the problem of topological structure change of complex contours in segmentation evolution by describing a level set function in a high-dimensional space, has the advantages of high precision, stable algorithm and the like, and is widely applied to morphology feature segmentation and topological structure design.
The Chan-Vese model is a typical and widely applied level set model, and has the advantages of the following two aspects: on one hand, the model does not depend on the edge gradient strength of the profile features any more, and the profile information of the surface of a local area is used as a segmentation basis, so that the model can well segment the profile features with fuzzy edge information; on the other hand, the function based on the local area surface topography information greatly simplifies the mathematical processing process and enhances the practicability of the algorithm.
However, the above model also has a problem that needs to be further improved, wherein, firstly, a level set function needs to be initialized in time in operation, and the level set function in the model is required to be kept as a symbol distance function in an evolution process, but in actual processing, because of uneven distribution of surface topography height data and large surface gradient difference, convergence speeds of segmentation contours at different positions are different, a singular point can be generated in a convergence process, so that wrong point segmentation can be caused, and in order to keep the level set function as the symbol distance function, a Chan-Vese model needs to reconstruct the level set function after a certain number of iterations, but repeated reconstruction operations in the iteration convergence process greatly increase the calculation amount of the algorithm.
On the other hand, the energy functional formula of the Chan-Vese model lacks the evidence of functional non-convexity, when a gradient descent method is used for solving the problem of the minimum value of the level set functional, the possible situation that the solving process is difficult to the local minimum value cannot be avoided, in the prior art, in order to avoid repeated reconstruction of the level set function in the iteration process, a solution scheme with a penalty term added in the energy functional is provided, the convergence speed of the level set function is limited according to the magnitude of the data gradient value, a larger convergence speed penalty is given to the penalty term at the position with large gradient and high convergence speed, the convergence speed of different positions of the profile gradient is ensured to be basically balanced, singularity is avoided, but the convergence speed of part of the region is seriously inhibited due to the addition of the penalty term, and the overall efficiency of the algorithm is reduced due to slow local convergence.
Disclosure of Invention
In response to the above-identified deficiencies in the art or needs for improvement, the present invention provides a system that may have multiple heights.
In order to achieve the above object, the present invention provides a method for segmenting a level set three-dimensional surface feature of an improved Lee-Seo model, which mainly comprises the following steps: acquiring and processing target image information, constructing an energy general function, acquiring a level set function and an evolution equation, and performing evolution to complete three-dimensional surface feature segmentation, wherein the energy general function E (f, phi) is as follows:
Further, the evolution equation of the level set function is as follows:
wherein a ═ 2(f (x) -c1)2+(f(x)-c2)2],B＝(f(x)-c2)2。
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
(1) according to the level set three-dimensional surface feature segmentation method of the improved Lee-Seo model, a level set algorithm Lee-Seo model energy functional construction thought is used, a new improved level set calculation model is provided, a level set function is not required to be kept as a symbolic distance function as mapping of image data in construction of the energy functional, and calculation complexity caused by repeated initialization of the level set function is avoided;
(2) according to the level set three-dimensional surface feature segmentation method for the improved Lee-Seo model, provided by the invention, the convex energy functional is reconstructed, and the problem of non-convexity lack proof of the traditional model energy functional is solved;
(3) according to the level set three-dimensional surface feature segmentation method of the improved Lee-Seo model, an implicit Euler method can be applied when a minimum value position is solved, iteration step length limitation is removed, and therefore the convergence process can be greatly accelerated;
(4) according to the level set three-dimensional surface feature segmentation method for the improved Lee-Seo model, the characteristic that the energy functional parameter gradually approaches a certain value along with the fixation of the segmentation region is found, the solving process of the algorithm is further simplified through the preset parameter, and the operation speed is improved. Different segmentation effects can be obtained by adjusting preset parameters.
Drawings
FIG. 1 shows the results of an experiment for extracting the surface topography of sandpaper according to the present invention: (a) the surface characteristic segmentation effect of the abrasive paper; (b) the initial value of the level set function and the value after the algorithm is completed; (c) the distribution density of the surface topography height data before algorithm processing and the distribution density of the level set function values after the algorithm processing are finished; (d) mapping the surface topography height data value at the same position with the level set function value to obtain an f-phi image;
FIG. 2 is a coordinate value corresponding to two peak values of the profile height data of the surface of the sandpaper for determining the parameter c1c2A suitable value of;
FIG. 3 is a graph of the results of an extraction experiment of the topographical features of structured MEMs according to the present invention: (a) structuring MEMs surface feature segmentation effect, segmenting circular features and square features; (b) the initial value of the level set function and the value after the algorithm is completed; (c) the distribution density of the surface topography height data before algorithm processing and the distribution density of the level set function values after the algorithm processing are finished; (d) mapping the surface topography height data value at the same position with the level set function value to obtain an f-phi image;
FIG. 4 is a coordinate schematic of the data distribution peak of the structured MEMs surface, the coordinate values being used to determine the parameter c1c2A suitable value of;
FIG. 5 is a diagram: (a) original data of the inner surface appearance of the honing of the engine cylinder to be processed; (b) the honing inner surface appearance data of the engine cylinder after the Gaussian regression filtering processing; (c) the height distribution curve of the profile data of the inner surface of the engine cylinder honing after the filtering treatment;
figure 6 defines the results of data processing for the same honing surface topography for two different parameters: (a) dividing and extracting the groove characteristics of the same honing surface; (b) obtaining different level set function values; (c) parameter c under two different definitions1c2Convergence in the iterative process; (d) obtaining data distribution states of different level set functions; (e) and mapping the same position level set function value and the surface appearance height parameter to obtain a mapping relation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a level set three-dimensional surface feature segmentation method for an improved LS model, which mainly comprises the following working steps: (1) collecting and processing a target image; (2) carrying out evolution according to an energy general function improved based on the Lee-Seo model provided by the invention; (3) the method is characterized in that an improved energy functional is provided, a slicing constant level set method is used as a basis, the construction idea of an LS model energy functional is inherited, and a direct mapping relation exists between the level set function and image data, so that the level set function is not limited by a distance function, the level set function does not need to be initialized repeatedly, the calculation amount of an algorithm is greatly reduced, the constructed energy functional also has function convexity, and the minimum solving process is ensured not to be difficult to a local extreme point.
In order to solve the problem of convexity of an energy functional, a Lee-Seo model (hereinafter referred to as an LS model) in the prior art improves a construction method of the energy functional in a Chan-Vese model, the newly constructed energy functional completes the proof of functional convexity, only one minimum value point is present and is the minimum value point, the situation that contour convergence is difficult to a local minimum point is avoided, the key of the LS model is the construction of the convex energy functional, so that the situation that convergence is difficult to a local minimum value is avoided, and the energy functional of the LS model is shown in the following formula (1):
ELS(φ)＝λ1∫Ω(f-c1)2φH(α+φ)dx-λ2∫Ω(f-c2)2φH(α-φ)dx (1)
wherein λ is1，λ2To be in the value range of [0,1]Phi represents a level set function which represents a region divided by a curve, f represents a data value of an original collected image, omega integral domain refers to a region of the whole surface topography height data to be processed, c1And c2Is a desired value representing a feature in the delineated region after segmentation, wherein,
wherein the content of the first and second substances,
it should be noted that x represents the position of the energy functional data in the integral domain Ω, and the value form of x is determined by the dimension of the data to be processed. When processing surface topography image data, the data to be processed is a two-dimensional image, so the value is in a two-dimensional form (x, y), which is briefly described here by x, in addition, the omega integral domain also corresponds to a two-dimensional coordinate integral, dx represents a pixel variable of the image information, which is also briefly described here, and in the following description of the salient content of the present invention, the function part omits the brief description of the image coordinate expression.
The LS model has the advantages that the construction of the related item of the level set function phi (x) is realized, a part with function convexity is constructed by adding phi (x) in front of the Heaviside function and introducing a positive parameter alpha, only one global extreme value exists, the interference of the local extreme value to the evolution process of the level set function is avoided, the level set function value has an upper boundary and a lower boundary, the upper boundary and the lower boundary of the outline inner and outer level set functions are influenced by the parameter alpha, and the upper boundary and the lower boundary of the level set function evolution are used as the definite stopping condition of the evolution process, so that the situation of the level set function over-evolution is avoided.
Summarizing from the above LS model, it can be seen that: the basic form of the construction concept of the energy functional is shown in the following formula (5):
E(f,φ)＝∑∫ΩA(f,ci)B(φ)dx (5)
A(f,ci) B (phi) is a function to be determined in the integral domain omega, A (f, c)i) The independent variables of the function are the original data value f and the characteristic information parameter value c of the expression area at a specific positioniThe effect is to introduce the influence of the original data value on the energy, ciThe value is a statistic which can represent the characteristics of the divided region, the independent variable of B (phi) is the corresponding level set function value phi at the specific position, and the function of the independent variable is to convert the influence of original data into the change of the level set function to drive the iterative evolution of the level set function, A (f, c)i) The defined freedom enables the level set algorithm to have good expansibility, and can be combined with other morphology analysis methods such as characteristic local similarity analysis and fuzzy clustering analysis.
The invention further improves the convexity of the LS model, namely, the following level set energy general function model is provided:
solving the above formula as partial differential equation, wherein the result of the evolution equation of the level set function is as follows:
wherein A ═ 2(f (x) -c1)2+(f(x)-c2)2],B＝(f(x)-c2)2，
A commonly used solving method of a general level set model algorithm is a gradient descent method, a constructed energy functional adjusts a segmentation result in a mode of adding various additional penalty terms, but as the constructed result of the gradient descent method is an Euler method, the step length selection needs to meet the requirement of stable conditions, otherwise, an iteration result is diverged. In practical application, iteration step sizes meeting conditions are often selected to be small, so that iteration times are very large, calculation amount is increased, and algorithm efficiency is seriously reduced. According to the energy universal function provided by the invention, an implicit Euler formula is obtained by solving through a partial differential equation method, the unconditional stability is met, the iteration step length is not limited, and the iteration times can be greatly reduced by selecting a larger step length to improve the algorithm efficiency.
In the embodiment of the technical scheme of the invention, A (f, c)i) The same definition as the LS model is partially chosen, but in practical applications f and ciCan be more flexible, ciThe standard value of a certain attribute of the entire divided region, A (f, c)i) Then watchThe difference from the standard is achieved at each position in the area, and the similarity with the clustering analysis theory is certain. A (f, c)i) The definition of (B) can be expanded, so that the corresponding energy functional equation can be constructed by the formula (5) according to different requirements, and the upper and lower boundaries of the level set value range are determined by the definition of B (phi). Analyzing the energy of a specific position under the definition of the formula (6), and assuming that the data value of the surface topography height is close to c1That point should belong to partition 1 region, when (f-c)1)2The term approaches to 0, the size of the overall energy functional of E (f, phi) mainly depends on the value of a second term, and the energy functional is determined by a partial formula value:
it can be known that, for this position, the energy spread function value E (f, Φ) can take a minimum value when Φ is 1, and the minimum value exists and is the only minimum value due to the convexity of the energy spread function, and it can be known from the above demonstration that the magnitude of the level set function value in the region 1 exists in the upper bound 1, the level set function value in the region 2 in the same theory exists in the lower bound 0, and the overall value-taking domain of the level set function is [0,1 ].
The parameter c can be seen from the formulae (2) and (3)1c2The value geometric meaning of (1) is an average value of surface topography height data in the segmentation region, and the value geometric meaning of (2) is adjusted along with the change of the segmentation region after each iteration. C is known to converge to a constant value gradually over multiple iterations and the region segmentation is fixed gradually1c2It will converge to a constant value.
Parameter c1c2The parameter c is used as the standard center of some parameter attribute of the segmentation region in the energy functional1c2Which in theory could not be obtained by a level set algorithm but is pre-specified as a fixed value, when denoted by c1c2When the constant value is assumed, the integral unknown number of the energy functional is reduced to two, c1c2The value of (c) is not limited by the derivation result of the Euler-Lagrange equation any more, and the appropriate adjustment of c can be tried1c2To obtain different segmentation effects.
With c1c2Assuming a constant value as a precondition, the energy functional formula can be further derived,
from equation (10) above, the energy at any given location is relatively independent, independent of the parameters at other locations, and only related to the level set function value φ and the data value f, so that the essential condition for the energy function to obtain the minimum under this assumption is that the minimum at each location is obtained within the entire surface topography data region Ω, and the level set function value φ gradually approaches a value when the minimum at a given location is required:
as the number of iterations increases, the region segmentation becomes increasingly fixed, c1c2Will approach to a fixed value, a fixed functional relationship will be generated between the level set function value phi and the original data value f, and the fixed functional relationship is only related to the parameter c1c2Is relevant to the selection of (2).
Although the specific construction method of the energy general function implemented according to the invention is different from the Lee-Seo method, the convexity of the construction method needs to be proved, and the proving process is as follows:
suppose that
a + b is 1, phi is present1,φ2∈L2(Ω) and φ1≠φ2L (omega) is the value range of the single dimension of the level set function on the omega integral domain, and the convexity verification is respectively carried out on two terms of the energy general function, and the first term is proved as follows:
(aφ1+bφ2)2＝(aφ1)2+(bφ2)2+2abφ1φ2
＜(aφ1)2+(bφ2)2+ab(φ1 2+φ2 2)
＝a(a+b)φ1 2+b(a+b)φ2 2
＝aφ1 2+bφ2 2 (12)
for the second term, it turns out that:
(aφ1+bφ2)2-2(aφ1+bφ2)＝(aφ1)2+(bφ2)2+2abφ1φ2-2(aφ1+bφ2)
＜(aφ1)2+(bφ2)2+ab(φ1 2+φ2 2)-2(aφ1+bφ2)
＝a(a+b)φ1 2+b(a+b)φ2 2-2(aφ1+bφ2)
＝aφ1 2+bφ2 2-2(aφ1+bφ2)
＝a(φ1 2-2φ1)+b(φ2 2-2φ2) (13)
in summary, it can be concluded that:
E(aφ1+bφ2,f)＜aE(aφ1,f)+bE(bφ2,f) (14)
the energy functional realized according to the invention has functional convexity, only one minimum value can exist, namely the minimum value, and the situation of being difficult to the local minimum value can not occur in the iteration process of the level set model.
Besides the improvement of the original LS model, the functional parameters of the method provided by the invention have the convergence phenomenon in iteration, and according to the convergence phenomenon, the structure of the functional can be further simplified by a method of presetting the functional parameters, so that the algorithm efficiency is improved, and different segmentation effects can be obtained by controlling the preset parameters.
In the specific implementation mode of the invention, the sand paper surface and the structured MEMs surface are tested by the method, the segmentation effect of the algorithm on different types of characteristics is verified, different preset parameter definitions are adopted for the honing surface of the same engine cylinder block, and the influence of the preset parameter adjustment on the algorithm segmentation effect is verified.
Structured surfaces commonly used in engineering practice are widely used for their good performance, and quality control of such surfaces usually requires separation of various structured features and comparison with designed specifications, and therefore, the process of segmenting the measurement data is usually an indispensable step.
In the experiment, because the data distribution of the structured surface has obvious characteristics, parameters in the algorithm need to be readjusted according to the distribution condition of the processed data, and c1c2The calculation can highlight the region where the feature to be segmented and extracted is located according to the distribution condition of the surface data.
Example one
According to the method, the surface topography height data of the abrasive paper is processed and tested, and the surface topography height parameter value approaches to c1c2The obtained level set function values approach to the upper and lower boundaries of the level set function values respectively, so that the profile height is c1c2Surface features near the value can be mapped to two ends of a level set function value taking domain, and then are segmented and extracted.
Fig. 1 is an experimental result of extracting surface topography features of abrasive paper according to an energy general function proposed in the present invention, in which fig. 1(a) is a surface feature segmentation effect of abrasive paper, in which groove regions between protruding regions are extracted, fig. 1(b) is an initial value of a level set function and a value after completion of an algorithm, fig. 1(c) is a distribution density of surface topography height data before the algorithm processing and a distribution density of level set function values after the algorithm processing, and fig. 1(d) is an f-phi image obtained by mapping a surface topography height data value at the same position with a level set function value;
as can be seen from the formula (11),the surface topography height parameter value approaches to c1c2The obtained level set function values approach to the upper and lower boundaries of the level set function values respectively, so that the profile height is c1c2Surface features near the value can be mapped to two ends of a level set function value taking domain, and then are segmented and extracted. As can be seen from fig. 1(c), after the data is mapped onto the level set function, the data is respectively concentrated at two ends of the value-taking domain of the level set function, and for the surface topography height data of the sandpaper, the feature desired to be extracted is a groove feature between the protruding regions. As can be seen from the height distribution density of the surface topography in FIG. 2, the trench feature height is concentrated near the peak value of-19.89, the height data of the surface protrusion area is near the peak value of-2.252, and the parameter c is selected to better extract the trench feature1c2The values of (a) are two peaks-19.89 and-2.252, respectively. And respectively mapping and concentrating the groove characteristic region and the surface convex characteristic region to the upper and lower boundaries of the level set function value taking region so as to extract.
Example two
Processing structured MEMs surface topography height data in a well-defined hierarchy according to the method of the present invention, as shown in FIG. 3, FIG. 3 is an experimental result of extracting the structured MEMs surface topography feature by improving an LS algorithm model, FIG. 3(a) a structured MEMs surface feature segmentation effect, segmenting a circular feature and a square feature, FIG. 3(b) an initial value of a level set function and a value after the completion of the algorithm, FIG. 3(c) a distribution density of surface topography height data before the algorithm processing and a distribution density of level set function values after the algorithm processing are completed, and FIG. 3(d) an f-phi image obtained by mapping a surface topography height data value at the same position with a level set function value;
parameter c1c2The data distribution diagram is shown in fig. 4, the peak point corresponding to the circular feature in the expected extracted features is (0.9988,1.359), the peak point corresponding to the square feature is (4.353,0.3614), and the processing parameter is c selected to highlight the specific feature1＝0.9988，c2＝4.353。
The two kinds of fruitsThe surface topography data processed in the examples are characterized by a well-defined number distribution layer characterized by distinct number distribution peaks. One of the advantages of the improved algorithm is embodied by the algorithm, namely that the parameter c can be adjusted1c2Taking values, extracting the characteristics in a specific surface topography height numerical range, mapping the specific range into a smaller range on a level set function through the algorithm, conveniently extracting the characteristics and reducing extraction errors, simultaneously mapping other unfocused data into a more distant area to highlight the characteristic range, and considering adjustment parameter c for surface topography characteristic segmentation with various height characteristics1c2The values of (a) are extracted separately, or a multi-level set is introduced for segmentation.
EXAMPLE III
The grooves on the inner surface of the engine cylinder honing have important functions of storing lubricating oil and collecting abrasive dust and are important features for realizing the function of the honing surface, the evaluation of the traditional engine cylinder honing inner surface depends on a two-dimensional surface contour line, the information loss is serious, an algorithm capable of segmenting and extracting groove features from three-dimensional surface topography data is needed, and the common extraction algorithm is Radon transformation because the groove features have obvious linear shape characteristics, in the actual situation, the surface topography data is noisy, and the extraction effect of the Radon algorithm is very dependent on parameter adjustment due to the fuzzy groove edge.
The method has the characteristics of high algorithm efficiency and stable and excellent effect, the selected cylinder honing surface topography data and the numerical value distribution thereof are shown in the following figure 5, wherein figure 5(a) is original data of the inner surface topography of the engine cylinder to be processed, figure 5(b) is inner surface topography data of the engine cylinder after the Gaussian regression filtering processing, and figure 5(c) is a height distribution curve of the inner surface topography data of the engine cylinder after the filtering processing.
The honed surface differs from the structured surface of the previous embodiments in that the topography height value distribution of the honed surface is absentObvious layering characteristic, the characteristic boundary of the groove is fuzzy, so the parameter c1c2The value of (c) is determined according to the characteristics of the divided region, and the parameter c is determined according to the characteristics of the divided region1c2Two different definitions were made for the experiments.
The first method adopts the mean value of the heights of the appearances of different segmentation areas as a parameter c1c2Taking the value of (A); secondly, in consideration of uneven distribution of the height of the surface topography, the following formula is adopted:
for parameter c1c2The original data of the surface topography height is introduced into the calculation as a weight value, the condition that the surface topography height is integrally concentrated is considered, the surface topography height is introduced as the weight value, reasonable segmentation can be carried out in a numerical concentration region, two different parameter definitions are applied, and the provided improved LS model level set algorithm is used for processing the honing surface topography data.
Figure 6 is a graph of the results of processing the same honing topography data using two different parameter definitions of equations (2) (3) and (15) (16): FIG. 6(a) shows the result of trench feature segmentation extraction for the same honing surface, FIG. 6(b) shows the resulting different level set function values, and FIG. 6(c) shows the parameters c for two different definitions1c2In the convergence condition in the iterative process, fig. 6(d) shows the data distribution states of different level set functions, and fig. 6(e) shows the mapping relationship obtained by mapping the level set function value at the same position with the surface topography height parameter.
It can be seen from the figure that when the parameter c is1c2When the definitions of the formulas (2) and (3) are satisfied, the obtained level set function values are more concentrated at two ends of a value-taking domain, and the algorithm is more prone to a level set method of slicing constant values as a whole.
After adjustment, the parameters are defined by the equations (15) and (16), the concentrated values are mapped to the level set function to form three distribution peaks, compared with the original parameter definition, a better segmentation effect can be obtained by using an algorithm of the parameters under the definition, and in the final segmentation result, the deep trench region (-14, -1.832) and the shallow trench region (-1.592, -0.7749) in the trench feature region are also separated.
The deep and shallow groove regions mainly give different functional characteristics to the honing surface, the deep grooves are favorable for storing abrasive dust and lubricating oil, excessive deep grooves can damage the construction of a lubricating oil film, the shallow grooves are favorable for constructing the lubricating oil film, the excessive shallow grooves cause the storage capacity of the abrasive dust and the lubricating oil to be reduced, and the self-construction algorithm can respectively extract the characteristics of the two deep and shallow grooves.
The level set algorithm can describe the curve evolution process with complex topological change, and has wide research and application in the fields of image segmentation algorithms and topological structure design. The method is based on the characteristics of a level set LS model, provides a construction idea of a level set energy functional, constructs a new improved level set algorithm for carrying out feature extraction and segmentation on three-dimensional surface topography features, and avoids repeated initialization operation of the level set function because the algorithm avoids the use of a normalized Heaviside function and the level set function does not need to be kept as a distance function, thereby greatly simplifying mathematical processing of the algorithm.
In a word, according to the phenomenon that part of parameters gradually converge along with the region segmentation in the iteration process of the level set algorithm, a new level set image segmentation method is provided. Since some parameters gradually converge to a certain value along with the region segmentation, a functional relationship between the level set function value and the original data value can be derived, and the functional relationship is gradually fixed along with iteration, so that the level set algorithm can be understood as an algorithm for mapping the feature to be extracted to a prominent numerical region convenient for extraction.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (2)
1. A method for segmenting the three-dimensional surface characteristics of a level set of an improved Lee-Seo model mainly comprises the following steps: acquiring and processing target image information, constructing an energy general function, acquiring a level set function and an evolution equation, and performing evolution to complete three-dimensional surface feature segmentation, wherein the energy general function E (f, phi) is as follows:
wherein phi represents a level set function, f represents the target image information data, omega integral domain refers to the region of the whole surface topography height data to be processed, c1And c2Is an expected value representing a feature in the segmented description area, where c1And c2Taking a fixed value; or
Hε(phi) is a normalized Heaviside function, epsilon is a positive parameter, and the fitting degree of the normalized Heaviside function and the ideal Heaviside function is represented; or
HεAnd (phi) is a normalized Heaviside function, and epsilon is a positive parameter, and the fitting degree of the normalized Heaviside function and the ideal Heaviside function is characterized.
2. An improved Lee as claimed in claim 1-a level set three-dimensional surface feature segmentation method of the Seo model, characterized in that the level set function evolution equation is:
wherein A is- [2 (f-c)1)2+(f-c2)2],B＝(f-c2)2And the delta t is an iteration step of the evolution time.
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