CN103745084B - Chinese medicine tongue color sensation based on psychophysical testing knows quantization method - Google Patents

Chinese medicine tongue color sensation based on psychophysical testing knows quantization method Download PDF

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CN103745084B
CN103745084B CN201310689336.9A CN201310689336A CN103745084B CN 103745084 B CN103745084 B CN 103745084B CN 201310689336 A CN201310689336 A CN 201310689336A CN 103745084 B CN103745084 B CN 103745084B
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tongue
colour
component
psychological response
amount
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CN103745084A (en
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蔡轶珩
郭松
张琳琳
张新峰
林沙沙
王立娜
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Beijing University of Technology
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Abstract

Chinese medicine tongue color sensation based on psychophysical testing knows that quantization method belongs to the research field that objectifies of tcm inspection.In colour of the tongue gamut range, take out part representational colour of the tongue color block, perceptually stimulate value.With the description rule of colour of the tongue type in Evolution of Tongue Inspection of TCM, instruct foundation as psychological response evaluation, carry out psychophysical testing, set up psychological response interval scale, determine colour of the tongue psychological response amount.By building the numerical relationship model between colour of the tongue magnitude of physical quantity and psychological response value, obtain the psychological response value meeting traditional Chinese medical science colour of the tongue cognitive law that colour of the tongue physical quantity is corresponding.In modeling process, it is first determined one-dimensional physical quantity and the functional relationship of perception amount, build the function model between comprehensive physical amount and perception amount on this basis.The feature of this invention aims at the colour of the tongue one-dimensional perception quantization meeting Evolution of Tongue Inspection of TCM description custom, reaches really to combine the colour of the tongue quantitative description purpose of the traditional Chinese medical science.

Description

Chinese medicine tongue color sensation based on psychophysical testing knows quantization method
Technical field
The invention belongs to the research field that objectifies of tcm inspection, particularly to tongue color quantizing field in tcm inspection, Quantify for realizing changing with disease and meeting the colour of the tongue of traditional Chinese medical science cognitive law.
Background technology
Evolution of Tongue Inspection of TCM is by observing picture of the tongue change understanding human body physiological function and the examination method of pathological change, in the traditional Chinese medical science Clinical diagnosis plays an important role.Traditional inspection of the tongue method depends on visualization and language description, the shortage amount of the traditional Chinese medical science Change description indexes and objective record means, describe to Evolution of Tongue Inspection of TCM and classification aspect brings difficulty.Along with modern science and technology Means development in terms of Evolution of Tongue Inspection of TCM, tongue reconstruction, standardized research have become as the development side that Evolution of Tongue Inspection of TCM is important To.
In the treatment research that colour of the tongue objectifies, commonly used Digital Image Processing and mode identification technology carry out colour of the tongue and divide Analysis.In such a mode, each tongue color all at the multiple representation in components of certain color space, and then must provide classification genus Property, still lack a kind of one-dimensional quantification manner changed with disease and meet traditional Chinese medical science cognition custom, traditional Chinese medical science colour of the tongue is quantitatively spent Amount.Hence set up colour of the tongue change one-dimensional quantificational description means, and determine that the relation that color space component and colour of the tongue one-dimensional quantify has Objective necessity.
Summary of the invention
In the traditional Chinese medical science, the quantization in rule dimension is described to realize colour of the tongue, need to by human eye to colour of the tongue under this Changing Pattern Psychological response quantify, and psychophysics is exactly to carry out, for human perception, a subject quantifying.To color this Subjective feeling carries out the subject colorimetry measured, and is also by the vision matching experiment development of observer in psychophysics And come.Owing to the mankind have subjectivity and diversity to the perception of physical stimulation, process perception quantified is by sensation, the heart The impact of the many factors such as reason, therefore often through the sensory data of the multiple normal subjectses of statistics, obtains having certain public affairs The quantificational description specification of degree of recognizing.
The present invention have employed visual psychology physics method targetedly, solves colour of the tongue and describes in rule dimension in the traditional Chinese medical science Quantification problem.Owing to the perception of traditional Chinese medical science colour of the tongue quantifies to need each several part in quantized directions to have equal unit, therefore select Select interval scale method and realize colour of the tongue quantization, obtain colour of the tongue physical quantity and Chinese medicine tongue color psychological response amount eventually through mathematical modeling Relation.
Concrete scheme of the present invention design is as follows: in colour of the tongue gamut range, takes out part representational colour of the tongue color block, Perceptually stimulate value.With the description rule of colour of the tongue type in Evolution of Tongue Inspection of TCM, instruct foundation as psychological response evaluation, carry out Psychophysical testing, sets up psychological response interval scale, determines colour of the tongue psychological response amount.By building colour of the tongue magnitude of physical quantity and the heart Numerical relationship model between reason perception value, obtains the psychology sense meeting traditional Chinese medical science colour of the tongue cognitive law that colour of the tongue physical quantity is corresponding Know value.In modeling process, it is first determined one-dimensional physical quantity and the functional relationship of perception amount, build synthesis on this basis Function model between reason amount and perception amount.The feature of this invention aims at the colour of the tongue one-dimensional meeting Evolution of Tongue Inspection of TCM description custom Perception quantifies, and reaches really to combine the colour of the tongue quantitative description purpose of the traditional Chinese medical science.In turn include the following steps:
1. the determination in colour of the tongue territory:
(1), gather all kinds of Chinese medicine tongue colour standard image pattern (with standard sRGB spatial description), need to comprise light red, light In vain, all kinds of use-case of green grass or young crops red, deep red, purple, totally 5 class;Every class use-case needs to comprise the example of more than 100 examples, and by more than three traditional Chinese medical science Doctor provides affiliated type and demarcates.
(2), extract the color magnitude of physical quantity of body of the tongue part in all image patterns, and be converted into and human eye perception phase Corresponding HSI color space;According to all colour of the tongues in H, S, the distribution of I component, extend 1% respectively to both sides, determine tongue Colour gamut interval on H, S, I component.
2. the relation of colour of the tongue magnitude of physical quantity simple component and psychological response amount determines:
Owing to colour of the tongue magnitude of physical quantity generally comprises 3 components, it is also that each component produces with the relation of psychological response amount The result of psychological response comprehensive function, first determines colour of the tongue magnitude of physical quantity simple component and the relation of psychological response amount, in order to The most more effectively build the relational model of colour of the tongue multidimensional magnitude of physical quantity and psychological response amount.Concrete grammar is: fixing Two components in H, S, I, utilize psychophysical testing, study another component variation and the relation of psychological response amount.
(1), in the range of colour of the tongue under simple component situation of change, the determination of physical stimulation amount: be distributed model in fixed colour of the tongue In enclosing, carry out uniform segmentation sampling, such as, in the range of H, S, I component, carry out point samplings such as 12 respectively.Choose two of which to divide The central point of weight range, as component fixed value, makes another component for different sampling point value, the most only changes single component group respectively Close out different colours block, obtain the colour of the tongue quantity of stimulus of simple component change.Be converted to show by the colour of the tongue quantity of stimulus HSI value obtained SRGB value, show over the display with the form of image color lump, allow observer observe judgement, carry out psychophysical testing.
(2), psychophysical testing, set up interval scale: according to the description rule of colour of the tongue type in Diagnostics of Chinese Medicine, by tongue Color as the Appreciation gist of psychological response amount, instructs observer to compare according to the gradual change order of deep red, purple green grass or young crops light white, light red, red Relatively judge.
First pass through the method such as paired comparison or hierarchical arrangement, by multiple observers the colour of the tongue that simple component changes stimulated into Row judges sequence, sets up the perception order of the colour of the tongue quantity of stimulus of simple component change.Perception serial number is rating, by multiple Observer is in addition average to the same grade stimulating evaluation, thus obtains the respective average rank of each stimulation.Calculating normal state is divided Plant the probit that each average rank is corresponding, calculate Z score further according to POZ conversion table, i.e. can get the psychological response of each stimulation The interval scale of amount composition.
(3), by mathematical modeling, obtaining simple component change colour of the tongue stimulates and the functional relationship of psychological response amount change.
Colour of the tongue stimulates each simple component change (H, S, I) as independent variable, and psychological response amount, as dependent variable, uses minimum Square law carries out curve fitting, and determines the matched curve functional relationship between each component variation and psychological response amount.
3. the relation of colour of the tongue magnitude of physical quantity and psychological response amount determines:
(1), in the range of colour of the tongue under the comprehensive situation of change of multi-components, the determination of physical stimulation amount: divide in fixed colour of the tongue In the range of cloth, carry out uniform segmentation sampling.Three-component is respectively combined out different colours block, and the colour of the tongue comprehensively changed stimulates Amount.The colour of the tongue quantity of stimulus HSI value obtained is converted to displayable sRGB value, shows at display with the form of image color lump On, allow observer observe judgement, carry out psychophysical testing.
(2), psychophysical testing, set up interval scale: concrete grammar step and " colour of the tongue magnitude of physical quantity simple component and psychology The relation of perception amount determines " in (2) identical.
(3), by mathematical modeling, the functional relationship of colour of the tongue magnitude of physical quantity and psychological response amount is obtained.
Colour of the tongue stimulates physical quantity (H, S, I) as independent variable, and psychological response amount, as dependent variable, uses polynomial regression Both functional relationships set up by model.Wherein, the number of times of each component of physical quantity stimulates and psychology sense according to simple component change colour of the tongue The functional relationship of the amount of knowing change determines.Such as, if the fitting function of H component and psychological response amount is quadratic function, then multinomial In model, H component uses quadratic term.Each component cross term, the selection of low order item, then carry out preferably according to regression accuracy, the most really Determine form and the parameter of polynomial regression model.
(4), Chinese medicine tongue color sensation knows quantization.
Extract in tongue image the colour of the tongue rgb value needing to quantify, and be converted into HSI value, substitute into colour of the tongue magnitude of physical quantity and The polynomial regression model of psychological response amount, i.e. can obtain the perception quantized result of this colour of the tongue.
Beneficial effect
This method can be by the description rule of Diagnostics of Chinese Medicine colour of the tongue type, it is achieved in inspection of the tongue, the one-dimensional perception of colour of the tongue quantifies, I.e. being obtained an one-dimensional value by colour of the tongue pixel value in tongue image, the size of its quantity represents that colour of the tongue is in inspection of the tongue gradual change law Degree.First this method determines traditional Chinese medical science colour of the tongue gamut range according to normal tongue and disease tongue sample, in this range according to human eye Visually-perceptible space uniform is sampled, and obtains colour of the tongue physical stimulation amount;According to traditional Chinese medical science hierarchical categories order, observer colour of the tongue is stung Swashing sequence, be calculated interval scale, the most each colour of the tongue stimulates corresponding psychological response value;By mathematical modeling, obtain colour of the tongue Magnitude of physical quantity and the functional relationship of psychological response amount, thus to arbitrary colour of the tongue, can obtain in the traditional Chinese medical science cognition dimension of its correspondence Psychological response amount.
In Traditional Chinese Medicine inspection of the tongue, the description to colour of the tongue is qualitatively, i.e. describes traditional Chinese medical science colour of the tongue classification belonging to it with word.One As comprise green grass or young crops light white, light red, red, deep red, purple.The ambiguity described due to word and subjective differences, to traditional Chinese medical science analysis of cases, data Excavate, therapeutic evaluation brings inconvenience, hinders the further development of Diagnostics of Chinese Medicine.In recent years, standard picture number is used According to or chroma data colour of the tongue is described, become colour of the tongue describe walk vectorization beginning.Although these describe means and use numerical quantities Change form, and there is relatively uniform specification, but the cognitive law changed colour of the tongue with the traditional Chinese medical science cannot well merge.In three-dimensional The most high-dimensional image or chroma data describe space, and a color is described by multiple numerical value.Due to combining of multiple passages Group photo rings, and is difficult to judge the attribute change (the reddest, the lightest) that colour of the tongue data variation is brought intuitively, and attribute change degree is the most more Being difficult to measure, this is the most disadvantageous to the collection of traditional Chinese medical science diagnostic message with analysis.In tcm diagnosis analysis of cases is studied, right Statistical analysis in colour of the tongue feature also tends to, because the restriction of multidimensional quantificational description, to carry out statistical from each dimension Analysis, and this statistics tends not to obtain real valuable result.The colour of the tongue scope of statistics of such as certain disease be R ∈ [*, *], G ∈ [*, *], B ∈ [*, *], and actually in this scope, the colour of the tongue of some combined colors not this disease.
Use this method, then can describe rule for traditional Chinese medical science colour of the tongue, blue or green order foundation amount the most light white, light red, red, deep red, purple Value number axis.As shown in accompanying drawing 5,6, arbitrary colour of the tongue can draw the value on this number axis by the functional relationship set up.By This, can with one-dimensional value simple, intuitive describe colour of the tongue attribute and deviate the degree of certain reference colours.And at colour of the tongue diagnosis letter In the statistical analysis of breath, it is also possible to scope on this one-dimensional value number axis, value probability of occurrence etc. represent.This description hands Section, combines quantificational description with traditional Chinese medical science cognitive law, breaches and uses multidimensional color space to describe the limitation of colour of the tongue at present, Achieve Chinese medicine tongue color quantization means truly.There is provided quantitative foundation for disease degree, development trend, be conducive to Promotion tongue reconstruction is studied.
Accompanying drawing explanation
Fig. 1: Chinese medicine tongue color sensation knows quantization method flow process
Fig. 2: colour of the tongue HSI distribution of color rectangular histogram example
Fig. 3: POZ conversion method flow process
Fig. 4: H component variation colour of the tongue stimulates and psychological response magnitude relation fits curve example
Fig. 5: Chinese medicine tongue color sensation knows quantized result data instance
Fig. 6: Chinese medicine tongue color sensation knows quantized result color lump example
Detailed description of the invention
The psychophysical testing related in this method is all to carry out under dark room conditions, by one through color correction Light-emitting diode display display stimulates color lump, and the observer to more than 10 with normal color vision carries out psychophysical testing.It is embodied as Process is as follows:
1. the determination in colour of the tongue territory:
(1), all kinds of Chinese medicine tongue colour standard image is gathered.Need to comprise all kinds of use-case of green grass or young crops light red, light white, red, deep red, purple, totally 5 Class;Every class use-case needs to comprise the example of more than 100 examples, and is provided the demarcation of affiliated type by more than three traditional Chinese medical doctors.Image Collection need to use white balance and exposure accurately to arrange, and with the color space determined, such as sRGB space, exports view data, protects The standardization of card view data.
(2), extract the color magnitude of physical quantity of body of the tongue part in all image patterns, and be converted into and human eye perception phase Corresponding HSI color space;Add up the HIS value of all colour of the tongues, determine colour of the tongue in H, S, the distribution of I component, respectively to two Side extension 1%, determines interval on H, S, I component, the colour of the tongue territory.Accompanying drawing 2, for colour of the tongue distribution Nogata on H, S, I component Figure.
2. the relation of colour of the tongue magnitude of physical quantity simple component and psychological response amount determines:
Two components in fixing H, S, I, utilize psychophysical testing, study another component variation and psychological response amount Relation.
(1), in the range of colour of the tongue under simple component situation of change, the determination of physical stimulation amount: be distributed model in fixed colour of the tongue In enclosing, carry out uniform segmentation sampling, such as, in the range of H, S, I component, carry out point samplings such as 12 respectively.
Fixing S, I component, H component variation produces color stimulus: take S, I component colour of the tongue scope central point as fixing Value, in H components range, 12 grades divide sampling, obtain changing one group of color stimulus amount of H component;
Equally, fixing I, H component, S component variation produces color stimulus;Fixing H, S component, I component change produces color Stimulate.
The colour of the tongue quantity of stimulus HSI value obtained is converted to displayable sRGB value, shows aobvious with the form of image color lump Show and (typically show under neutral ash background) on device, allow observer carry out observing judgement, carry out psychophysical testing.
(2), psychophysical testing, set up interval scale: according to the description rule of colour of the tongue type in Diagnostics of Chinese Medicine, by tongue Color as the Appreciation gist of psychological response amount, instructs observer to compare according to the gradual change order of deep red, purple green grass or young crops light white, light red, red Relatively judge.
Flow process sees accompanying drawing 3.First pass through the method such as paired comparison or hierarchical arrangement, multiple observers simple component is become The colour of the tongue changed stimulates and carries out judging sequence, sets up the perception order of the colour of the tongue quantity of stimulus of simple component change.Wherein, paired comparison is By colour of the tongue quantity of stimulus pair-wise combination, observer is presented in display, allows observer select the most more and is partial to gradual change order side Color lump, then adds up the comparative result of multiple observer, obtains perception order.And hierarchical arrangement is that all colour of the tongue quantity of stimulus are same Time present to observer, allow observer by gradual change order arrange, obtain perception order.Perception serial number is observer to stimulation Rating.For convenience of explanation, table 1, as a example by 5 observers are to 4 colour of the tongue sorting datas, introduced interval scale and is set up Process.
1. multiple observers are in addition average to the same grade stimulating evaluation, thus obtain the average of each stimulation Grade, is designated as MRi
MR i = Σ j = 1 N Q i j N ( i = 1 , 2 , ... n )
Wherein, n is that colour of the tongue stimulates quantity, and N is observer's quantity, QijFor observer j, colour of the tongue is stimulated the rating of i.
In table 1 example, n=4, N=5, in table, numerical value is rating Q.Calculate each colour of the tongue to be graded by 5 observers Meansigma methods, i.e. the every column average in table, obtains average rank MR of this colour of the tongue.Average rank MR of colour of the tongue 1 in this example1=3.
2. average selection mark Mc is calculatedi
Mci=n-MRi(i=1,2 ... n)
In table 1 example, n=4, therefore the average of colour of the tongue 1 selects mark Mc1=4-MR1=1.
3. calculate average selection and adjust mark Mci’。
Mci'=Mci+ 0.5 (i=1,2 ... n)
In table 1 example, the average selection of colour of the tongue 1 adjusts mark Mc1'=Mc1+ 0.5=1.5.
4. the average percent P selecting to adjust mark is calculatedi’;
P i ′ = Mc i ′ n ( i = 1 , 2 , ... n )
In table 1 example, the average percent P selecting to adjust mark of colour of the tongue 11'=Mc1'/4=0.375
5. by statistical POZ look-up table by probability Pi' it is converted into standard score zi’;
Pi′→zi' (i=1,2 ... n)
6. by zi' eliminate negative value, i.e. plus ziNegative value minimum in ', obtains final interval scale value Vi
Vi=zi′+|z′min| (i=1,2 ... n)
ViIt is the psychological response amount of each stimulation.
Table 1: interval scale Establishing process breviary example
(3), by mathematical modeling, the functional relationship of colour of the tongue list physical components and the change of psychological response amount is obtained.
Colour of the tongue stimulates each simple component change (H, S, I) as independent variable, and psychological response amount, as dependent variable, uses minimum Square law carries out curve fitting, and determines the matched curve functional relationship between each component variation and psychological response amount.Accompanying drawing 4, for H Component variation colour of the tongue stimulates and psychological response magnitude relation segmentation fits curve, and this curve is conic section.
2. the relation of colour of the tongue magnitude of physical quantity and psychological response amount determines:
(1), in the range of colour of the tongue under the comprehensive situation of change of multi-components, the determination of physical stimulation amount: divide in fixed colour of the tongue In the range of cloth, carry out uniform segmentation sampling.Three-component is respectively combined out different colours block, and the colour of the tongue comprehensively changed stimulates Amount.As each component 4 grade divides sampling, available 125 quantity of stimulus combination.Be converted to show by the colour of the tongue quantity of stimulus HSI value obtained The sRGB value shown, shows over the display with the form of image color lump, allows observer observe judgement, carries out psychophysical testing.
(2), psychophysical testing, set up interval scale: concrete grammar step and " colour of the tongue magnitude of physical quantity simple component and psychology The relation of perception amount determines " in (2) identical.
(3), by mathematical modeling, the functional relationship of colour of the tongue magnitude of physical quantity and psychological response amount is obtained.
Colour of the tongue stimulates physical quantity (H, S, I) as independent variable, and psychological response amount, as dependent variable, uses polynomial regression Both functional relationships set up by model.Wherein, the number of times of each component of physical quantity stimulates and psychology sense according to simple component change colour of the tongue The functional relationship of the amount of knowing change determines.Such as, if the fitting function of H component and psychological response amount is quadratic function, then multinomial In model, H component uses quadratic term.Each component cross term, the selection of low order item and combination, then carry out preferably according to regression accuracy, Determine polynomial regression model form and parameter.
(4), Chinese medicine tongue color sensation knows quantization.
Extract in tongue image the colour of the tongue rgb value needing to quantify, and be converted into HSI value, substitute into colour of the tongue magnitude of physical quantity and The polynomial regression model of psychological response amount, i.e. can obtain the perception quantized result of this colour of the tongue.

Claims (1)

1. Chinese medicine tongue color sensation based on psychophysical testing knows quantization method, it is characterised in that in turn include the following steps:
1) determination in colour of the tongue territory:
(1), gather all kinds of Chinese medicine tongue colour standard image pattern, need to comprise all kinds of use-case of green grass or young crops light red, light white, red, deep red, purple, totally 5 Class;Every class use-case needs to comprise the example of more than 100 examples, and is provided the demarcation of affiliated type by more than three traditional Chinese medical doctors;
(2), extract the color magnitude of physical quantity of body of the tongue part in all image patterns, and be converted into corresponding with human eye perception HSI color space;According to all colour of the tongues in H, S, the distribution of I component, extend 1% respectively to both sides, determine colour of the tongue territory Interval on H, S, I component;
2) relation of colour of the tongue magnitude of physical quantity simple component and psychological response amount determines:
Two components in fixing H, S, I, utilize psychophysical testing, study another component variation and the pass of psychological response amount System;
(2.1), in the range of colour of the tongue under simple component situation of change, the determination of physical stimulation amount: in fixed colour of the tongue distribution In, carry out uniform segmentation sampling;Choose the central point of two of which components range, as component fixed value, make another component be Different sampling point value, the most only change single component and are respectively combined out different colours block, obtain the colour of the tongue quantity of stimulus of simple component change; The colour of the tongue quantity of stimulus HSI value obtained is converted to displayable sRGB value, shows over the display with the form of image color lump, allow Observer observes judgement, carries out psychophysical testing;
(2.2), psychophysical testing, set up interval scale: according to the description rule of colour of the tongue type in Diagnostics of Chinese Medicine, by colour of the tongue According to the gradual change order of green grass or young crops light white, light red, red, deep red, purple as the Appreciation gist of psychological response amount, observer is instructed to compare Judge;
First pass through paired comparison or hierarchical arrangement, multiple observers the colour of the tongue changed simple component stimulates and carries out judging row Sequence, sets up the perception order of the colour of the tongue quantity of stimulus of simple component change;Perception serial number is rating, by multiple observers couple The same grade stimulating evaluation is in addition average, thus obtains the respective average rank of each stimulation;Calculate under normal distribution each flat The probit that all grade is corresponding, calculates Z score further according to POZ conversion table, i.e. obtain each stimulation psychological response amount composition etc. Away from scale;
(2.3), by mathematical modeling, obtaining simple component change colour of the tongue stimulates and the functional relationship of psychological response amount change;
Colour of the tongue stimulates each simple component change H, S, I as independent variable, and psychological response amount, as dependent variable, uses method of least square Carry out curve fitting, determine the matched curve functional relationship between each component variation and psychological response amount;
3) relation of colour of the tongue magnitude of physical quantity and psychological response amount determines:
(1), in the range of colour of the tongue under the comprehensive situation of change of multi-components, the determination of physical stimulation amount: be distributed model in fixed colour of the tongue In enclosing, carry out uniform segmentation sampling;Three-component is respectively combined out different colours block, the colour of the tongue quantity of stimulus comprehensively changed;Will The colour of the tongue quantity of stimulus HSI value obtained is converted to displayable sRGB value, shows over the display with the form of image color lump, allows sight The person of examining observes judgement, carries out psychophysical testing;
(2), psychophysical testing, set up interval scale: concrete grammar step and " colour of the tongue magnitude of physical quantity simple component and psychological response Amount relation determine " in (2.2) identical;
(3), by mathematical modeling, the functional relationship of colour of the tongue magnitude of physical quantity and psychological response amount is obtained;
Colour of the tongue stimulates physical quantity H, S, I as independent variable, and psychological response amount, as dependent variable, uses polynomial regression model to build Found both functional relationships;Wherein, the number of times of each component of physical quantity stimulates and psychological response quantitative change according to simple component change colour of the tongue The functional relationship changed determines;If H component is quadratic function with the fitting function of psychological response amount, then H component in multinomial model Use quadratic term;Each component cross term, the selection of low order item, then carry out preferably, finally determining that multinomial returns according to regression accuracy Return form and the parameter of model;
(4), Chinese medicine tongue color sensation knows quantization;
Extract the colour of the tongue rgb value needing to quantify in tongue image, and be converted into HSI value, substitute into colour of the tongue magnitude of physical quantity and psychology The polynomial regression model of perception amount, i.e. obtains the perception quantized result of this colour of the tongue.
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