CN115239909B - Spectral analysis-based craniofacial relationship research method and device - Google Patents
Spectral analysis-based craniofacial relationship research method and device Download PDFInfo
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Abstract
The invention belongs to the technical field of craniofacial morphological informatics, and particularly relates to a craniofacial relationship research method and a craniofacial relationship research device based on spectral analysis, wherein a triangular mesh model of a skull and a human face is obtained; according to triangular mesh models of a skull and a human face, a shape feature space is constructed on the basis of a wave diffusion distance distribution curve; calculating a typical correlation coefficient between a skull set and a face set wave diffusion distance distribution curve in a shape feature space, and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis; calculating Frey pause distances among the skull wave diffusion distance distribution curves, calculating Frey pause distances among the face wave diffusion distance distribution curves, and obtaining a second craniofacial correlation rule R2 according to the correlation between the variation trend of the skull similarity and the variation trend of the similarity among the faces; and verifying the correlation of the craniofacial data base. By constructing the shape feature space, the strong correlation between the skull and the face is accurately verified.
Description
Technical Field
The invention belongs to the technical field of craniofacial morphological informatics, and particularly relates to a craniofacial relationship research method and a craniofacial relationship research device based on spectral analysis.
Background
The study of craniofacial relationship is mainly used for craniofacial identification, craniofacial reconstruction, and the like. Craniofacial recognition refers to matching the most similar registered face with an unknown face and determining the identity of the unknown skull by using craniofacial relationships respectively. Craniofacial reconstruction a single face is restored from the skull by computing the appearance of the skull via computer-aided and craniofacial techniques. Therefore, craniofacial relationships may significantly improve the accuracy and efficiency of craniofacial identification and craniofacial reconstruction.
Anthropologists and anatomists have discovered the relationship between human skull and human face. In addition to sex, race and environmental factors, the skull is a major factor in determining the appearance of a human face. The skull is an inherent biological feature having the appearance of a human face, and the shape of the skull determines the position and structure of the face feature. Thus, according to the studies of anthropologists and anatomists, the following craniofacial relationships were observed:
r1: for human skull and human face, the skull has strong correlation with the corresponding human face.
R2: for human skull and human face, the similarity change trend of the skull is generally consistent with the corresponding human face similarity; in other words, if the skull is more similar, the corresponding face should be more similar.
The craniofacial relationship describes the relationship between the skull and the corresponding face and the similarity change rule of the skull and the face. In previous studies, some investigators studied craniofacial relationship R1. In fact, however, the craniofacial relationship R2 provides strong theoretical support for craniofacial identification and craniofacial reconstruction. Effective craniofacial relationship verification not only provides theoretical support for relevant craniofacial research, but also is beneficial to improving the understanding of researchers to craniofacial models. However, most investigator poses study craniofacial applications based on craniofacial relationships; only a few researchers really verify the craniofacial relationship.
In the prior art:
1. facial Soft Tissue Thickness (FSTT): traditionally, anthropologists and anatomists have obtained and used the craniofacial relationship R1 by measuring FSTT. Prokopec et al reconstructed the shape of the nose on the basis of the skull with the nasal bone; they drawn an orthogonally projected contour of the skull and modified the cartilage components according to guidelines; increasing the thickness of the soft part, drawing the outer contour of the nose and the position of the eyes and ears. Wilkinson et al explored the relationship between oral soft tissue and bone details. It has been found that the most reliable indicator of oral width is the distance between the lips, with lip thickness being positively correlated to tooth height for both men and women. Stephan considers that many face approximation methods for estimating soft tissue based on bone are subjective and without scientific testing, he tested several common methods for determining oral cavity width based on soft tissue prediction of the skull. Rynn discusses the anatomical and morphological interrelationships between the cranium and the face of a person from craniofacial morphology, the mandible, the oral cavity, the nose and the eyes, and the authors believe that the shape of the adult cranium is based on the face of the person and the internal and external soft tissues of the head, just as the face and head are based on the cranium. Pavla evaluated the strength of the association between cranial shape and soft tissue contour shape and described the most important features, a significant joint change of the two shape contours based on the central european population database. In addition to the forehead contour of the skull, the closest relationship between the curve of the skull and the soft tissues occurs in the upper jaw, with little relationship between the inferior and medial half of the face.
2. Statistical Shape Model (SSM): recently, SSM is used to study craniofacial relationships and to estimate the shape of facial organs. Berar M et al applied SSM for the first time to craniofacial studies and class p. After this work was completed, researchers applied SSM based on PCA refinement to study craniofacial relationship R1, and continued to improve the technique, including the study of dense craniofacial models and landmark guided craniofacial models. However, the craniofacial relationship is not discussed in detail in the above methods. Therefore, researchers have introduced different regression methods in craniofacial relationship studies. Among them, duan et al propose a PCA-based skull recognition method in which the mapping between the skull and the face is obtained by canonical correlation analysis. Dune et al proposed an improved computerized craniofacial reconstruction region approach that explores craniofacial relationships using 80 craniofacial and 25 facial landmarks, respectively, and found strong associations between the shapes of the soft tissue and the underlying skeleton of a particular facial region. Shui et al investigated to what extent the choice of Principal Component (PC) affected the analysis of craniofacial relationship and gender-type two. In essence, duan and Shui reduce the dimensionality of the skull and face sampling points by PCA and use the calculated correlation coefficients of the skull and face features as the craniofacial relationship.
These methods all have some drawbacks and cannot fundamentally verify craniofacial relationships, especially in the context of rule R2. (1) The first disadvantage is that the skull and face data formats studied by researchers such as Duan and Shui are point cloud formats, which are suitable for using PCA to reduce the size of the skull and face; however, the point cloud data format ignores the geometric information of the skull and face. (2) Another disadvantage is that the PCA reduced dimension data cannot contain all skull and face information, but only a large portion of the principal information in the principal components. In contrast, in practical applications, the principal component with a smaller contribution also contains explicit information to distinguish different skulls or faces. (3) Finally, it is also important that craniofacial data be strictly required when using SSM and PCA. The researcher needs to perform pre-processing on the craniofacial data, including registration of the craniofacial data, alignment of physiological points, and selection of appropriate landmark points.
Based on the above, how to provide an effective method for verifying craniofacial relationship is a problem to be solved urgently.
Disclosure of Invention
The invention aims to overcome the defect that the craniofacial relationship cannot be fundamentally verified in the prior art, and provides a craniofacial relationship research method and a craniofacial relationship research device based on spectral analysis.
In order to achieve the purpose, the invention adopts the following technical scheme:
in a first aspect,
the application provides a craniofacial relationship research method based on spectral analysis, which comprises the following steps:
acquiring triangular mesh models of a skull and a human face;
according to the triangular mesh models of the skull and the face, a shape feature space is constructed on the basis of a wave diffusion distance distribution curve;
calculating a typical correlation coefficient between wave diffusion distance distribution curves of a skull set and a face set in the shape feature space, and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis;
calculating Frecher distances among skull wave diffusion distance distribution curves in the shape characteristic space to obtain the variation trend of skull similarity;
in the shape feature space, calculating the Frechst distance between the human face wave diffusion distance distribution curves to obtain the change trend of the similarity between human faces;
obtaining a second craniofacial correlation rule R2 according to the correlation between the variation trend of the skull similarity and the variation trend of the similarity between the human faces;
and verifying craniofacial correlation according to the first craniofacial correlation rule R1 and the second craniofacial correlation rule R2 in a real craniofacial database.
Further, the constructing a shape feature space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the human face includes:
acquiring a three-dimensional skull or human face of a shape feature space to be constructed;
defining a real-valued function f on the surface of the three-dimensional skull or face;
calculating a Laplace-Bellamy (LB) operator of the real-valued function f according to the real-valued function f, and obtaining a characteristic value and a characteristic vector of the Laplace-Bellamy operator based on spectral decomposition of the Laplace-Bellamy operator;
calculating the wave diffusion distance of any two points on the surface of the three-dimensional skull or the human face shape according to the characteristic value and the characteristic vector of the Laplace-Bellamy operator to obtain a wave diffusion distance matrix, calculating the cumulative distribution curve of the wave diffusion distance, and defining a wave diffusion distance distribution curve;
and mapping the three-dimensional skull and the human face to the same shape characteristic space based on the wave diffusion distance distribution curve.
Further, the mapping the three-dimensional skull and the human face to the same shape feature space includes:
and calculating the wave diffusion distance distribution curve of the three-dimensional skull and the human face shape surface, wherein the wave diffusion distance distribution curve is used as the shape characteristic for representing the shape.
Further, the constructing a shape feature space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the face includes:
extracting features from the shape, and mapping the shape to a low-dimensional feature space based on the features of the shape;
the fluctuation-based kernel signature WKS for any point on the shape surface can be calculated as:
defining two points on the surface of a shapeBased on fluctuation kernel signature WKS 2 The distance is the wave dispersion distance:
the discrete calculation of the wave dispersion distance is in the form:
wherein e is N As an energy scale parameter, e N ＝log(E)，λ i For the i-th feature vector of LB operator, σ is the variance of normal distribution, ce is the regularized WKS function, v pi And v qi The ith characteristic function respectively represents LB operators at any vertex p and q on the triangular mesh;
calculating a cumulative distribution curve of wave diffusion distances, defining the wave diffusion distance distribution curve as a shape descriptor, wherein the wave diffusion distance distribution curve is calculated in the following way:
(1) Normalized wave dispersion distance:
normalization of the distance matrix, μ (D), using Z-score M ) Denotes the average wave propagation distance, σ (D), over M M ) Denotes the standard deviation of the wave propagation distance, d, over M w * (x, y) represents the wave dispersion distance between x and y after normalization;
(2) Frequency histogram for calculating wave dispersion distance
D L ＝{d w *(x,y)|d w *(x,y)-((n-1)δ+D MIN )>0,d w *(x,y)∈D}；
D R ＝{d w *(x,y)|(nδ+D MIN )-d w *(x,y)≥0,d w *(x,y)∈D} (5)
δ is the distance threshold, n is the number of bins of the histogram, p (i δ) is the frequency of the different bins of the wave dispersion distance, D MIN Denotes the minimum distance in D, N is the sum of the distances in D, num (D) L ∩D R ) Representing the number of intersections of the left and right subsets, it is necessary to add a translation value D in equation (5) since the distances have been normalized MIN Wherein D is L Represents a left subset of D, wherein D w * (x, y) is greater than (n-1) delta + D MIN Distance, D R Represents a right subset of D, wherein D w * (x, y) is less than or equal to (n) delta + D MIN The distance of (d);
(3) Calculating cumulative distribution curve of wave dispersion distance
Since δ is the distance threshold of any dw (x, y), the cumulative distribution curve of dw (x, y) can be calculated as discrete, F M (δ) is a mathematical expression of the wave dispersion distance distribution curve:
p (i δ) is the frequency of the different frequency bands of the wave dispersion distance.
Further, also included in the shape feature space is formally defining craniofacial relationships, including:
mapping the skull and the face into a feature space by a wave diffusion distance distribution curve:
in the feature space, a wave diffusion distance distribution curve is used to represent a skull or a human face, and the skull can be represented as Si = [ xi1, xi 2., xiN ]; the face corresponding to the skull can be represented as Fi = [ yi1, yi 2.,. YiN ], where i represents the skull or face number, N represents the number of sampling points of the descriptor wave diffusion distance distribution curve, xi represents the ith characteristic sampling point, si represents the characteristic set of the i skull, and Sj represents the characteristic point set of the j skull;
the formal simplification of skull similarity and face similarity in craniofacial relationships is represented as:
the similarity between the skulls is simplified and expressed as Ds (i, j), and the similarity between the faces can be expressedShown as D F (i, j), ds (i, j) is defined as the shape similarity measure, D, of the skull Si and the skull Sj F (i, j) is a measure of similarity of the shape of the face Fi and the face Fj, then:
D S (i，j)＝D(S i ，S j )＝Di st(S i ，S j )or C orr(S i ，S j ) (7)
the shape similarity measure of the face Fi and the face Fj is expressed as:
D F (i，j)＝D(F i ，F j )＝Dist(F i ，F j )or Corr(F i ，F j ) (8)
wherein D (Si, sj) represents the distance between the wave dispersion distance profiles of a pair of craniums i and j, dist (Si, sj) represents the Freund's distance or Corr (Si, sj) represents a typical correlation coefficient; d (Fi, fj) represents the distance between the wave dispersion distance profiles for calculating a pair of faces i and j, dist (Fi, fj) represents the freschel distance or Corr (Fi, fj) represents a typical correlation coefficient.
Further, in the shape feature space, a typical correlation coefficient between the wave diffusion distance distribution curves of the skull set and the face set is calculated, a first craniofacial correlation rule R1 is obtained based on hypothesis testing analysis, and a typical correlation coefficient R of an arbitrary shape M and an arbitrary shape N can be calculated as:
F M (δ) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N;
and calculating a typical correlation coefficient between the skull set and the face set based on a typical correlation analysis statistical method of hypothesis test to obtain a strong positive correlation between the skull set and the face set.
Further, in the shape feature space, the fraunher distances between the skull wave diffusion distance distribution curves are calculated to obtain the variation trend of the skull similarity, and the fraunher distances of the wave diffusion distance distribution curves between the arbitrary shape M and the arbitrary shape N can be calculated as follows:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N.
Further, in the shape feature space, the fraunher distance between the human face wave diffusion distance distribution curves is calculated to obtain the variation trend of the similarity between human faces, and the fraunher distance of the wave diffusion distance distribution curves between the arbitrary shape M and the arbitrary shape N can be calculated as follows:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N.
In a second aspect of the present invention,
the application provides a craniofacial relationship research method device based on spectral analysis, which comprises the following steps:
the acquisition module is used for acquiring triangular mesh models of the skull and the face;
the shape feature space building module is used for building a shape feature space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the human face;
the first calculation module is used for calculating a typical correlation coefficient between a skull set and a face set wave diffusion distance distribution curve in the shape feature space, and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis;
the second calculation module is used for calculating Freusch distances among the skull wave diffusion distance distribution curves in the shape feature space to obtain a variation trend of the skull similarity;
the third calculation module is used for calculating the Freusch distance between the distribution curves of the diffusion distances of the face waves in the shape feature space to obtain the change trend of the similarity between the faces;
the craniofacial correlation module is used for obtaining a second craniofacial correlation rule R2 according to the correlation between the change trend of the skull similarity and the change trend of the similarity between the human faces;
and the verification module is used for verifying craniofacial correlation according to the first craniofacial correlation rule R1 and the second craniofacial correlation rule R2 in a real craniofacial database.
The invention has the advantages that:
the invention provides a craniofacial relationship research method based on spectral analysis, which is characterized in that triangular mesh models of a skull and a human face are obtained; according to the triangular mesh models of the skull and the human face, a shape feature space is constructed on the basis of a wave diffusion distance distribution curve; calculating a typical correlation coefficient between a skull set and a face set wave diffusion distance distribution curve in the shape feature space, and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis; calculating Frecher distances among skull wave diffusion distance distribution curves in the shape characteristic space to obtain the variation trend of skull similarity; in the shape feature space, calculating the Frechst distance between the human face wave diffusion distance distribution curves to obtain the change trend of the similarity between human faces; obtaining a second craniofacial correlation rule R2 according to the correlation between the variation trend of the skull similarity and the variation trend of the similarity between the human faces; and verifying craniofacial correlation according to the first craniofacial correlation rule R1 and the second craniofacial correlation rule R2 in a real craniofacial database. By constructing the shape feature control and using the shape similarity method to calculate the similarity between the skulls and the similarity between the faces, the similarity change trend of the skulls is accurately verified to be generally consistent with the similarity of the corresponding faces.
Drawings
FIG. 1 is a flow chart of the steps of a craniofacial relationship research method based on spectral analysis according to the present invention.
FIG. 2 is a schematic diagram of a craniofacial relationship verification framework shown in one embodiment of the present application.
FIG. 3 is a diagram of a skull set and a face set in one embodiment of the present application.
FIG. 4 is a male test result of the relevance formula R1 shown in one embodiment of the present application.
FIG. 5 shows the results of a female test of the relevance rule R1 according to one embodiment of the present application.
Fig. 6 is a line graph test result of the correlation rule R2 shown in one embodiment of the present application.
Fig. 7 is a thermodynamic diagram test result of the correlation rule R2 according to an embodiment of the present application.
FIG. 8 is a schematic structural diagram of a craniofacial relationship research apparatus based on spectral analysis according to an embodiment of the present application.
Detailed Description
The following further describes a specific embodiment of the craniofacial relationship research method based on spectral analysis according to the present invention with reference to fig. 1. The craniofacial relationship research method based on spectral analysis of the present invention is not limited to the description of the following examples.
Referring to fig. 1, fig. 1 is a flowchart illustrating specific steps of a craniofacial relationship research method based on spectral analysis according to an embodiment of the present application, and as shown in fig. 1, the craniofacial relationship research method based on spectral analysis includes:
s101, acquiring triangular mesh models of a skull and a human face;
s102, constructing a shape feature space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the human face;
and storing the storage formats of the skull and the face according to a preset storage rule.
In the prior art, a plurality of storage methods are adopted, and a triangular mesh model is adopted in the method. The topological relation of the triangle can well reflect the topological relation between the vertex and the neighborhood. The correct topological connection effectively reveals the original information and topology of the skull and face.
By calculating the cumulative distribution function curve of the three-dimensional skull and the human face shape surface, the wave diffusion distance distribution curve is used as the shape characteristic for shape representation, so that when the three-dimensional skull and the three-dimensional human face are analyzed, the model space formed by the three-dimensional skull and the three-dimensional human face can be converted into the shape characteristic space formed by the wave diffusion distance distribution curve for analysis.
Step S103, calculating a typical correlation coefficient between Wave diffusion distance Distribution curves of the skull set and the face set in the shape feature space, and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis, wherein the Wave diffusion distance Distribution curves are abbreviated as WKDD (Wave Kernel distance Distribution);
step S104, calculating Freusch distances among the skull wave diffusion distance distribution curves in the shape characteristic space to obtain the variation trend of the skull similarity;
step S105, calculating Freusch distances among human face wave diffusion distance distribution curves in the shape feature space to obtain the change trend of the similarity among human faces;
s106, obtaining a second craniofacial relevance rule R2 according to the correlation between the change trend of the skull similarity and the change trend of the similarity between the human faces;
and S107, verifying craniofacial correlation according to the first craniofacial correlation rule R1 and the second craniofacial correlation rule R2 in a real craniofacial database.
The wave diffusion distance distribution curve (WKDD) is a non-rigid three-dimensional shape descriptor suitable for describing the same type of shape difference, a simple same type global three-dimensional shape representation method is obtained by defining the wave diffusion distance distribution curve (WKDD), and the complicated same type non-rigid three-dimensional shape similarity measurement is converted into the simple one-dimensional vector similarity measurement. The method based on the wave diffusion distance distribution curve (WKDD) is robust to topology, so that the similarity between a pair of shapes can be directly measured, complex topological and processing work is not needed before the shape is measured, for example, hole filling and other operations are carried out on a three-dimensional skull and a three-dimensional face, the method based on the wave diffusion distance distribution curve (WKDD) is not needed to search the same number of corresponding points or carry out descriptor alignment before the shape similarity is measured, and the same type of shapes can be accurately and directly measured.
It is well known that the human head is mainly composed of the skull and the human face, including the muscles and skin. The human face is the most direct recognition basis among the human beings. The skull is an intrinsic biological feature of a human face, and its shape determines the location and structure of the face features. In addition to the limitations of the skull, many factors, such as age, gender, and Body Mass Index (BMI), affect the shape of a human face. The research result of anthropology shows that the skull has important restriction on the face characteristics and the position and the structure of the soft tissue of the face. The shape of the skull has a certain correlation with the human face, which is mainly shown in two aspects. First, the skull determines the basic outline of the face and the face is a soft tissue representation that overlays the skull. Secondly, the local features of the face do not have a one-to-one correspondence with the skull features. Therefore, in the shape feature space, the correlation between the skull and the face and the change trend of the similarity between the skull and the face are calculated, namely, the correlation of the craniofacial is verified.
The invention provides a craniofacial relationship research method based on spectral analysis, which comprises the steps of obtaining triangular mesh models of a skull and a human face; according to the triangular mesh models of the skull and the human face, a shape feature space is constructed on the basis of a wave diffusion distance distribution curve; calculating typical correlation coefficients between the skull set and the face set WKDD in the shape feature space, and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis; in the shape characteristic space, calculating the Freusch distance between skull wave diffusion distance distribution curves to obtain the variation trend of skull similarity; in the shape feature space, calculating the Frechst distance between the face wave diffusion distance distribution curves to obtain the change trend of the similarity between the faces; obtaining a second craniofacial correlation rule R2 according to the correlation between the variation trend of the skull similarity and the variation trend of the similarity between the human faces; and verifying craniofacial correlation according to the first craniofacial correlation rule R1 and the second craniofacial correlation rule R2 in a real craniofacial database. By constructing the shape feature control, the similarity between the skulls and the similarity between the faces are calculated by using a shape similarity method, and the similarity change trend of the skulls is verified to be generally consistent with the similarity of the corresponding faces.
As a further improvement of the above method, in an embodiment, the constructing a shape feature space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the human face includes:
acquiring a three-dimensional skull or human face of a shape feature space to be constructed;
defining a real-valued function f on the surface of the three-dimensional skull or face;
calculating a Laplace-Belt Lame (LB) operator of the real-valued function f according to the real-valued function f, and obtaining a characteristic value and a characteristic vector of the Laplace-Belt Lame operator based on spectral decomposition of the Laplace-Belt Lame operator;
calculating the wave diffusion distance of any two points on the surface of the three-dimensional skull or the human face shape according to the characteristic value and the characteristic vector of the Laplace-Bellamy operator to obtain a wave diffusion distance matrix, calculating the cumulative distribution curve of the wave diffusion distance, and defining a wave diffusion distance distribution curve;
and mapping the three-dimensional skull and the human face to the same shape characteristic space based on a wave diffusion distance distribution curve.
Specifically, the mapping the three-dimensional skull and the human face to the same shape feature space includes:
and calculating the wave motion kernel signature and the wave diffusion distance matrix of the three-dimensional skull and the face shape surface, and taking a wave diffusion distance distribution curve (WKDD) as the characteristic of the shape for representing the shape.
In recent years, local non-rigid three-dimensional shape matching based on spectral analysis has been widely studied, researchers have characterized non-rigid three-dimensional shapes based on local shape descriptors such as GPS, HKS, and WKS, however, non-rigid three-dimensional shape matching can be generalized into two key steps: (1) extracting valid shape descriptors; and (2) selecting a proper measuring method. After extracting the shape descriptors, the researcher wishes to calculate the distance between the shape descriptors of a pair of shapes as the shape similarity. The above work presupposes that preprocessing operations are required on the shapes, including but not limited to: the shapes are registered in the same coordinate system in advance, and the number of sampling points of the shapes is the same; researchers have manually calibrated feature points or have found the same number of one-to-one corresponding points on a pair of shapes based on some algorithm. These pretreatments are challenging for researchers and often take a high degree of time complexity. In order to avoid the above preprocessing, a global shape descriptor is studied, and a shape distance distribution is a global descriptor for extracting shape geometry information and topology by counting a histogram of distances on a shape surface. A new local description Fu Bo diffusion distance Distribution curve (WKDD) is defined based on Wave Kernel Signature (WKS), and the WKS continues the advantages of the WKS and can distinguish different shape models in the same shape class. Compared with other methods, the method focuses more on the description of the shape details, and can better reflect the difference of different shapes in the same type of shapes. By defining a wave dispersion distance distribution curve (WKDD), the shape is mapped into a new space, called the shape feature space. In the shape feature space, each shape is mapped to a cumulative distribution function curve of its wave dispersion distance, and shape matching is performed by calculating the distance between the curves.
The Wave Kernel Signature (WKS) can clearly separate different frequency sets on a shape by measuring the average probability distribution of quantum particles of different energy levels for each point on the shape by using a band-pass filter, and allows access to high-frequency information, thereby increasing the accurate matching capability of an operator. Furthermore, WKS has multi-scale characteristics by selecting different energy scales. WKS is a relatively stable descriptor that can encode more geometric features, and has multi-scale properties by selecting different energy levels.
In some embodiments, constructing a shape feature space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the human face comprises:
extracting features from the shape, and mapping the shape to a low-dimensional feature space based on the features of the shape;
the fluctuation-based kernel signature WKS for any point on the shape surface can be calculated as:
defining L based on fluctuation kernel signature WKS between two points on shape surface 2 The distance is the wave diffusion distance:
the discrete calculation form of the wave dispersion distance is:
wherein e is N As an energy scale parameter, e N ＝log(E)，λ i For the i-th feature vector of LB operator, σ is the variance of normal distribution, ce is the regularized WKS function, v pi And v qi The ith characteristic function respectively represents LB operators at any vertex p and q on the triangular mesh;
calculating a cumulative distribution curve of wave diffusion distances, defining the wave diffusion distance distribution curve as a shape descriptor, wherein the wave diffusion distance distribution curve is calculated in the following way:
(1) Normalized wave dispersion distance:
normalization of the distance matrix, μ (D), using Z-score M ) Denotes the average wave propagation distance, σ (D), over M M ) Denotes the standard deviation of the wave propagation distance, d, over M w * (x, y) represents the wave dispersion distance between x and y after normalizationSeparating;
(2) Frequency histogram for calculating wave dispersion distance
D L ＝{d w *(x,y)|d w *(x,y)-((n-1)δ+D MIN )>0,d w *(x,y)∈D}；
D R ＝{d w *(x,y)|(nδ+D MIN )-d w *(x,y)≥0,d w *(x,y)∈D} (5)
δ is the distance threshold, n is the number of bins of the histogram, p (i δ) is the frequency of the different bins of the wave dispersion distance, D MIN Denotes the minimum distance in D, N is the sum of the distances in D, num (D) L ∩D R ) Representing the number of intersections of the left and right subsets, it is necessary to add a translation value D in equation (5) since the distances have been normalized MIN Wherein D is L Represents a left subset of D, wherein D w * (x, y) is greater than (n-1) delta + D MIN Distance, D R Represents a right subset of D, wherein D w * (x, y) is less than or equal to (n) delta + D MIN The distance of (d);
(3) Calculating cumulative distribution curve of wave dispersion distance
Since δ is the distance threshold of any dw (x, y), the cumulative distribution curve of dw (x, y) can be calculated as discrete, F M (δ) is a mathematical expression of the wave dispersion distance distribution curve:
p (i δ) is the frequency of the different frequency bands of the wave dispersion distance.
In one embodiment, shape features are defined by applying a wave-dispersion distance distribution curve (WKDD) to construct a shape feature space that is closely related to the laplacian-belterra-nomide concept.
The Laplace-Belladrami (Laplace-Beltrami) operator is a second-order partial differential operator (LB operator for short) of the shape surface, the LB operator is popularization of the Laplace operator on Riemann flow patterns, the Laplace operator is defined as a divergence value of a real-valued function f gradient defined at any point of the shape, and the expression formula of the Laplace operator is as follows:
if the Laplace operator is popularized to the Riemann manifold, an LB operator is obtained, and the LB operator can be expressed in a local coordinate system as follows:
where G is the metric tensor and G is the determinant of the matrix { gij }. Since the shape format studied here is a mesh, the definition of the discrete LB operator on a triangular mesh is given as follows:
where wij is a coefficient matrix, f (vi) and f (vj) are the values of the discrete LB operator acting on the function f at the vertices vi and vj, respectively, and the above formula can be calculated as:
where n is the number of vertices of the shape, α j and β j respectively represent the diagonal connecting vertices vi and vj edges eij, and Neigh (vi) represents the set of vertices adjacent to vi. If the LB operator is spectrally resolved, λ i and
the characteristic vector corresponding to the ith characteristic value and the ith characteristic value of the LB operator.
Δ M φ i ＝λ i φ i
As a smooth differential operator, the LB operator satisfies the following properties:
(1) Self-tracing property：
(2) Semi-positive nature:
(3) Zero eigenvalue: the minimum Laplace eigenvalue is zero, and the corresponding eigenfunction is a constant;
(4) The locality is as follows: Δ f (p) is independent of Δ f (q) for any different point p, q, Δ f (p);
(5) Linear precision: if M is a plane and f is a linear function, Δ f =0.
In one embodiment, formally defining craniofacial relationships in the shape feature space comprises:
mapping the skull and the face into a feature space by a wave diffusion distance distribution curve:
in the feature space, a wave diffusion distance distribution curve is used to represent a skull or a human face, and the skull can be represented as Si = [ xi1, xi 2., xiN ]; the face corresponding to the skull may be represented as Fi = [ yi1, yi 2.,. YiN ], where i represents the skull or the face number, N represents the number of sampling points of the descriptor wave diffusion distance distribution curve (100 in this example), xi represents the ith feature sampling point, si represents the feature set of the i skull, and Sj represents the feature set of the j skull;
the formal simplification of skull similarity and face similarity in craniofacial relationships is represented as:
the similarity between the skulls is simplified and expressed as Ds (i, j), and the similarity between the faces can be expressed as D F (i, j), ds (i, j) is defined as the shape similarity measure, D, of the skull Si and the skull Sj F (i, j) is a measure of similarity of the shape of the face Fi and the face Fj, then:
D S (i，j)＝D(S i ，S j )＝Dist(S i ，S j )or Corr(S i ，S j ) (7)
the shape similarity measure of the face Fi and the face Fj is expressed as:
D F (i，j)＝D(F i ，F j )＝Dist(F i ，F j )or Corr(F i ，F j ) (8)
wherein D (Si, sj) represents the distance between the wave diffusion distance distribution curves of a pair of skull i and j, dist (Si, sj) represents the Frey distance or Corr (Si, sj) represents a typical correlation coefficient; d (Fi, fj) represents the distance between the wave dispersion distance profiles for calculating a pair of faces i and j, dist (Fi, fj) represents the freschel distance or Corr (Fi, fj) represents a typical correlation coefficient.
Mapping the skull and the face to a feature space through WKDD, and displaying the shape similarity between the initial skull and the randomly selected skull in order to clearly describe the craniofacial relationship, as shown in FIG. 2, FIG. 2 is a relationship diagram of a skull set and a face set in one embodiment of the present application, GS is a similarity set of the initial skull and all skull in Ω S, GS = { Ds (i), 1 ≦ i ≦ q, i ∈ Z }, GF is a similarity set of the initial face and all face in Ω F, GF = { Df (i), 1 ≦ i ≦ q, i ∈ Z }.
R2:ΔD s (i)≈ΔD f (i)
As can be seen from fig. 2 and the above formula, there is a double mapping between the skull set and the face set. There is a strong positive correlation between them (CCA coefficient is high). Meanwhile, if a pair of skull bones are similar, their corresponding faces will also be similar. Specifically, the increment rate Δ Ds (i) of the inter-skull similarity is approximately equal to the increment rate corresponding to the similarity between the faces Δ D f (i).
Referring to fig. 3, fig. 3 is a schematic diagram of a craniofacial relationship verification framework according to an embodiment of the present application, where in an embodiment, the calculating shape similarity of a skull set and shape similarity of a face set based on a shape feature space includes:
in one embodiment, in the shape feature space, a typical correlation coefficient between the wave diffusion distance distribution curves of the skull set and the face set is calculated, a first skull face correlation rule R1 is obtained based on hypothesis testing analysis, and a typical correlation coefficient R of an arbitrary shape M and an arbitrary shape N can be calculated as:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N;
and calculating a typical correlation coefficient between the skull set and the face set based on a typical correlation analysis statistical method of hypothesis test to obtain a strong positive correlation between the skull set and the face set.
The typical correlation coefficient is an application of covariance matrix, and is a multivariate statistical analysis method for reflecting the overall correlation between two groups of indexes by using the correlation between multiple variables respectively. R calculates the correlation coefficient between M and N, where M and N are matrices or vectors of the same size.
The value of R is between-1 and +1, i.e.: -1. Ltoreq. R.ltoreq.1 with the following properties: A. when R >0, the two variables are positively correlated;
B. when R =1, the two variables are completely linearly related;
C. when R =0, there is no linear correlation between the two variables.
D. When 0 s are R s are woven over 1, there is a certain degree of linear correlation between the two variables.
The closer R is to 1, the stronger the linear relationship between the two variables;
the closer R is to 0, the weaker the linear correlation between the two variables.
Analyzing the relationship between the skull and the human face by using SPSS analysis tool, and adopting typical correlation analysis
The method processes data for males and females, respectively. Suppose that:
h0, the skull of the male is not positively correlated with the face;
h1, the male skull is positively correlated with the face;
confidence interval: 0.005.
h0' that the female skull and face are not positively correlated;
h1, the skull of a female is positively correlated with the face;
confidence interval: 0.005.
in one embodiment, in the shape feature space, the fraunher distances between the skull wave diffusion distance distribution curves are calculated to obtain the variation trend of the skull similarity, and the fraunher distances of the wave diffusion distance distribution curves between the arbitrary shape M and the arbitrary shape N can be calculated as follows:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N.
In one embodiment, in the shape feature space, the fraunher distances between the human face wave diffusion distance distribution curves are calculated to obtain the variation trend of the similarity between human faces, and the fraunher distances between the wave diffusion distance distribution curves of the arbitrary shape M and the arbitrary shape N can be calculated as follows:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N.
Comparing the variation trend of the similarity between the craniums with the variation trend of the similarity between the human faces, and verifying the craniofacial correlation.
The present application provides descriptions and mathematical expressions of craniofacial relationships. The skull and face are mapped to the same shape feature space. The method selects a wave diffusion distance distribution curve (WKDD) to construct a three-dimensional skull and human face shape feature space, wherein the shape feature space is a vector space, and a 1D vector (referred to as the wave diffusion distance distribution curve (WKDD)) can simply and effectively represent a 3D shape through feature extraction. The present application uses two steps to verify craniofacial relationships comprehensively in shape feature space. The first step is to obtain a strong positive correlation between the skull set and the face set by calculating a typical correlation coefficient between the WKDD values of the skull and the face based on a hypothetical typical correlation analysis. The canonical correlation analysis is a multi-component analysis method that uses the correlation of complex variables to reflect the overall correlation between two groups. The second step is a three-dimensional shape similarity calculation based on shape analysis. By comparing the skull similarity with the growth rate of the face similarity, the consistent change trend of the corresponding face when the skull changes is researched. Finally, the two methods are combined to obtain the whole craniofacial relationship, so that the result is more accurate.
The present application provides for the expression of craniofacial relationships, including two rules: rules R1 and R2. Based on this expression, a data-driven craniofacial relationship validation framework is proposed to validate rules R1 and R2. An asian-mongolian craniofacial database (100 groups of craniofacial and facial data for males and females) was used to validate the craniofacial relationship described above. The shape feature space is introduced for the first time to verify the craniofacial relationship. The shape feature space displays all the geometric information and topological relation of the skull and the human face, and realizes data dimension reduction without using principal component analysis. Furthermore, there is no need to align the skull and face data, nor to manually mark landmarks before constructing the shape feature space. Using statistical correlation analysis methods, R1 was verified by calculating typical correlation coefficients between the male and female skull and face groups, consistent with the results obtained by previous methods. In addition, the method describes all skull and face information in the shape feature space, and the statistical result is very accurate. The similarity between the craniums and the similarity between the faces of the male and female are calculated using a shape similarity method to verify the rule R2. The growth rates of the skull similarity and the face similarity are compared, and the rule R2 is explained from the variation trend of the skull similarity and the face similarity.
Referring to fig. 4-7 of the drawings,
FIG. 4 is a male test result of the relevance rule R1 shown in one embodiment of the present application;
FIG. 5 shows the results of a female test of the relevance rule R1 according to one embodiment of the present application;
FIG. 6 is a line graph test result of the relevance rule R2 shown in one embodiment of the present application;
fig. 7 is a thermodynamic diagram test result of the correlation rule R2 according to an embodiment of the present application.
Referring to fig. 8, fig. 8 is a schematic structural diagram of a craniofacial relationship research apparatus based on spectral analysis according to an embodiment of the present application, where the apparatus of the craniofacial relationship research method based on spectral analysis includes:
an obtaining module 801, configured to obtain triangular mesh models of a skull and a human face;
a shape feature space construction module 802, configured to construct a shape feature space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the face;
a first calculation module 803, configured to calculate a typical correlation coefficient between the skull set and the face set WKDD in the shape feature space, and obtain a first craniofacial correlation rule R1 based on hypothesis testing analysis;
a second calculating module 804, configured to calculate a fretsch distance between skull wave diffusion distance distribution curves in the shape feature space, so as to obtain a variation trend of skull similarity;
a third calculating module 805, configured to calculate a fratsch distance between the human face wave diffusion distance distribution curves in the shape feature space, so as to obtain a variation trend of similarity between human faces;
a craniofacial correlation module 806, configured to obtain a second craniofacial correlation rule R2 according to a correlation between the variation trend of the skull similarity and the variation trend of the similarity between the faces;
a verification module 807 for verifying craniofacial relevance according to the first craniofacial relevance rule R1 and the second craniofacial relevance rule R2 in a real craniofacial database.
With regard to the spectral analysis-based craniofacial relationship research apparatus in the above embodiment, the specific manner in which each module performs operations has been described in detail in the above embodiment of the related method, and will not be described in detail here.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all should be considered as belonging to the protection scope of the invention.
Claims (9)
1. A craniofacial relationship research method based on spectral analysis is characterized by comprising the following steps:
acquiring triangular mesh models of a skull and a human face;
according to the triangular mesh models of the skull and the face, a shape feature space is constructed on the basis of a wave diffusion distance distribution curve;
calculating a typical correlation coefficient between a skull set and a face set wave diffusion distance distribution curve in the shape feature space, and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis;
calculating Frecher distances among skull wave diffusion distance distribution curves in the shape characteristic space to obtain the variation trend of skull similarity;
in the shape feature space, calculating the Frechst distance between the human face wave diffusion distance distribution curves to obtain the change trend of the similarity between human faces;
obtaining a second craniofacial correlation rule R2 according to the correlation between the change trend of the skull similarity and the change trend of the similarity between the human faces;
and verifying craniofacial correlation according to the first craniofacial correlation rule R1 and the second craniofacial correlation rule R2 in a real craniofacial database.
2. The method of claim 1, wherein constructing a shape feature space based on wave diffusion distance distribution curves from the triangular mesh models of the skull and the human face comprises:
acquiring a three-dimensional skull or human face of a shape feature space to be constructed;
defining a real-valued function f on the surface of the three-dimensional skull or face;
calculating a Laplace-Belt Lame (LB) operator of the real-valued function f according to the real-valued function f, and obtaining a characteristic value and a characteristic vector of the Laplace-Belt Lame operator based on spectral decomposition of the Laplace-Belt Lame operator;
calculating the wave diffusion distances of any two points on the three-dimensional skull or human face shape surface according to the eigenvalues and eigenvectors of the Laplacian-Beltelamer operator to obtain a wave diffusion distance matrix, calculating the cumulative distribution curve of the wave diffusion distances, and defining a wave diffusion distance distribution curve;
and mapping the three-dimensional skull and the human face to the same shape feature space based on the wave diffusion distance distribution curve.
3. The method of claim 2, wherein said mapping the three-dimensional skull and face to the same shape feature space comprises:
and calculating the wave diffusion distance distribution curve of the three-dimensional skull and the human face shape surface, wherein the wave diffusion distance distribution curve is used as the shape characteristic for representing the shape.
4. The method according to claim 1 or 2, wherein the constructing of the shape feature space based on the wave diffusion distance distribution curve according to the triangular mesh model of the skull and the human face comprises:
extracting features from the shape, and mapping the shape to a low-dimensional feature space based on the features of the shape;
the fluctuation-based kernel signature WKS for any point on the shape surface can be calculated as:
defining L based on fluctuation kernel signature WKS between two points on shape surface 2 The distance is the wave diffusion distance:
the discrete calculation of the wave dispersion distance is in the form:
wherein e is N As an energy scale parameter, e N ＝log(E)，λ i For the i-th feature vector of LB operator, σ is the variance of normal distribution, ce is the regularized WKS function, v pi And v qi Respectively representing ith characteristic functions of LB operators at any vertex p and any vertex q on the triangular mesh;
calculating a cumulative distribution curve of wave diffusion distances, defining the wave diffusion distance distribution curve as a shape descriptor, wherein the wave diffusion distance distribution curve is calculated in the following way:
(1) Normalized wave dispersion distance:
normalization of the distance matrix, μ (D), using Z-score M ) Denotes the average wave propagation distance, σ (D), over M M ) Denotes the standard deviation of the wave propagation distance, d, over M w * (x, y) represents the wave dispersion distance between x and y after normalization;
(2) Frequency histogram for calculating wave dispersion distance
D L ＝{d w *(x,y)|d w *(x,y)-((n-1)δ+D MIN )>0,d w *(x,y)∈D}；
D R ＝{d w *(x,y)|(nδ+D MIN )-d w *(x,y)≥0,d w *(x,y)∈D} (5)
δ is the distance threshold, n is the number of bins of the histogram, p (i δ) is the frequency of the different bins of the wave dispersion distance, D MIN Denotes the minimum distance in D, N is the sum of the distances in D, num (D) L ∩D R ) Representing the number of intersections of the left and right subsets, it is necessary to add a translation value D in equation (5) since the distances have been normalized MIN Wherein D is L Represents a left subset of D, wherein D w * (x, y) is greater than (n-1) delta + D MIN Distance, D R Represents the right subset of D, where D w * (x, y) is less than or equal to (n) delta + D MIN The distance of (a);
(3) Calculating cumulative distribution curve of wave dispersion distance
Since δ is the distance threshold of any dw (x, y), the cumulative distribution curve of dw (x, y) can be calculated as discrete, F M (δ) is a mathematical expression of the wave dispersion distance distribution curve:
p (i δ) is the frequency of the different frequency bands of the wave dispersion distance.
5. The method of claim 1, further comprising formally defining craniofacial relationships in the shape feature space, comprising:
mapping the skull and the face into a feature space by a wave diffusion distance distribution curve:
in the feature space, a wave diffusion distance distribution curve is used to represent a skull or a human face, and the skull can be represented as Si = [ xi1, xi 2., xiN ]; the face corresponding to the skull can be represented as Fi = [ yi1, yi 2.,. YiN ], wherein i represents the skull or face number, N represents the number of sampling points of the descriptor wave diffusion distance distribution curve, xi represents the ith characteristic sampling point, si represents the characteristic set of i skull, and Sj represents the characteristic point set of j skull;
the formal simplification of skull similarity and face similarity in craniofacial relationships is represented as:
the similarity between the skulls is simplified and expressed as Ds (i, j), and the similarity between the faces can be expressed as D F (i, j), ds (i, j) is defined as the shape similarity measure, D, of the skull Si and the skull Sj F (i, j) is a measure of similarity of shape of face Fi and face Fj, then:
D S (i，j)＝D(S i ，S j )＝Dist(S i ，S j )or Corr(S i ，S j ) (7)
the shape similarity measure of the face Fi and the face Fj is expressed as:
D F (i，j)＝D(F i ，F j )＝Dist(F i ，F j )or Corr(F i ，F j ) (8)
wherein D (Si, sj) represents the distance between the wave dispersion distance profiles of a pair of craniums i and j, dist (Si, sj) represents the Freund's distance or Corr (Si, sj) represents a typical correlation coefficient; d (Fi, fj) represents the distance between the wave dispersion distance profiles for calculating a pair of faces i and j, dist (Fi, fj) represents the freschel distance or Corr (Fi, fj) represents a typical correlation coefficient.
6. The method according to claim 1, wherein in the shape feature space, a typical correlation coefficient between the wave diffusion distance distribution curves of the skull set and the face set is calculated, a first skull face correlation rule R1 is obtained based on hypothesis testing analysis, and the typical correlation coefficient R of the arbitrary shape M and the arbitrary shape N can be calculated as:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) isA wave dispersion distance distribution curve of an ideogram N;
and calculating a typical correlation coefficient between the skull set and the face set based on a typical correlation analysis statistical method of hypothesis test to obtain a strong positive correlation between the skull set and the face set.
7. The method according to claim 1, wherein in the shape feature space, freusch distances between the skull wave diffusion distance profiles are calculated to obtain a variation trend of the skull similarity, and the Freusch distances of the wave diffusion distance profiles between the arbitrary shape M and the arbitrary shape N can be calculated as:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N.
8. The method according to claim 1, wherein in the shape feature space, the fraunher distances between the human face wave diffusion distance distribution curves are calculated to obtain the variation trend of the similarity between human faces, and the fraunher distances of the wave diffusion distance distribution curves between the arbitrary shape M and the arbitrary shape N can be calculated as follows:
F M (delta) is a wave dispersion distance distribution curve of arbitrary shape M, F N (δ) is a wave dispersion distance distribution curve of arbitrary shape N.
9. A craniofacial relationship research method device based on spectral analysis is characterized by comprising the following steps:
the acquisition module is used for acquiring triangular mesh models of a skull and a human face;
the shape characteristic space building module is used for building a shape characteristic space based on a wave diffusion distance distribution curve according to the triangular mesh models of the skull and the face;
the first calculation module is used for calculating a typical correlation coefficient between a skull set and a face set wave diffusion distance distribution curve in the shape feature space and obtaining a first craniofacial correlation rule R1 based on hypothesis test analysis;
the second calculation module is used for calculating the Freusch distance between the skull wave diffusion distance distribution curves in the shape characteristic space to obtain the variation trend of the skull similarity;
the third calculation module is used for calculating the Fourier distance between the human face wave diffusion distance distribution curves in the shape feature space to obtain the change trend of the similarity between the human faces;
the craniofacial correlation module is used for obtaining a second craniofacial correlation rule R2 according to the correlation between the variation trend of the craniofacial similarity and the variation trend of the similarity between the human faces;
and the verification module is used for verifying the correlation of the craniofacial model according to the first craniofacial correlation rule R1 and the second craniofacial correlation rule R2 in a real craniofacial database.
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