CN105139367A - Visible light polarization image fusion method based on non-subsampled shear wave - Google Patents
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Abstract
The invention provides a non-downsampling shear wave-based visible light polarization image fusion method, which comprises the steps of firstly carrying out Stokes calculation on images in different polarization states simultaneously acquired by a plurality of detector cameras to obtain polarization degree, polarization angle images and light intensity images, extracting polarization characteristic images of a target by using the polarization characteristic images and the light intensity images, then respectively carrying out non-downsampling Shearlets transform (NSST) decomposition on the polarization characteristic images and the light intensity images, respectively determining high and low frequency fusion coefficients according to window energy and a mean value in a frequency domain, reconstructing a primary fusion image by using NSST inverse transformation, and finally carrying out target enhancement on the primary fusion image to obtain final fusion image output. Compared with the traditional target detection method utilizing multi-scale decomposition, the method has the advantages that the polarization characteristic extraction and target enhancement means are added, the fused image details are effectively increased, the contrast ratio of the target and the background is improved, the polarization characteristic of the target is highlighted, the scene perception and target detection capabilities are improved, and the method is suitable for a target detection system.
Description
Technical field
The present invention relates to a kind of visible ray polarization image fusion method, particularly a kind of visible ray polarization image fusion method based on down-sampling shearing wave belongs to Digital Image Processing and photodetection field.This method realizes the Polarization Image Fusion based on non-lower sampling shearing wave, the different polarization states image collected to camera lens camera lens and many photoelectric sensors carries out effective integration, and do further targets improvement processing, details is exported to enrich, the high image of contrast, the polarization characteristic of effectively prominent target, improves the ability of scene perception and target acquisition.It can be widely applied in various photoelectronic imaging equipment and target detection system.
Background technology
Existing target acquisition means mainly include visible optical detection, radar, infrared acquisition etc., wherein infrared acquisition is imaged by gathering target radiant intensity information, because of its image-forming range far, the advantages of strong antijamming capability, visualization, turns into most important Detection Techniques.With the development of infrared camouflage technology, new infrared camouflage material causes the radiation discrimination of target and background to reduce, and causes infrared camera to be difficult to effectively detect small temperature-difference target and camouflaged target, and infrared detection technique application is limited.
Polarization is one of inherent characteristic of light.Object is during reflection, scattering sunshine, the polarization information determined by its own property can be produced, the target properties such as its refractive index, surface roughness are more sensitive, insensitive to the temperature difference, i.e. the polarization state change of light contains the physical state information of effective object.Polarization imaging is a kind of emerging Detection Techniques, it is detected by the radiation and polarization characteristic difference of target and background, obtaining radiation intensity simultaneously, it also can obtain polarization information, so can by radiation intensity is identical and object that polarization characteristic is different makes a distinction, thus a useful supplement as conventional detection means, is favorably improved detectivity and accuracy.It is external that polarization imaging technology is progressively used for the numerous areas of military and civilian, and the country also gradually spreads out relation technological researching.
The content of the invention
The invention solves the problems that technical problem is：For the deficiency of existing Detection Techniques, a kind of visible ray polarization image fusion method based on down-sampling shearing wave is provided, on the basis of keeping existing detection method effectively to distinguish radiation intensity and higher detectivity, further increase polarization characteristic is extracted and targets improvement means, the profile information and detailed information of image are taken full advantage of, the polarization characteristic of target is highlighted, the recognition capability of target is improved, also human eye vision observation is more met, it is adaptable in scene perception and target identification system.
To realize such purpose, technical scheme：A kind of visible ray polarization image fusion method based on down-sampling shearing wave, comprises the following steps：
Step 1: Stokes is resolved：
Visible ray polarization image fusion method based on non-lower sampling shearing wave, mainly uses different polarization states information to carry out effective integration, and target is protruded to target to reach, is observed beneficial to human eye vision, improves the purpose of detectivity.The method of conventional description optical polarization has two kinds, and one kind is Jones vector methods, for describing complete polarized light；One kind is Stokes vector methods, and it can represent complete polarized light, partial poolarized light or even natural light, and Stokes vector parameters are proportional to light intensity, can directly be perceived by detector.Therefore, 4 width polarization imagings use Stokes vectors and describe polarization state and be：
(formula 1)
Wherein, Iθ(θ=0 °, 45 °, 90 °, 135 °) represents the polarization state image of different polarization deflection, ILAnd IRLeft and right rounding polarization image is represented respectively.s0It is directly proportional to incident intensity, s1And s2The linear polarization information of two mutually orthogonal directions, s are represented respectively3Represent circular polarization information.In natural environment, circular component very little can be neglected.Therefore, the polarization image (degree of polarization DoLP and angle of polarization AoLP) of target is represented by：
(formula 2)
(formula 3).
Step 2: polarization characteristic is extracted：
Intensity image s can be obtained according to formula 10, it is however generally that, intensity image brightness is big, details is enriched, but target-to-background contrast is not enough, and degree of polarization image DoLP and angle of polarization image AoLP can be obtained according to formula in step one 2 and formula 3, degree of polarization image DoLP overall contrasts are higher but brightness is relatively low, details is less；And angle of polarization image AoLP can preferably reflect target physical surface characteristic, but noise is also exaggerated simultaneously.Therefore, the present invention considers to propose a kind of integrated polarization characteristic image F, and calculating formula is as follows：
F=α * DoLP+ β * (DoLP*cos (2*AoLP)) (formula 4)
Weight representative value is obtained for α=0.8, β=0.2 by many experiments com-parison and analysis.
Step 3: non-lower sampling Shearlets multi-resolution decompositions：
Shearing wave (Shearlets) is a kind of multiresolution wavelet proposed in 2005, compared with other multi-scale transform methods, it has good directional sensitivity and anisotropy, marginal information that can accurately in capture images, and pseudo- Gibbs effects will not be introduced, thus just progressively it is being applied to image co-registration and rim detection.Intensity image s can be directly obtained according to formula 10The polarization characteristic image F that can be extracted with reference to formula 1, formula 2 and formula 3, intensity image reflects the overall profile and monochrome information of target and background, and polarization characteristic image reflects the polarization characteristic of target, it is therefore proposed that using non-lower sampling Shearlets (NSST) to intensity image and polarization characteristic image by intensity image s0Decomposed with polarization characteristic image F on different scale and direction.To improve precision, yardstick j takes 4 here, and the 1st, 2 floor height frequency components are carried out with 10 Directional Decompositions, and 3,4 floor height frequency components carry out 18 Directional Decompositions.NSST realization is broadly divided into two steps：The multi-resolution decomposition of non-lower sampling and direction localization.4 layers of non-lower sampling pyramid (non-subsampledpyramid are carried out to intensity image and polarization characteristic image respectively, NSP) decompose, sampled in the absence of being decomposed due to NSST, therefore, after image is decomposed through 4 layers of NSP, 5 and artwork size same sub-band image are finally given, including 1 low-frequency image and 4 band logical images.Then 4 band logical image difference travel directions are decomposed again, to realize that high frequency imaging direction localizes.
Step 4: low-and high-frequency coefficient is merged：
Intensity image s can be obtained by step 30With the sub-band images on polarization characteristic image F different scale different directions, the low-frequency component capture element in each layer all directions is chosen averagely as the low frequency coefficient of this layer of fused images；High frequency coefficient fusion rule uses window energy maximal criterion, chooses mask convolution and maximum pixel as the high frequency coefficient of this layer of fused images, 3 × 3 template windows are as follows：
(formula 5).
Step 5: Image Reconstruction and targets improvement：
By step 4, after completing to the low frequency coefficient and high frequency coefficient fusion treatment of two images, the high and low frequency fusion coefficients on different scale different directions can be obtained, these coefficients are carried out with NSST inverse transformations, preliminary fused images output.Preliminary fused images are compared to original image, the existing larger lifting of its contrast, definition and brightness.To further enhance contrast, prominent target polarization characteristic, using based on instructing the enhancing algorithm of wave filter to carry out targets improvement to NSST inverse transformations output image.Algorithm is first to rebuilding image denoising and transforming to log-domain, then instruct the wave filter of two different scales to extract the enhancing detail view of two width in various degree by the mean square deviation of image, then be superimposed to artwork and carry out the final fused images of transformation transformation output.
The beneficial effect of the present invention compared with prior art is：
(1) present invention uses the visible ray polarization image fusion method based on non-lower sampling shearing wave, compared with method of the tradition just with radiation intensity difference section partial objectives for and background, the polarization characteristic differentiation to target and background is added, target acquisition rate is effectively increased.
(2) present invention uses the visible ray polarization image fusion method based on non-lower sampling shearing wave, compared with conventional Stokes vector methods describe the polarization state of target, add the effective extraction and fusion to degree of polarization and angle of polarization image, the polarization characteristic index of comprehensive description polarization state is proposed, is more beneficial for describing the polarization characteristic of target.
(3) present invention uses the visible ray polarization image fusion method based on non-lower sampling shearing wave, compared with the Polarization Image Fusion of conventional multi-resolution decomposition, non-lower sampling Shearlets conversion has good directional sensitivity and anisotropy, marginal information that can accurately in capture images, and pseudo- Gibbs effects will not be introduced, it is more suitable for Polarization Image Fusion and target identification.
(4) present invention uses the visible ray polarization image fusion method based on non-lower sampling shearing wave, when carrying out fusion treatment, average be have chosen as low frequency fusion rule, 3 × 3 window energies obtain preferable balance as high frequency fusion rule between syncretizing effect and computational efficiency.
(5) present invention uses the visible ray polarization image fusion method based on non-lower sampling shearing wave, compared with usual polarization image fusion method, targets improvement processing is added, target detail is further increased, contrast is improved, is more suitable for eye-observation and scene Recognition.
In a word：The present invention is on the basis of the higher detectivity of conventional detection method is kept, choose fine multi-resolution decomposition shearing wave, strengthen and expand the discrimination of target and background using polarization characteristic, add fused images details, improve contrast, highlight polarization characteristic of target etc., it is adaptable in Polarization Image Fusion and target detection system.
Brief description of the drawings
Fig. 1 is the general frame implementation process figure of the inventive method；
Fig. 2 be the inventive method use based on the enhancing algorithm principle figure for instructing wave filter, first to the denoising of NSST reconstruction images and transform to log-domain, then instruct the wave filter of two different scales to extract the enhancing detail view of two width in various degree by the mean square deviation of image, then be superimposed to artwork and carry out the enhanced fused images of transformation transformation output；
Fig. 3 is the gray scale source images for the different polarization states that the inventive method carries out object of experiment 1, target 1 is metal cylinder in figure, wherein Fig. 3 (a)~(d) is 0 °, 45 °, 90 °, the polarization state image at 135 ° of polarization directions angle respectively, and image resolution ratio is 224 × 224 pixels.
Fig. 4 is the gray scale source images for the different polarization states that the inventive method carries out object of experiment 2, target 2 is figure medium and long distance street lamp, wherein Fig. 4 (a)~(d) is 0 °, 45 °, 90 °, the polarization state image at 135 ° of polarization directions angle respectively, and image resolution ratio is 224 × 224 pixels.
Fig. 5 is the result that the inventive method is tested to target 1, and image resolution ratio is 224 × 224 pixels.Wherein Fig. 5 (a) is the polarization state image at 0 ° of polarization direction angle, and Fig. 5 (b) is intensity image s0Fig. 5 (c) is degree of polarization image DoLP, Fig. 5 (d) is angle of polarization image AoLP, the polarization characteristic image F that Fig. 5 (e) extracts for the present invention, Fig. 5 (f) is the output image that average fusion is carried out to polarization characteristic image and intensity image, Fig. 5 (g) is the output image that 3 layers of Daubechies wavelet decompositions fusion is carried out to polarization characteristic image and intensity image, and Fig. 5 (h) is the fusion output image that the inventive method is handled polarization characteristic image and intensity image.
Fig. 6 is the result that the inventive method is tested to target 2, and image resolution ratio is 224 × 224 pixels.Wherein Fig. 6 (a) is the polarization state image at 0 ° of polarization direction angle, and Fig. 6 (b) is intensity image s0Fig. 6 (c) is degree of polarization image DoLP, Fig. 6 (d) is angle of polarization image AoLP, the polarization characteristic image F that Fig. 6 (e) extracts for the present invention, Fig. 6 (f) is the output image that average fusion is carried out to polarization characteristic image and intensity image, Fig. 6 (g) is the output image that 3 layers of Daubechies wavelet decompositions fusion is carried out to polarization characteristic image and intensity image, and Fig. 6 (h) is the fusion output image that the inventive method is handled polarization characteristic image and intensity image.
Tables 1 and 2 is to use image information entropy (informationentropy, IE), average gradient (AverageGradient, AG the objective evaluation value that the non-reference picture contrast entropy HVSNRC objective evaluations index) and under the contrast sensitivity based on human eye vision is provided to Fig. 5 and Fig. 6 experimental result images respectively, wherein contrast are that negative value represents that target is covered by background.Image information entropy, average gradient and contrast are bigger, show that syncretizing effect is better.
Embodiment
Embodiments of the invention are elaborated below in conjunction with the accompanying drawings.The present embodiment is implemented lower premised on technical solution of the present invention, gives detailed embodiment and specific operating process, but protection scope of the present invention is not limited to following embodiment.
As shown in figure 1, the algorithm flow of the present embodiment is divided into：Stokes resolvings, polarization characteristic extraction, the fusion of non-lower sampling Shearlets multi-resolution decompositions, low-and high-frequency coefficient and five parts of image reconstruction and targets improvement.
This example provides a kind of visible ray polarization image fusion method based on non-lower sampling shearing wave, specifically includes following steps：
Step 1: Stokes is resolved：
The present embodiment carries out Stokes resolvings to 4 width resolution ratio in Fig. 3 and Fig. 4 for the different polarization states image of 224 × 224 pixels respectively first.Visible ray polarization image fusion method based on non-lower sampling shearing wave, mainly uses different polarization states information to carry out effective integration, and target is protruded to target to reach, is observed beneficial to human eye vision, improves the purpose of detectivity.The method of conventional description optical polarization has two kinds, and one kind is Jones vector methods, for describing complete polarized light；One kind is Stokes vector methods, and it can represent complete polarized light, partial poolarized light or even natural light, and Stokes vector parameters are proportional to light intensity, can directly be perceived by detector.Therefore, polarization imaging uses Stokes vectors and describes polarization state and be：
(formula 1)
Wherein, Iθ(θ=0 °, 45 °, 90 °, 135 °) represents the polarization state image of different polarization deflection, ILAnd IRLeft and right rounding polarization image is represented respectively.s0It is directly proportional to incident intensity, s1And s2The linear polarization information of two mutually orthogonal directions, s are represented respectively3Represent circular polarization information.In natural environment, circular component very little can be neglected.Therefore, the polarization image (degree of polarization DoLP and angle of polarization AoLP) of target is represented by：
(formula 2)
(formula 3)
Operation can respectively obtain the intensity image s of target 1 and target 2 more than0, degree of polarization image DoLP and angle of polarization image AoLP, image resolution ratio is 224 × 224.
Step 2: polarization characteristic is extracted：
In general, intensity image s0Brightness is big, and details is enriched, but target-to-background contrast is not enough, and degree of polarization image DoLP overall contrasts are higher but brightness is relatively low, details is less；And angle of polarization image AoLP can preferably reflect target physical surface characteristic, but noise is also exaggerated simultaneously.Therefore, the present invention considers to propose a kind of integrated polarization characteristic image F, and calculating formula is as follows：
F=α * DoLP+ β * (DoLP*cos (2*AoLP)) (formula 4)
Weight representative value is obtained for α=0.8, β=0.2 by many experiments com-parison and analysis.It is possible thereby to respectively obtain the polarization characteristic image of target 1 and target 2, image resolution ratio is 224 × 224.
Step 3: non-lower sampling Shearlets multi-resolution decompositions：
Shearing wave (Shearlets) is a kind of multiresolution wavelet proposed in 2005, compared with other multi-scale transform methods, it has good directional sensitivity and anisotropy, marginal information that can accurately in capture images, and pseudo- Gibbs effects will not be introduced, thus just progressively it is being applied to image co-registration and rim detection.Intensity image s can be directly obtained according to formula 10The polarization characteristic image F that can be extracted with reference to formula 1, formula 2 and formula 3, intensity image reflects the overall profile and monochrome information of target and background, and polarization characteristic image reflects the polarization characteristic of target, it is therefore proposed that using non-lower sampling Shearlets (NSST) to intensity image and polarization characteristic image by intensity image s0Decomposed with polarization characteristic image F on different scale and direction.To improve precision, yardstick j takes 4 here, and the 1st, 2 floor height frequency components are carried out with 10 Directional Decompositions, and 3,4 floor height frequency components carry out 18 Directional Decompositions.NSST realization is broadly divided into two steps：The multi-resolution decomposition of non-lower sampling and direction localization.4 layers of non-lower sampling pyramid (non-subsampledpyramid are carried out to intensity image and polarization characteristic image respectively, NSP) decompose, sampled in the absence of being decomposed due to NSST, therefore, after image is decomposed through 4 layers of NSP, 5 and artwork size same sub-band image are finally given, including 1 low-frequency image and 4 band logical images, image resolution ratio is 224 × 224.Then 4 band logical image difference travel directions are decomposed again, to realize that high frequency imaging direction localizes.
Step 4: low-and high-frequency coefficient is merged：
Target 1 and the corresponding intensity image s of target 2 can be obtained by step 30With sub-band images of the polarization characteristic image F on different scale different directions, the low-frequency component capture element in each layer all directions is chosen averagely as the low frequency coefficient of this layer of fused images；High frequency coefficient fusion rule uses window energy maximal criterion, chooses mask convolution and maximum pixel as the high frequency coefficient of this layer of fused images, 3 × 3 template windows are as follows：
(formula 5).
Step 5: Image Reconstruction and targets improvement：
By step 4, complete to target 1 and the corresponding intensity image s of target 20And after polarization characteristic image F low frequency coefficient and high frequency coefficient fusion treatment, the high and low frequency fusion coefficients on different scale different directions can be obtained, these coefficients are carried out with NSST inverse transformations, preliminary fused images output.Preliminary fused images are compared to original image, the existing larger lifting of its contrast, definition and brightness.To further enhance contrast, prominent target polarization characteristic, using based on instructing the enhancing algorithm of wave filter to carry out targets improvement to NSST inverse transformations output image.Algorithm is first to rebuilding image denoising and transforming to log-domain, then the wave filter of two different scales is instructed to extract the enhancing detail view of two width in various degree by the mean square deviation of image, artwork is superimposed to again and transformation transformation is carried out and exports final fused images, and image resolution ratio is 224 × 224.
In order to verify the validity of the inventive method, the source images of 4 width target 2 in the source images of 4 width target 1 and Fig. 4 in Fig. 3 are tested respectively, as a result such as Fig. 5 and as shown in fig. 6, such as the metal cylinder in Fig. 5 (a), illumination is dark to be unfavorable for target identification and eye-observation respectively.Fig. 5 (b) intensity images have merged different polarization states information, and details and brightness are increased slightly, but target and background contrast is inadequate；Fig. 5 (c) degree of polarization missing images tabletop section details, screen edge is also not clear enough, but highlights metal target cylinder, improves the contrast of target and background；Fig. 5 (d) angles of polarization image preferably reflects metal cylinder target and the surface characteristics of computer screen, but is also exaggerated noise simultaneously；And Fig. 5 (e) polarization characteristics brightness of image is lifted, details increase, contrast is preferable.Comparison diagram 5 (f)~(h), figure (h) contrast is higher, and details is stronger, and visual effect is more preferable.Such as Fig. 6 (a), more remote street lamp is chosen as object of experiment 2, and the natural cause reduction image quality such as haze, illumination influences Effect on Detecting.Fig. 6 (b) intensity images merge different polarization states image, and background luminance increase is obvious, the enhancing of woods details, but contrast is still inadequate；Fig. 6 (e) polarization characteristics image preferably keeps the advantages of Fig. 6 (c) and Fig. 6 (d) target is protruded, contrast is higher, and brightness is effectively improved in combination with Fig. 6 (b).Comparison diagram 6 (f)~(h), it is same it can be found that wick and woods details can be clearly seen in figure (h), and contrast is high, is more suitable for eye-observation.
To carry out objective evaluation, because source images to be fused herein are intensity image and polarization characteristic image, therefore use comentropy (informationentropy, IE), average gradient (AverageGradient, AG), 3 objective indicators of contrast evaluate fused image quality, wherein contrast index uses the non-reference picture contrast entropy HVSNRC under the contrast sensitivity based on human eye vision, calculating formula such as formula 6,7,8.
(formula 6)
(formula 7)
(formula 8)
In formula 6, Q is the total number of greyscale levels of image；peThe probability occurred in the picture for gray value e.In formula 7, pixel center is (m, n), and Size of Neighborhood is M × N.In formula 8, Q is the CSF weights of image, and CE is band limit contrast entropy, and m, n are the length and width of image, and k is wavelet decomposition series.
Objective evaluation is carried out to the result in Fig. 5, Fig. 6 using above-mentioned 3 kinds of evaluation indexes, as a result as shown in Table 1 and Table 2.
Table 1
Table 2
As can be seen from the table, proposing the fused images of method has the characteristics of comentropy is abundant, average gradient is big, contrast is high, highlights the polarization characteristic of target.Therefore, generally speaking, the present invention is on the basis of the higher detectivity of conventional detection method is kept, choose fine multi-resolution decomposition shearing wave, strengthen and expand the discrimination of target and background using polarization characteristic, add fused images details, improve contrast, highlight polarization characteristic of target etc., it is adaptable in Polarization Image Fusion and target detection system.
Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.
Those of ordinary skill in the art will be appreciated that, embodiment above is intended merely to the explanation present invention, and be not used as limitation of the invention, as long as in the spirit of the present invention, embodiment described above is changed, modification will all fall in the range of claims of the present invention.
Claims (4)
1. a kind of visible ray polarization image fusion method based on non-lower sampling shearing wave, it is characterised in that comprise the following steps：
Step 1: the polarization image Stokes of target is resolved：
The Stokes vectors of the polarization image of 4 width targets describe polarization state and are：
Wherein, Iθ(θ=0 °, 45 °, 90 °, 135 °) represents the polarization state image of different polarization deflection, ILAnd IRLeft and right rounding polarization image, intensity intensity image s are represented respectively0It is directly proportional to incident intensity, s1And s2The linear polarization information of two mutually orthogonal directions, s are represented respectively3Circular polarization information is represented, in natural environment, circular component very little can be neglected, therefore, the degree of polarization DoLP and angle of polarization AoLP of the polarization image of target are represented by：
Step 2: polarization characteristic is extracted：
Integrated polarization characteristic image F is calculated, calculating formula is as follows：
F=α * DoLP+ β * (DoLP*cos (2*AoLP)) (formula 4)
Wherein α, β are weight coefficient；
Step 3: non-lower sampling Shearlets multi-resolution decompositions：
Frequency domain decomposition is carried out using non-lower sampling shearing wave conversion (NSST), NSST realization is broadly divided into two steps：
The multi-resolution decomposition and direction localization of non-lower sampling are carried out first, i layers of non-lower sampling pyramid (non-subsampledpyramid are carried out to intensity image and polarization characteristic image respectively, NSP) decompose, sampled in the absence of being decomposed due to NSST, therefore, after image is decomposed through i layers of NSP, i+1 and artwork size same sub-band image are finally given, including 1 low-frequency image and i band logical image；
Then i band logical image difference travel direction is decomposed again, to realize that high frequency imaging direction localizes；
Intensity image s can be obtained by the step 30With the sub-band images on polarization characteristic image F different scale different directions, the low-frequency component capture element in each layer all directions is chosen averagely as the low frequency coefficient of this layer of fused images；
Step 4: low-and high-frequency coefficient is merged：
High frequency coefficient fusion rule uses window energy maximal criterion, chooses mask convolution and maximum pixel as the high frequency coefficient of this layer of fused images, 3 × 3 template windows are as follows：
Step 5: Image Reconstruction and targets improvement：
By step 4, the high and low frequency fusion coefficients on different scale different directions can be obtained, NSST inverse transformations are carried out to these coefficients, preliminary fused images output, to further enhance contrast, prominent target polarization characteristic, using based on instructing the enhancing algorithm of wave filter to carry out targets improvement to NSST inverse transformations output image, to obtain final fused images.
2. the visible ray polarization image fusion method according to claim 1 based on non-lower sampling shearing wave, it is characterised in that 4 width polarization state images are obtained simultaneously by multi-detector camera in the step one.
3. the visible ray polarization image fusion method according to claim 1 based on non-lower sampling shearing wave, it is characterised in that weight coefficient α, the β typical value in the step 2 is respectively 0.8 and 0.2.
4. the visible ray polarization image fusion method according to claim 1 based on non-lower sampling shearing wave, it is characterized in that, the step 3 Scale Decomposition number of plies i values 4, Directional Decomposition is that the 1st, 2 floor height frequency components are carried out with 10 Directional Decompositions, and 3,4 floor height frequency components carry out 18 Directional Decompositions.
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