CN104573678B - The method and device of sex character analysis based on footprint image - Google Patents

The method and device of sex character analysis based on footprint image Download PDF

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CN104573678B
CN104573678B CN201510058919.0A CN201510058919A CN104573678B CN 104573678 B CN104573678 B CN 104573678B CN 201510058919 A CN201510058919 A CN 201510058919A CN 104573678 B CN104573678 B CN 104573678B
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footprint
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CN104573678A (en
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陈伟卿
何晓光
金玮
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DALIAN EVERSPRY SCI & TECH Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V40/00—Recognition of biometric, human-related or animal-related patterns in image or video data
    • G06V40/10—Human or animal bodies, e.g. vehicle occupants or pedestrians; Body parts, e.g. hands
    • G06V40/12—Fingerprints or palmprints
    • G06V40/1347—Preprocessing; Feature extraction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/40—Extraction of image or video features
    • G06V10/46—Descriptors for shape, contour or point-related descriptors, e.g. scale invariant feature transform [SIFT] or bags of words [BoW]; Salient regional features
    • G06V10/462—Salient features, e.g. scale invariant feature transforms [SIFT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/40—Extraction of image or video features
    • G06V10/46—Descriptors for shape, contour or point-related descriptors, e.g. scale invariant feature transform [SIFT] or bags of words [BoW]; Salient regional features
    • G06V10/462—Salient features, e.g. scale invariant feature transforms [SIFT]
    • G06V10/464—Salient features, e.g. scale invariant feature transforms [SIFT] using a plurality of salient features, e.g. bag-of-words [BoW] representations

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Abstract

The invention discloses a kind of method and device of the sex character analysis based on footprint image, belong to criminal investigation field, comprise the following steps：S1. multilayer pressure face extraction is carried out to footprint image；S2. according to the multilayer pressure face image of footprint, at least following footprint Morphologic Characteristics are obtained：Foot length, foot breadth, the area in each stressor layer face；S3. the mathematical modeling established between footprint Morphologic Characteristics and sex, above-mentioned Morphologic Characteristics is inputted to the mathematical modeling, obtain the proprietary sex character of the footprint.The present invention can automate realization to sex character analysis, and sex character analysis is stable, accurate.

Description

The method and device of sex character analysis based on footprint image
Technical field
The present invention relates to Digital Image Processing, computer vision and technique of criminal investigation field, more particularly to one kind is based on foot The method and device of the sex character analysis of mark image.
Background technology
Footprint is one of " brothers' work rifle " most common during criminal investigation is handled a case four major class vestiges.With the change of form of crimes with And Characteristics of Crime is increasingly intelligent, more and more stronger, the impression of the hand vestige number that scene of a crime can extract is realized in the counterreconnaissance of perpetrator Amount greatly reduces, and therefore, importance of the footprint analysis during solving criminal cases is more and more prominent.In current complicated social ring Under the influence of border, the female crime induced by a variety of causes rises situation in obvious, therefore accurately analyzes sex using footprint, And then determine that investigation direction is particularly important.The sex of people is different, and its build, physiological structure, motion function have significant difference, this A little difference have different degrees of reflection in footprint, and this according to footprint analysis sex just to provide foundation.Based on footprint figure The feature as used in carrying out gender analysis has foot length, foot breadth, pressure distribution uniformity coefficient etc., and measurement foot length, foot breadth are relative to be held Easily, pressure distribution uniformity coefficient is then mainly by the subjective judgement of reviewer；And these features integrate in use, being also mostly fixed Property description, lack quantizating index, therefore general survey personnel are difficult to grasp this technology.
The content of the invention
In order to solve the above problems, the invention provides a kind of method and dress of the sex character analysis based on footprint image Put, by establishing the model of science, artificial experience is quantified, avoid examination of footprint personnel subjective impact and human error Introduce, so as to reach quick, quantitative, accurate, objectively sex character analysis purpose.
To achieve these goals, the technical solution adopted by the present invention is：A kind of sex character based on footprint image point The method of analysis, comprises the following steps：
S1. multilayer pressure face extraction is carried out to footprint image；
S2. according to the multilayer pressure face image of footprint, at least following footprint Morphologic Characteristics are obtained：It is foot length, foot breadth, each The area in stressor layer face；
S3. the mathematical modeling established between footprint Morphologic Characteristics and sex, above-mentioned form is inputted to the mathematical modeling Architectural feature, obtain the proprietary sex character of the footprint；Concretely comprise the following steps：
S3.1. the mathematical modeling of sex and foot length is established：Sample x to overall G mahalanobis distance is
Wherein：μ and Σ is respectively overall G average and covariance matrix；X is foot length, and man, woman's foot length are respectively to obey Normal distributionWithOverall G1、G2, μ1、μ2Respectively G1、G2Average,Respectively G1、 G2Variance；
Test footprint foot length is calculated to overall G according to formula (1)1、G2Distance d1、d2,
Using formula (2), the proprietary sex character of footprint is obtained.
Further, step 3.1 replaces with：
Establish the mathematical modeling of sex and the length-width ratio of footprint：
The length-width ratio r=foot lengths of footprint/foot breadth (3)
Man, woman's footprint length-width ratio are respectively Normal DistributionWithOverall G3、G4, its Middle μ3、μ4Respectively G3、G4Average,Respectively G3、G4Variance；Test footprint length is calculated in reference formula (1) It is wide than with overall G3、G4Mahalanobis distance d3、d4；
Calculated using formula (4) and obtain the proprietary sex character of footprint.
Further, step S3.1 is replaced with：
Establish the mathematical modeling of sex interlayer pressure change rate adjacent with multilayer pressure face：Remember Si, i=1,2 ..., n, it is The area of i-th layer of footprint pressure face, the area relative change rate of the footprint pressure face of adjacent interlayer are
ΔSi=(Si+1-Si)/Si, i=1,2 ..., n-1 (5)
Its coefficient of variation is
Cv=σ/μ (6)
Wherein, μ, σ are respectively { Δ SiAverage and variance；
Given threshold value T, coefficient of variation cv are more than threshold value T, then judge all artificial males of the footprint, otherwise judge the footprint All artificial women.
Further, step S3.1 is replaced with：
Using the S3.1 of each step in above three technical scheme, 3 gender attributes are obtained, male, 1 generation are represented with 0 Table women, the gender attribute sum s of above-mentioned 3 kinds of mathematical modelings is calculated, if s≤1, judges all artificial males of the footprint；It is no Then, all artificial women of the footprint are judged.
Further, it is the step of the extraction of multilayer pressure face in step S1：
S1.1. to barefoot or wearing sock print image preprocessing：Barefoot or sock print image will be worn it is filtered, image filter The formula of ripple is as follows：
I=F*G
I (i, f)=ΣmΣnF (i, j) G (i-m, j-n) (7)
Wherein, * represents convolution, and F represents original wear shoes footprint image, and G represents wave filter, and I represents filtered footprint figure Picture, (i, j) represent current pixel position, and m, n represent size of the filter window in x, y direction respectively；
S1.2. pressure face extracts：
S1.2.1. bilateral filtering operation is carried out to pretreated footprint image, can be represented with equation below：
Wherein, WpIt is weighting function, is defined as follows
IFIt is the footprint image after bilateral filtering, I represents filtered footprint image in pre-treatment step, and x represents image I The position coordinates of middle current pixel, Ω are current bilateral filtering window centered on x, frIt is the codomain core of smooth luminance difference Function, gsIt is the space kernel function of smooth Spaces difference；
S1.2.2. quantization modulation：Color space conversion is carried out to the footprint image after bilateral filtering first, from rgb space It is transformed into Lab space；Luminance channel L is taken, it is quantified according to footprint pressure face number of plies n；Then by Lab mode images again Rgb space is transformed into, obtains footprint multilayer pressure mapping picture；
Wherein：Wave filter in step S1.1 is defined as：
Wherein, u, v are coordinate variables, and σ is standard deviation.
Further, the method for acquisition footprint Morphologic Characteristics is in step S2：
S2.1. footprint coordinate system is established：Take the pressure outermost layer in multilayer pressure mapping picture, Zuo Zhang areas and with area The common tangent of inside and outside both sides, if palm area, the inner side most salient point with area are respectively A, B, palm area, the outside most salient point difference with area For C, D, then the angular bisector of two common tangent AB, CD angle is footprint center line, footprint center line and the intersection point with area's lower edge For O, footprint is adjusted to its center line is vertical and tiptoe is upward, then in footprint institute in the planes, using O as origin, with center line It is straight up Y-axis positive direction for Y-axis, level is to the right X-axis positive direction, establishes footprint coordinate system；
S2.2. footprint Morphologic Characteristics are calculated：The outermost upper limb salient point T of pressure face, it is barefoot big toe leading edge point, The length that point T and origin O line projects on footprint centerline direction is foot length；
The length for slapping the line AC of the inside and outside both sides in area most salient point is foot breadth；
Length with the line BD of the inside and outside both sides in area most salient point is with width；
Outermost layer footprint pressure face in the part folded by line segment AC, BD, and inside and outside the part two sections of profiles at footprint center Beeline MN in line vertical direction is the wide a of bow；
The secondary outer layer pressure face in mark multilayer pressure mapping picture is taken fully, obtains the Ceng Shangzhang areas pressure span, the area Minimum point of the overseas profile on footprint centerline direction, to slap the lower edge salient point S of area pressure span.
Further, can also be the step of the extraction of multilayer pressure face in step S1：
S1.1. wear shoes footprint image is pre-processed：Shoe sole print in wear shoes footprint image is removed using image filtering operations Interference, the yardstick of wave filter adaptively determines according to the size of decorative pattern；The formula of image filtering is as follows：
I=F*G
I (i, j)=ΣmΣnF (i, j) G (i-m, j-n) (10)
Wherein, * represents convolution, and F represents original wear shoes footprint image, and G represents wave filter, and I represents filtered footprint figure Picture, (i, j) represent current pixel position, and m, n represent size of the filter window in x, y direction respectively；
Wave filter is defined as：
Wherein, u, v are coordinate variables, and σ is standard deviation；
It is adaptive should determine that filter scales method be：Wear shoes footprint image is subjected to binarization operation first, makes wear shoes The object that each independent decorative pattern corresponds in bianry image in footprint image；The area of all objects is calculated, and removes face Product obtains effective object less than the object of wear shoes footprint image 0.05%；Calculate the equivalent redius of each effectively object, i.e., with this Object has the radius of circle of the same area, and this radius is to characterize the form parameter that the object corresponds to decorative pattern, and it is all effectively right to take As yardstick σ of the average value as wave filter of equivalent redius.
S1.2. bilateral filtering operation is carried out to the footprint image after adaptive-filtering, represented with equation below：
Wherein, WpIt is weighting function, is defined as follows
IFIt is the footprint image after bilateral filtering, I represents the footprint image after adaptive-filtering, and x represents current in image I The position coordinates of pixel, Ω are current bilateral filtering window centered on x, frIt is the codomain kernel function of smooth luminance difference, gs It is the space kernel function of smooth Spaces difference；
S1.3. quantization modulation：Color space conversion is carried out to the footprint image after bilateral filtering first, turned from rgb space Change to Lab space；Luminance channel L is taken, it is quantified according to footprint pressure face number of plies n；Then Lab mode images are turned again Rgb space is changed to, obtains footprint multilayer pressure mapping picture.
Further, for wear shoes footprint, the method that footprint Morphologic Characteristics are obtained in step S2 is：
S2.1. footprint coordinate system is established：Take the pressure outermost layer in multilayer pressure mapping picture, Zuo Zhang areas and with area The common tangent of inside and outside both sides, if palm area, the inner side most salient point with area are respectively A, B, palm area, the outside most salient point difference with area For C, D, then the angular bisector of two common tangent AB, CD angle is footprint center line, footprint center line and the intersection point with area's lower edge For O, footprint is adjusted to its center line is vertical and tiptoe is upward, then in footprint institute in the planes, using O as origin, with center line It is straight up Y-axis positive direction for Y-axis, level is to the right X-axis positive direction, establishes footprint coordinate system；
S2.2. footprint Morphologic Characteristics are calculated：The most upper limb salient point T of the secondary outer layer pressure facial contour of ecto-entad, it is Barefoot big toe leading edge point, the length that point T and origin O line projects on footprint centerline direction is foot length；
The length for slapping the line AC of the inside and outside both sides in area most salient point is foot breadth；
Length with the line BD of the inside and outside both sides in area most salient point is with width；
Outermost layer footprint pressure face in the part folded by line segment AC, BD, and inside and outside the part two sections of profiles at footprint center Beeline MN in line vertical direction is the wide a of bow；
The third layer pressure face of ecto-entad in mark multilayer pressure mapping picture is taken fully, obtains the Ceng Shangzhang areas pressure area Domain, the lower edge salient point S of the Dian Weizhang area pressure span nearest with origin of coordinates O vertical range on the region outline.
The invention further relates to a kind of device of the sex character analysis based on footprint image, including：
Multilayer pressure face extraction element, for carrying out multilayer pressure face extraction to footprint image；
Footprint Morphologic Characteristics obtain device：For the multilayer pressure face image according to footprint, at least following foots are obtained Mark Morphologic Characteristics：Foot length, foot breadth, the area in each stressor layer face；
Mathematical Models and gender analysis device, for establishing the mathematical modulo between footprint Morphologic Characteristics and sex Type, above-mentioned Morphologic Characteristics are inputted to the mathematical modeling, obtain the proprietary sex character of the footprint.
Beneficial effect：
1. the present invention can automate realization to sex character analysis, without manual intervention, sex character analysis is directly obtained As a result.
Carried out, can had using Exemplary statistical data founding mathematical models 2. sex signature analysis of the present invention is stable, during judgement Effect avoids the influence of people's subjective factor.
3. gender analysis is more accurate, calculates footprint Morphologic Characteristics on pixel level using high-definition picture, keep away Exempt from human error introducing.
Brief description of the drawings
Fig. 1 is barefoot or wears sock print multilayer pressure face and Morphologic Characteristics schematic diagram；
Fig. 2 is wear shoes footprint image；
Fig. 3 is wear shoes footprint multilayer pressure face and Morphologic Characteristics schematic diagram.
Embodiment
Embodiment 1：A kind of method of the sex character analysis based on footprint image, comprises the following steps：
S1. multilayer pressure face extraction is carried out to footprint image；
S1.1. to barefoot or wearing sock print image preprocessing：Barefoot or sock print image will be worn it is filtered, image filter The formula of ripple is as follows：
I=F*G
I (i, j)=ΣmΣnF (i, j) G (i-m, j-n) (7)
Wherein, * represents convolution, and F represents original wear shoes footprint image, and G represents wave filter, and I represents filtered footprint figure Picture, (i, j) represent current pixel position, and m, n represent size of the filter window in x, y direction respectively；
S1.2. pressure face extracts：
S1.2.1. bilateral filtering operation is carried out to pretreated footprint image, can be represented with equation below：
Wherein, WpIt is weighting function, is defined as follows
IFIt is the footprint image after bilateral filtering, I represents filtered footprint image in pre-treatment step, and x represents image I The position coordinates of middle current pixel, Ω are current bilateral filtering window centered on x, frIt is the codomain core of smooth luminance difference Function, gsIt is the space kernel function of smooth Spaces difference；
S1.2.2. quantization modulation：Color space conversion is carried out to the footprint image after bilateral filtering first, from rgb space It is transformed into Lab space；Luminance channel L is taken, it is quantified according to footprint pressure face number of plies n；Then by Lab mode images again Rgb space is transformed into, obtains footprint multilayer pressure mapping picture；
Wherein：Wave filter in step S1.1 is defined as：
Wherein, u, v are coordinate variables, and σ is standard deviation.
S2. according to the multilayer pressure face image of footprint, at least following footprint Morphologic Characteristics are obtained：It is foot length, foot breadth, each The area in stressor layer face；
S2.1. footprint coordinate system is established：Take the pressure outermost layer in multilayer pressure mapping picture, Zuo Zhang areas and with area The common tangent of inside and outside both sides, if palm area, the inner side most salient point with area are respectively A, B, palm area, the outside most salient point difference with area For C, D, then the angular bisector of two common tangent AB, CD angle is footprint center line, footprint center line and the intersection point with area's lower edge For O, footprint is adjusted to its center line is vertical and tiptoe is upward, then in footprint institute in the planes, using O as origin, with center line It is straight up Y-axis positive direction for Y-axis, level is to the right X-axis positive direction, establishes footprint coordinate system；
S2.2. footprint Morphologic Characteristics are calculated：The outermost upper limb salient point T of pressure face, it is barefoot big toe leading edge point, The length that point T and origin O line projects on footprint centerline direction is foot length；
The length for slapping the line AC of the inside and outside both sides in area most salient point is foot breadth；
Length with the line BD of the inside and outside both sides in area most salient point is with width；
Outermost layer footprint pressure face in the part folded by line segment AC, BD, and inside and outside the part two sections of profiles at footprint center Beeline MN in line vertical direction is the wide a of bow；
The secondary outer layer pressure face in mark multilayer pressure mapping picture is taken fully, obtains the Ceng Shangzhang areas pressure span, the area Minimum point of the overseas profile on footprint centerline direction, to slap the lower edge salient point S of area pressure span.
S3. the mathematical modeling established between footprint Morphologic Characteristics and sex, above-mentioned form is inputted to the mathematical modeling Architectural feature, obtain the proprietary sex character of the footprint；Concretely comprise the following steps：
S3.1. the mathematical modeling of sex and foot length is established：Sample x to overall G mahalanobis distance is
Wherein：μ and Σ is respectively overall G average and covariance matrix；X is foot length, and man, woman's foot length are respectively to obey Normal distributionWithOverall G1、G2, μ1、μ2Respectively G1、G2Average,Respectively G1、 G2Variance；
Test footprint foot length is calculated to overall G according to formula (1)1、G2Distance d1、d2,
Using formula (2), the proprietary sex character of footprint is obtained.
That is d1≤d2, test footprint belongs to male, d in terms of foot length2＜ d1, test footprint belongs to women in terms of foot length.
The present embodiment further relates to a kind of device of the sex character analysis based on footprint image, including：
Multilayer pressure face extraction element, for carrying out multilayer pressure face extraction to footprint image；
Footprint Morphologic Characteristics obtain device：For the multilayer pressure face image according to footprint, at least following foots are obtained Mark Morphologic Characteristics：Foot length, foot breadth, the area in each stressor layer face；
Mathematical Models and gender analysis device, for establishing the mathematical modulo between footprint Morphologic Characteristics and sex Type, above-mentioned Morphologic Characteristics are inputted to the mathematical modeling, obtain the proprietary sex character of the footprint.
Embodiment 2：Identical with the technical scheme of embodiment 1, its difference is that step S3.1 is replaced with：
Establish the mathematical modeling of sex and the length-width ratio of footprint：
The length-width ratio r=foot lengths of footprint/foot breadth (3)
Man, woman's footprint length-width ratio are respectively Normal DistributionWithOverall G3、G4, its Middle μ3、μ4Respectively G3、G4Average,Respectively G3、G4Variance；Test footprint length is calculated in reference formula (1) It is wide than with overall G3、G4Mahalanobis distance d3、d4；
Calculated using formula (4) and obtain the proprietary sex character of footprint.
That is d3≤d4, test footprint belongs to male, d in terms of the length-width ratio of footprint4＜ d3, in terms of the length-width ratio of footprint Test footprint belongs to women.
Embodiment 3：Identical with the technical scheme of embodiment 1, its difference is that step S3.1 is replaced with：
Establish the mathematical modeling of sex interlayer pressure change rate adjacent with multilayer pressure face：Remember Si, i=1,2 ..., n, it is The area of i-th layer of footprint pressure face, the area relative change rate of the footprint pressure face of adjacent interlayer are
ΔSi=(Si+1-Si)/Si, i=1,2 ..., n-1 (5)
Its coefficient of variation is
Cv=σ/μ (6)
Wherein, μ, σ are respectively (Δ Si) average and variance；
In general, the plantar nervous arch of women is uniform, therefore the relative change of corresponding adjacent interlayer pressure face area Rate is more stable, i.e., its coefficient of variation is smaller, given threshold value T=0.3, and coefficient of variation cv is more than threshold value T, then judges the footprint All artificial males, otherwise judge all artificial women of the footprint.
Embodiment 4：Identical with the technical scheme of embodiment 1, its difference is that step S3.1 is replaced with：
Using the S3.1 of each step of three technical schemes in embodiment 1-3,3 gender attributes are obtained, man is represented with 0 Property, 1 represents women, calculates the gender attribute sum s of above-mentioned 3 kinds of mathematical modelings, if s≤1, judges all artificial men of the footprint Property；Otherwise, all artificial women of the footprint are judged.
Embodiment 5：A kind of method of the sex character analysis based on footprint image, including following step：
S1. multilayer pressure face extraction is carried out to footprint image；
S1.1. wear shoes footprint image is pre-processed：Shoe sole print in wear shoes footprint image is removed using image filtering operations Interference, the yardstick of wave filter adaptively determines according to the size of decorative pattern；The formula of image filtering is as follows：
I=F*G
I (i, j)=ΣmΣnF (i, j) G (i-m, j-n) (10)
Wherein, * represents convolution, and F represents original wear shoes footprint image, and G represents wave filter, and I represents filtered footprint figure Picture, (i, j) represent current pixel position, and m, n represent size of the filter window in x, y direction respectively；
Wave filter is defined as：
Wherein, u, v are coordinate variables, and σ is standard deviation；
It is adaptive should determine that filter scales method be：Wear shoes footprint image is subjected to binarization operation first, makes wear shoes The object that each independent decorative pattern corresponds in bianry image in footprint image；The area of all objects is calculated, and removes face Product obtains effective object less than the object of wear shoes footprint image 0.05%；Calculate the equivalent redius of each effectively object, i.e., with this Object has the radius of circle of the same area, and this radius is to characterize the form parameter that the object corresponds to decorative pattern, and it is all effectively right to take As yardstick σ of the average value as wave filter of equivalent redius.
S1.2. bilateral filtering operation is carried out to the footprint image after adaptive-filtering, represented with equation below：
Wherein, WpIt is weighting function, is defined as follows
IFIt is the footprint image after bilateral filtering, I represents the footprint image after adaptive-filtering, and x represents current in image I The position coordinates of pixel, Ω are current bilateral filtering window centered on x, frIt is the codomain kernel function of smooth luminance difference, gs It is the space kernel function of smooth Spaces difference；
S1.3. quantization modulation：Color space conversion is carried out to the footprint image after bilateral filtering first, turned from rgb space Change to Lab space；Luminance channel L is taken, it is quantified according to footprint pressure face number of plies n, in the present embodiment, the pressure face number of plies For 8 layers, i.e. n=8, ecto-entad is followed successively by first layer to the 8th layer；Then by Lab mode images reconvert to rgb space, obtain To footprint multilayer pressure mapping picture.
S2. according to the multilayer pressure face image of footprint, at least following footprint Morphologic Characteristics are obtained：It is foot length, foot breadth, each The area in stressor layer face；
S2.1. footprint coordinate system is established：Take the pressure outermost layer in multilayer pressure mapping picture, Zuo Zhang areas and with area The common tangent of inside and outside both sides, if palm area, the inner side most salient point with area are respectively A, B, palm area, the outside most salient point difference with area For C, D, then the angular bisector of two common tangent AB, CD angle is footprint center line, footprint center line and the intersection point with area's lower edge For O, footprint is adjusted to its center line is vertical and tiptoe is upward, then in footprint institute in the planes, using O as origin, with center line It is straight up Y-axis positive direction for Y-axis, level is to the right X-axis positive direction, establishes footprint coordinate system；
S2.2. footprint Morphologic Characteristics are calculated：The most upper limb salient point T of the secondary outer layer pressure facial contour of ecto-entad, it is Barefoot big toe leading edge point, the length that point T and origin O line projects on footprint centerline direction is foot length；
The length for slapping the line AC of the inside and outside both sides in area most salient point is foot breadth；
Length with the line BD of the inside and outside both sides in area most salient point is with width；
Outermost layer footprint pressure face in the part folded by line segment AC, BD, and inside and outside the part two sections of profiles at footprint center Beeline MN in line vertical direction is the wide a of bow；
The third layer pressure face of ecto-entad in mark multilayer pressure mapping picture is taken fully, obtains the Ceng Shangzhang areas pressure area Domain, the lower edge salient point S of the Dian Weizhang area pressure span nearest with origin of coordinates O vertical range on the region outline.
S3. the mathematical modeling established between footprint Morphologic Characteristics and sex, above-mentioned form is inputted to the mathematical modeling Architectural feature, obtain the proprietary sex character of the footprint；Concretely comprise the following steps：
S3.1. the mathematical modeling of sex and foot length is established：Sample x to overall G mahalanobis distance is
Wherein：μ and Σ is respectively overall G average and covariance matrix；X is foot length, and man, woman's foot length are respectively to obey Normal distributionWithOverall G1、G2, μ1、μ2Respectively G1、G2Average,Respectively G1、 G2Variance；
Test footprint foot length is calculated to overall G according to formula (1)1、G2Distance d1、d2,
Using formula (2), the proprietary sex character of footprint is obtained.
That is d1≤d2, test footprint belongs to male, d in terms of foot length2＜ d1, test footprint belongs to women in terms of foot length.
The present embodiment further relates to a kind of device of the sex character analysis based on footprint image, including：
Multilayer pressure face extraction element, for carrying out multilayer pressure face extraction to footprint image；
Footprint Morphologic Characteristics obtain device：For the multilayer pressure face image according to footprint, at least following foots are obtained Mark Morphologic Characteristics：Foot length, foot breadth, the area in each stressor layer face；
Mathematical Models and gender analysis device, for establishing the mathematical modulo between footprint Morphologic Characteristics and sex Type, above-mentioned Morphologic Characteristics are inputted to the mathematical modeling, obtain the proprietary sex character of the footprint.
Embodiment 6：Identical with the technical scheme of embodiment 5, its difference is that step S3.1 is replaced with：
Establish the mathematical modeling of sex and the length-width ratio of footprint：
The length-width ratio r=foot lengths of footprint/foot breadth (3)
Man, woman's footprint length-width ratio are respectively Normal DistributionWithOverall G3、G4, its Middle μ3、μ4Respectively G3、G4Average,Respectively G3、G4Variance；Test footprint length is calculated in reference formula (1) It is wide than with overall G3、G4Mahalanobis distance d3、d4；
Calculated using formula (4) and obtain the proprietary sex character of footprint.
That is d3≤d4, test footprint belongs to male, d in terms of the length-width ratio of footprint4＜ d3, in terms of the length-width ratio of footprint Test footprint belongs to women.
Embodiment 7：Identical with the technical scheme of embodiment 5, its difference is that step S3.1 is replaced with：
Establish the mathematical modeling of sex interlayer pressure change rate adjacent with multilayer pressure face：Remember Si, i=1,2 ..., n, it is The area of i-th layer of footprint pressure face, the area relative change rate of the footprint pressure face of adjacent interlayer are
ΔSi=(Si+1-Si)/Si, i=1,2 ..., n-1 (5)
Its coefficient of variation is
Cv=σ/μ (6)
Wherein, μ, σ are respectively { Δ SiAverage and variance；
In general, the plantar nervous arch of women is uniform, therefore the relative change of corresponding adjacent interlayer pressure face area Rate is more stable, i.e., its coefficient of variation is smaller, given threshold value T=0.3, and coefficient of variation cv is more than threshold value T, then judges the footprint All artificial males, otherwise judge all artificial women of the footprint.
Embodiment 8：Identical with the technical scheme of embodiment 5, its difference is that step S3.1 is replaced with：
Using the S3.1 of each step of three technical schemes in embodiment 5-7,3 gender attributes are obtained, man is represented with 0 Property, 1 represents women, calculates the gender attribute sum s of above-mentioned 3 kinds of mathematical modelings, if s≤1, judges all artificial men of the footprint Property；Otherwise, all artificial women of the footprint are judged.

Claims (9)

  1. A kind of 1. method of the sex character analysis based on footprint image, it is characterised in that comprise the following steps：
    S1. multilayer pressure face extraction is carried out to footprint image；
    S2. according to the multilayer pressure face image of footprint, at least following footprint Morphologic Characteristics are obtained：Foot length, foot breadth, each lamination The area in power face；
    S3. the mathematical modeling established between footprint Morphologic Characteristics and sex, above-mentioned morphosis is inputted to the mathematical modeling Feature, obtain the proprietary sex character of the footprint；Concretely comprise the following steps：
    S3.1. the mathematical modeling of sex and foot length is established：Sample x to overall G mahalanobis distance is
    <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mo>&amp;Sigma;</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：μ and ∑ are respectively overall G average and covariance matrix；X is foot length, and man, woman's foot length are respectively to obey normal state DistributionWithOverall G1、G2, μ1、μ2Respectively G1、G2Average,Respectively G1、G2's Variance；
    Test footprint foot length is calculated to overall G according to formula (1)1、G2Distance d1、d2,
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>G</mi> <mn>1</mn> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>&amp;le;</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>G</mi> <mn>2</mn> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>&lt;</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Using formula (2), the proprietary sex character of footprint is obtained.
  2. A kind of 2. method of sex character analysis based on footprint image as claimed in claim 1, it is characterised in that step 3.1 replace with：
    Establish the mathematical modeling of sex and the length-width ratio of footprint：
    The length-width ratio r=foot lengths of footprint/foot breadth (3)
    Man, woman's footprint length-width ratio are respectively Normal DistributionWithOverall G3、G4, wherein μ3、 μ4Respectively G3、G4Average,Respectively G3、G4Variance；Test footprint length-width ratio is calculated in reference formula (1) With overall G3、G4Mahalanobis distance d3、d4；
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>r</mi> <mo>&amp;Element;</mo> <msub> <mi>G</mi> <mn>3</mn> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mn>3</mn> </msub> <mo>&amp;le;</mo> <msub> <mi>d</mi> <mn>4</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>r</mi> <mo>&amp;Element;</mo> <msub> <mi>G</mi> <mn>4</mn> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mn>4</mn> </msub> <mo>&lt;</mo> <msub> <mi>d</mi> <mn>3</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    Calculated using formula (4) and obtain the proprietary sex character of footprint.
  3. A kind of 3. method of sex character analysis based on footprint image as claimed in claim 1, it is characterised in that step S3.1 is replaced with：
    Establish the mathematical modeling of sex interlayer pressure change rate adjacent with multilayer pressure face：Remember Si, i=1,2 ..., n, it is i-th layer Footprint pressure face area, the area relative change rate of the footprint pressure face of adjacent interlayer is
    ΔSi=(Si+1-Si)/Si, i=1,2 ..., n-1 (5)
    Its coefficient of variation is
    Cv=σ/μ (6)
    Wherein, μ, σ are respectively { Δ SiAverage and variance；
    Given threshold value T, coefficient of variation cv are more than threshold value T, then judge all artificial males of the footprint, otherwise judge that the footprint owns Artificial women.
  4. A kind of 4. method of sex character analysis based on footprint image as claimed in claim 1, it is characterised in that step S3.1 is replaced with：
    Usage right requires the S3.1 of each step in 1-3, obtains 3 gender attributes, male is represented with 0, and 1 represents women, calculates The gender attribute sum s of above-mentioned 3 kinds of mathematical modelings, if s≤1, judge all artificial males of the footprint；Otherwise, the foot is judged All artificial women of mark.
  5. A kind of 5. method of sex character analysis based on footprint image as described in claim 1 or 4, it is characterised in that step It is the step of the extraction of multilayer pressure face in rapid S1：
    S1.1. to barefoot or wearing sock print image preprocessing：Barefoot or sock print image will be worn it is filtered, the image filtering Formula is as follows：
    I=F*G
    I (i, j)=∑m∑nF (i, j) G (i-m, j-n) (7)
    Wherein, * represents convolution, and F represents original wear shoes footprint image, and G represents wave filter, and I represents filtered footprint image, (i, j) represents current pixel position, and m, n represent size of the filter window in x, y direction respectively；
    S1.2. pressure face extracts：
    S1.2.1. bilateral filtering operation is carried out to pretreated footprint image, can be represented with equation below：
    <mrow> <msup> <mi>I</mi> <mi>F</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>W</mi> <mi>p</mi> </msub> </mfrac> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;Element;</mo> <mi>&amp;Omega;</mi> </mrow> </msub> <mi>I</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mi>I</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>I</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>x</mi> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, WpIt is weighting function, is defined as follows
    <mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;Element;</mo> <mi>&amp;Omega;</mi> </mrow> </munder> <msub> <mi>f</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mi>I</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>I</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>x</mi> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> </mrow>
    IFThe footprint image after bilateral filtering, I represents filtered footprint image in pre-treatment step, x represent in image I when The position coordinates of preceding pixel, Ω are current bilateral filtering window centered on x, frIt is the codomain core letter of smooth luminance difference Number, gsIt is the space kernel function of smooth Spaces difference；
    S1.2.2. quantization modulation：Color space conversion is carried out to the footprint image after bilateral filtering first, changed from rgb space To Lab space；Luminance channel L is taken, it is quantified according to footprint pressure face number of plies n；Then by Lab mode image reconverts To rgb space, footprint multilayer pressure mapping picture is obtained；
    Wherein：Wave filter in step S1.1 is defined as：
    <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msup> <mi>&amp;pi;&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>v</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, u, v are coordinate variables, and σ is standard deviation.
  6. A kind of 6. method of sex character analysis based on footprint image as claimed in claim 5, it is characterised in that step S2 It is middle obtain footprint Morphologic Characteristics method be：
    S2.1. footprint coordinate system is established：Take the pressure outermost layer in multilayer pressure mapping picture, Zuo Zhang areas and with area, The common tangent of outer both sides, if the palm area, the inner side most salient point with area are respectively A, B, palm area, the outside most salient point with area be respectively C, D, then the angular bisector of two common tangent AB, CD angle is footprint center line, and footprint center line is O with the intersection point with area's lower edge, Footprint is adjusted to its center line is vertical and tiptoe is upward, then in footprint institute in the planes, using O as origin, using center line as Y Axle, it is straight up Y-axis positive direction, level is to the right X-axis positive direction, establishes footprint coordinate system；
    S2.2. footprint Morphologic Characteristics are calculated：The outermost upper limb salient point T of pressure face, is barefoot big toe leading edge point, point T It is foot length with the length that origin O line projects on footprint centerline direction；
    The length for slapping the line AC of the inside and outside both sides in area most salient point is foot breadth；
    Length with the line BD of the inside and outside both sides in area most salient point is with width；
    Outermost layer footprint pressure face is in the part folded by line segment AC, BD, and two sections of profiles hang down in footprint center line inside and outside the part The upward beeline MN of Nogata is the wide a of bow；
    The secondary outer layer pressure face in mark multilayer pressure mapping picture is taken fully, obtains the Ceng Shangzhang areas pressure span, outside the region Minimum point of the profile on footprint centerline direction, to slap the lower edge salient point S of area pressure span.
  7. A kind of 7. method of sex character analysis based on footprint image as described in claim 1 or 4, it is characterised in that step It is the step of the extraction of multilayer pressure face in rapid S1：
    S1.1. wear shoes footprint image is pre-processed：The dry of shoe sole print in wear shoes footprint image is removed using image filtering operations Disturb, the yardstick of wave filter adaptively determines according to the size of decorative pattern；In step S1, the formula of image filtering is as follows：
    I=F*G
    I (i, j)=∑m∑nF (i, j) G (i-m, j-n) (10)
    Wherein, * represents convolution, and F represents original wear shoes footprint image, and G represents wave filter, and I represents filtered footprint image, (i, j) represents current pixel position, and m, n represent size of the filter window in x, y direction respectively；
    Wave filter is defined as：
    <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msup> <mi>&amp;pi;&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>v</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, u, v are coordinate variables, and σ is standard deviation；
    It is adaptive should determine that filter scales method be：Wear shoes footprint image is subjected to binarization operation first, makes wear shoes footprint The object that each independent decorative pattern corresponds in bianry image in image；The area of all objects is calculated, and it is small to remove area In the object of wear shoes footprint image 0.05%, effective object is obtained；Calculate the equivalent redius of each effectively object, i.e., with the object Radius with circle of the same area, this radius are to characterize the form parameter that the object corresponds to decorative pattern, take all effectively objects etc. Imitate yardstick σ of the average value of radius as wave filter；
    S1.2. bilateral filtering operation is carried out to the footprint image after adaptive-filtering, represented with equation below：
    <mrow> <msup> <mi>I</mi> <mi>F</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>W</mi> <mi>p</mi> </msub> </mfrac> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;Element;</mo> <mi>&amp;Omega;</mi> </mrow> </msub> <mi>I</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mi>I</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>I</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>x</mi> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, WpIt is weighting function, is defined as follows
    <mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;Element;</mo> <mi>&amp;Omega;</mi> </mrow> </munder> <msub> <mi>f</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mi>I</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>I</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>x</mi> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> </mrow>
    IFIt is the footprint image after bilateral filtering, I represents the footprint image after adaptive-filtering, and x represents current pixel in image I Position coordinates, Ω is current bilateral filtering window centered on x, frIt is the codomain kernel function of smooth luminance difference, gsIt is flat The space kernel function of sliding spatial diversity；
    S1.3. quantization modulation：Color space conversion is carried out to the footprint image after bilateral filtering first, is transformed into from rgb space Lab space；Luminance channel L is taken, it is quantified according to footprint pressure face number of plies n；Then Lab mode image reconverts are arrived Rgb space, obtain footprint multilayer pressure mapping picture.
  8. A kind of 8. method of sex character analysis based on footprint image as claimed in claim 7, it is characterised in that：Step S2 It is middle obtain footprint Morphologic Characteristics method be：
    S2.1. footprint coordinate system is established：Take the pressure outermost layer in multilayer pressure mapping picture, Zuo Zhang areas and with area, The common tangent of outer both sides, if the palm area, the inner side most salient point with area are respectively A, B, palm area, the outside most salient point with area be respectively C, D, then the angular bisector of two common tangent AB, CD angle is footprint center line, and footprint center line is O with the intersection point with area's lower edge, Footprint is adjusted to its center line is vertical and tiptoe is upward, then in footprint institute in the planes, using O as origin, using center line as Y Axle, it is straight up Y-axis positive direction, level is to the right X-axis positive direction, establishes footprint coordinate system；
    S2.2. footprint Morphologic Characteristics are calculated：The most upper limb salient point T of the secondary outer layer pressure facial contour of ecto-entad, is barefoot Big toe leading edge point, the length that point T and origin O line project on footprint centerline direction is foot length；
    The length for slapping the line AC of the inside and outside both sides in area most salient point is foot breadth；
    Length with the line BD of the inside and outside both sides in area most salient point is with width；
    Outermost layer footprint pressure face is in the part folded by line segment AC, BD, and two sections of profiles hang down in footprint center line inside and outside the part The upward beeline MN of Nogata is the wide a of bow；
    The third layer pressure face of ecto-entad in mark multilayer pressure mapping picture is taken fully, obtains the Ceng Shangzhang areas pressure span, The lower edge salient point S of the Dian Weizhang area pressure span nearest with origin of coordinates O vertical range on the region outline.
  9. A kind of 9. device of the sex character analysis based on footprint image, it is characterised in that including：
    Multilayer pressure face extraction element, for carrying out multilayer pressure face extraction to footprint image；
    Footprint Morphologic Characteristics obtain device：For the multilayer pressure face image according to footprint, at least following footprint shapes are obtained State architectural feature：Foot length, foot breadth, the area in each stressor layer face；
    Mathematical Models and gender analysis device, for establishing the mathematical modeling between footprint Morphologic Characteristics and sex, Above-mentioned Morphologic Characteristics are inputted to the mathematical modeling, obtain the proprietary sex character of the footprint；
    Mathematical Models obtain the proprietary sex character of the footprint with gender analysis device based on following manner：
    S1. multilayer pressure face extraction is carried out to footprint image；
    S2. according to the multilayer pressure face image of footprint, at least following footprint Morphologic Characteristics are obtained：Foot length, foot breadth, each lamination The area in power face；
    S3. the mathematical modeling established between footprint Morphologic Characteristics and sex, above-mentioned morphosis is inputted to the mathematical modeling Feature, obtain the proprietary sex character of the footprint；Concretely comprise the following steps：
    S3.1. the mathematical modeling of sex and foot length is established：Sample x to overall G mahalanobis distance is
    <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mo>&amp;Sigma;</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：μ and ∑ are respectively overall G average and covariance matrix；X is foot length, and man, woman's foot length are respectively to obey normal state DistributionWithOverall G1、G2, μ1、μ2Respectively G1、G2Average,Respectively G1、G2's Variance；
    Test footprint foot length is calculated to overall G according to formula (1)1、G2Distance d1、d2,
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>G</mi> <mn>1</mn> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>&amp;le;</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>G</mi> <mn>2</mn> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>&lt;</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Using formula (2), the proprietary sex character of footprint is obtained.
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