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CN112634156B - A method for estimating material reflection parameters based on images captured by portable devices - Google Patents

A method for estimating material reflection parameters based on images captured by portable devices Download PDF

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CN112634156B
CN112634156B CN202011530944.1A CN202011530944A CN112634156B CN 112634156 B CN112634156 B CN 112634156B CN 202011530944 A CN202011530944 A CN 202011530944A CN 112634156 B CN112634156 B CN 112634156B
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张锦博
沈会良
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Abstract

The invention discloses a method for estimating material reflection parameters based on images acquired by portable equipment. The method comprises the following steps: shooting a material environment light image and a flash lamp image; estimating the roughness, the specular reflection coefficient, the diffuse reflection coefficient and the normal mapping of the material according to the ambient light map; calibrating the direction, distance and real irradiance from pixel to the camera and the light source; solving a color channel correction vector between the ambient light map and the flash light map; and determining the positions of similar pixel points based on clustering, determining the final clustering class number by adopting a gradual iterative refinement mode, and endowing the points in each class with the same reflection parameters. The method can be used for conveniently estimating the SVBRDF parameters of the material, aiming at the phenomena of serious halation and the like of some material mapping images estimated by the existing neural network, the reflection parameters of the material are estimated again by shooting a material flashlight image and an environment light image, and the reality of rendering is improved.

Description

基于便携式设备采集图像估计材质反射参数的方法A method for estimating material reflection parameters based on images captured by portable devices

技术领域technical field

本发明涉及材质反射参数估计,尤其涉及一种基于便携式设备采集图像估计材质反射参数的方法。The invention relates to material reflection parameter estimation, in particular to a method for estimating material reflection parameters based on images collected by a portable device.

背景技术Background technique

在现实世界中,物体在不同光照条件、不同视角条件下的外观属性是由物体表面的材质决定的,如何便捷、高效的恢复材质是目前计算机图形学的重要话题,广泛应用于视觉效果、电子商务、产品设计和娱乐等领域。然而数字化从真实世界中获取高质量的材质外观仍然是一个具有挑战性的问题,最大的挑战是现实世界中材质外观具有很大的复杂性。现实世界中物体一般由多种材质组成,且材质表面具有复杂的几何,这会增大采集和建模的难度。In the real world, the appearance properties of objects under different lighting conditions and different viewing angles are determined by the material on the surface of the object. How to restore the material easily and efficiently is an important topic in computer graphics at present, which is widely used in visual effects, electronic business, product design and entertainment. However, digitally obtaining high-quality material appearances from the real world is still a challenging problem, and the biggest challenge is the great complexity of material appearances in the real world. Objects in the real world are generally composed of multiple materials, and the surfaces of the materials have complex geometry, which increases the difficulty of acquisition and modeling.

光源发出的光现照射到物体表面后,一部分光将会被吸收,另一部分光线将会被表面反射。BRDF定义为物体表面一点在某一特定波长下,沿ωo:(θo,φo)方向出射的亮度L和沿ωi:(θi,φi)方向入射光照度E之间的比值:When the light emitted by the light source hits the surface of the object, part of the light will be absorbed, and another part of the light will be reflected by the surface. BRDF is defined as the ratio between the outgoing luminance L along the ω o : (θ o , φ o ) direction and the incident illuminance E along the ω i : (θ i , φ i ) direction at a certain wavelength at a point on the surface of the object:

Figure BDA0002852111830000011
Figure BDA0002852111830000011

虽然BRDF模型能够有效表示物体的反射特性,但是从定义上来看,它的参数并不包含位置信息。所以BRDF模型一般仅适用于表示那些表面没有细微起伏的单一颜色物体,如金属、不透明塑料和单色布料等。然而,现实世界中,符合这类特性的材质是极少的,很多物体表面存在着细微起伏和颜色变化,为了描述此类物体,提出了空间变化的BRDF(SVBRDF)模型:Although the BRDF model can effectively represent the reflection characteristics of objects, its parameters do not contain positional information by definition. Therefore, the BRDF model is generally only suitable for representing single-color objects without subtle undulations on the surface, such as metals, opaque plastics, and single-color cloth. However, in the real world, there are very few materials that meet these characteristics, and there are subtle fluctuations and color changes on the surface of many objects. In order to describe such objects, a spatially varying BRDF (SVBRDF) model is proposed:

Figure BDA0002852111830000012
Figure BDA0002852111830000012

其中p:=(x,y)表示物体表面点的坐标。where p:=(x, y) represents the coordinates of the object surface point.

因此,目前一般采用SVBRDF(spatially-varying bi-directional reflectancedistribution function)来描述物体表面的反射特性。如何进行材质SVBRDF的采集与建模一直是一个重要的研究课题,目前的研究热点集中在使用手机等便携式设备对图像进行采集,采集少量图像恢复出材质的反射特性。Deschaintre等在文献【"Single-image svbrdfcapture with a rendering-aware deep network."ACM Transactions on Graphics(ToG)37(4),1-15,2018.】提出了一种通过训练深度神经网络来自动提取和理解纹理、高光和阴影等视觉线索,从而可以从单幅图像中感知材质的外观属性。这类方法通过学习大量数据集学习到一系列的先验和约束,得到一个视觉合理的解。但是大量的测试表明这种方法效果不鲁棒,特别是在高光材质这种亮度随着角度变化而剧烈变化的材质上,输出的结果在参数贴图上存在明显的伪影,而且有时粗糙度和镜面反射系数估计和真实值偏差较大。Therefore, SVBRDF (spatially-varying bi-directional reflectance distribution function) is generally used to describe the reflection characteristics of the object surface. How to acquire and model material SVBRDF has always been an important research topic. The current research focus is on using portable devices such as mobile phones to acquire images, and recovering the reflection characteristics of materials by acquiring a small number of images. Deschaintre et al. proposed a method to automatically extract the and understanding visual cues such as texture, highlights, and shadows so that the appearance properties of materials can be perceived from a single image. Such methods learn a series of priors and constraints by learning from a large dataset to obtain a visually plausible solution. However, a large number of tests show that this method is not robust, especially for materials such as specular materials whose brightness changes drastically with angle changes, the output results have obvious artifacts on the parameter map, and sometimes the roughness and The specular reflection coefficient estimate has a large deviation from the true value.

发明内容SUMMARY OF THE INVENTION

为克服上述缺陷,本发明提供一种基于便携式设备采集图像估计材质反射参数的方法,该方法通过手机等便携式设备拍摄少数图片,解决Deschaintre方法中容易出现的贴图中存在伪影的现象,并重新估计材质的高光参数和粗糙度,使得恢复出来的材质图像和真实图像更加接近。本方法拍摄一张环境光图像和闪光灯下的图像,来重新估计材质的反射参数。In order to overcome the above-mentioned defects, the present invention provides a method for estimating material reflection parameters based on images collected by a portable device. The method uses a portable device such as a mobile phone to take a few pictures, so as to solve the phenomenon of artefacts in the texture that is easy to occur in the Deschaintre method, and recreate the method. Estimate the specular parameters and roughness of the material, so that the recovered material image is closer to the real image. This method takes an ambient light image and a flash image to re-estimate the reflection parameters of the material.

本发明采用以下技术方案实现:The present invention adopts the following technical solutions to realize:

一种基于便携式设备采集图像估计材质反射参数的方法,通过拍摄一张闪光灯图和环境光图来估计材质的SVBRDF,主要包括如下步骤:A method for estimating material reflection parameters based on an image collected by a portable device. The SVBRDF of a material is estimated by taking a flash image and an ambient light image, which mainly includes the following steps:

结合辅助标定板,分别拍摄一张材质在环境光下和闪光灯下的图片;将环境光图输入到材质估计网络(如Deschaintre等提出的从单幅图像中感知材质的外观属性的方法)中估计材质的粗糙度、镜面反射系数、漫反射系数、法向四张贴图;逐像素标定闪光灯图和环境光图到相机和光源的方向、距离和真实辐照度;求解环境光图和闪光灯图之间的颜色通道校正向量;基于聚类的方法确定相似像素点的位置并采用逐步迭代细化的方式确定最终的聚类类数,为每一类中的点赋予相同反射参数。Combined with the auxiliary calibration board, take a picture of the material under ambient light and flash light respectively; input the ambient light map into the material estimation network (such as the method of perceiving the appearance properties of the material from a single image proposed by Deschaintre et al) to estimate Roughness, specular reflection coefficient, diffuse reflection coefficient, and normal four maps of the material; calibrate the direction, distance and true irradiance of the flash map and ambient light map to the camera and light source pixel by pixel; solve the relationship between the ambient light map and the flash map. The color channel correction vector between them; the clustering-based method determines the position of similar pixel points and adopts the method of step-by-step iterative refinement to determine the final number of cluster classes, and assigns the same reflection parameters to the points in each class.

作为本发明的一个改进,采用拟合方法对环境光图和闪光灯图之间颜色通道校正向量进行求解,由于光场不同,环境光图和闪光灯图颜色存在明显偏色,而决定图像颜色的部分是漫反射部分,因此在拟合时给漫反射项三个颜色通道加入比例系数,使得环境光漫反射部分色调和闪光灯图漫反射部分色调保持一致。As an improvement of the present invention, a fitting method is used to solve the color channel correction vector between the ambient light image and the flash image. Due to the different light fields, the colors of the ambient light image and the flash image have obvious color casts, and the part that determines the color of the image It is the diffuse reflection part, so a proportional coefficient is added to the three color channels of the diffuse reflection term during fitting, so that the tone of the diffuse reflection part of the ambient light is consistent with the tone of the diffuse reflection part of the flash map.

作为本发明的另一个改进,采用逐步迭代细化的方式确定聚类类别。首先初始时将图像中的类别分成较少的类别(如k=[3∶10]),然后逐步迭代细化,并将父类结果作为子类的初始值,直到不再满足继续细分条件。As another improvement of the present invention, the clustering category is determined in a step-by-step iterative refinement manner. First, the categories in the image are initially divided into fewer categories (such as k=[3:10]), and then iteratively refined step by step, and the result of the parent category is used as the initial value of the subcategory until the conditions for continuous subdivision are no longer satisfied. .

本发明的有益效果是:The beneficial effects of the present invention are:

本发明采用拟合方法对环境光图和闪光灯图之间颜色通道校正向量进行求解,使得环境光漫反射部分色调和闪光灯图漫反射部分色调保持了一致,起到了对图像白平衡的作用;采用了逐步迭代细化的聚类方法确定图像中像素类别数量,在保留图像的细节感和拟合的鲁棒性之间进行了平衡,解决了现有方法中该类问题聚类数目难以确定的问题。相比于仅基于神经网络方法估计材质的SVBRDF,本发明方法能够避免产生Deschaintre方法中由于闪光灯光斑引起的伪影,估计出更加合理的镜面反射系数和粗糙度,使得材质渲染结果和真实结果更加接近。The invention adopts the fitting method to solve the color channel correction vector between the ambient light image and the flash image, so that the color tone of the diffuse reflection part of the ambient light and the diffuse reflection part of the flash image are kept consistent, which plays a role in the white balance of the image; The clustering method of gradual iterative refinement is used to determine the number of pixel categories in the image, and a balance is made between retaining the sense of detail of the image and the robustness of the fitting, solving the problem that the number of clusters in the existing method is difficult to determine. question. Compared with the SVBRDF that only estimates the material based on the neural network method, the method of the present invention can avoid the artifacts caused by the flash light spot in the Deschaintre method, estimate a more reasonable specular reflection coefficient and roughness, and make the material rendering results and real results more accurate. near.

附图说明Description of drawings

下面结合附图对本发明的具体实施方式作进一步详细的说明;The specific embodiments of the present invention will be described in further detail below in conjunction with the accompanying drawings;

图1是本发明基于便携式设备采集少量图像估计材质反射参数的流程图;Fig. 1 is the flow chart of the present invention based on the portable device collecting a small amount of images to estimate the material reflection parameter;

图2是本发明采集的4种材质在分别在环境光和闪光灯下拍摄的图片;Fig. 2 is the picture that the 4 kinds of materials collected by the present invention are respectively photographed under ambient light and flash;

图3是本发明和现有方法在4种材质上恢复出来的法向、漫反射、粗糙度和高光贴图对比图。FIG. 3 is a comparison diagram of the normal, diffuse, roughness and specular maps recovered by the present invention and the existing method on four materials.

图4是本发明和现有方法在4种材质上在相同光源下渲染的结果对比图。FIG. 4 is a comparison diagram of the rendering results of the present invention and the existing method on four materials under the same light source.

具体实施方式Detailed ways

如图1所示,本发明提供一种基于便携式设备采集少量图像估计材质反射参数方法,具体步骤如下:As shown in FIG. 1 , the present invention provides a method for estimating material reflection parameters based on a small amount of images collected by a portable device. The specific steps are as follows:

1.材质环境光图和闪光灯图的拍摄。1. Shooting of material ambient light map and flash map.

1.1在相机RAW图模式下进行拍摄,保证图像没有经过ISP流程的非线性变换。1.1 Shoot in the RAW image mode of the camera to ensure that the image does not undergo nonlinear transformation in the ISP process.

1.2放置辅助标定纸在待采集材质区域,在环境光下拍摄一张图像记为I1。保持辅助标定纸位置不变,保持手机闪光灯开启,拍摄一张图像记为I2,拍摄时手机距离材质的距离尽可能近,让角度变化范围大。1.2 Place the auxiliary calibration paper in the area of the material to be collected, and take an image under ambient light, which is marked as I 1 . Keep the position of the auxiliary calibration paper unchanged, keep the mobile phone flash turned on, and take an image and mark it as I 2 . When shooting, the distance between the mobile phone and the material is as close as possible, so that the range of angle changes is large.

2.将环境光图输入到材质估计网络中估计材质的粗糙度、镜面反射系数、漫反射系数和法向贴图。2. Input the ambient light map into the material estimation network to estimate the roughness, specular coefficient, diffuse coefficient and normal map of the material.

将环境光图像I1输入到文献【Deschaintre,Valentin,et al."Single-imagesvbrdf capture with a rendering-aware deep network."ACM Transactions onGraphics(ToG)37(4),1-15,2018.】所提出的网络中,得到漫反射贴图、粗糙度贴图、高光贴图和法向贴图,分别记为ρd、α、ρs和n。其中漫反射贴图ρd、法向贴图n和真实值接近,将这两张贴图作为最终结果,对ρs和α重新进行估计。Input the ambient light image I 1 into the literature [Deshaintre, Valentin, et al. "Single-imagesvbrdf capture with a rendering-aware deep network." ACM Transactions onGraphics(ToG) 37(4), 1-15, 2018.] In the proposed network, diffuse map, roughness map, specular map and normal map are obtained, denoted as ρ d , α, ρ s and n, respectively. Among them, the diffuse reflection map ρ d and the normal map n are close to the real value, and the two maps are used as the final result to re-estimate ρ s and α.

3.逐像素标定到相机和光源的方向、距离和真实辐照度。3. Pixel-by-pixel calibration of the direction, distance and true irradiance to the camera and light source.

标定手机的相机响应曲线f,用于估计图像I1和I2对应的真实辐照度E1和E2,环境光强与相机曝光时间到图像像素亮度之间的映射关系为:The camera response curve f of the mobile phone is calibrated to estimate the true irradiances E 1 and E 2 corresponding to the images I 1 and I 2 . The mapping relationship between the ambient light intensity and the camera exposure time to the image pixel brightness is:

I=f(X)=f(EΔt)I=f(X)=f(EΔt)

其中,对于图像上每一个像素点,E表示单位时间内照射到该像素点的辐照度,即环境光强,X表示该像素点在曝光时间Δt内接收到的总能量,光度响应函数f表示了从X到像素点亮度I的非线性映射。f可逆,定义其逆函数为:Among them, for each pixel point on the image, E represents the irradiance irradiating the pixel point per unit time, that is, the ambient light intensity, X represents the total energy received by the pixel point within the exposure time Δt, and the photometric response function f represents the nonlinear mapping from X to pixel intensity I. f is invertible, and its inverse function is defined as:

g(I)=lnf-1=ln(E)+ln(Δt)g(I)=lnf -1 =ln(E)+ln(Δt)

标定手机的视场角FOV,用于估计图像中每个像素点到光源的方向l和距离d,到相机的方向v。由于闪光灯不可能准确的落在图像的正中央,所以选择图像上前5%最亮的点的矩心作为闪光灯的XY坐标原点。The field of view FOV of the mobile phone is calibrated, which is used to estimate the direction l and distance d from each pixel in the image to the light source, and the direction v to the camera. Since it is impossible for the flash to fall in the exact center of the image, the centroid of the top 5% brightest points on the image is selected as the XY coordinate origin of the flash.

4.求解环境光图和闪光灯图之间的颜色通道校正向量。4. Solve for the color channel correction vector between the ambient light map and the flash map.

由于光场的不同,环境光图和闪光灯图颜色存在明显偏色,而决定图像颜色的部分是漫反射部分,所以在拟合时给漫反射项三个颜色通道加入比例系数,拟合公式为:Due to the difference in the light field, the colors of the ambient light map and the flash map have obvious color casts, and the part that determines the color of the image is the diffuse reflection part, so a proportional coefficient is added to the three color channels of the diffuse reflection term during fitting, and the fitting formula is: :

Figure BDA0002852111830000051
Figure BDA0002852111830000051

其中,[r,g,b]为控制颜色通道比例向量;r2为像素到光源的距离;Lr为相机接收到辐照度,Li为光源射出的辐照度。Among them, [r, g , b] is the proportional vector of the control color channel; r 2 is the distance from the pixel to the light source; L r is the irradiance received by the camera, and Li is the irradiance emitted by the light source.

在闪光灯图中,环境光没有被明确的建模出来,而是被隐式的整合到SVBRDF模型中去。In the flash map, ambient light is not explicitly modeled, but is implicitly integrated into the SVBRDF model.

假设全图中所有的点的粗糙度和镜面反射系数是一致的,利用图像中所有的点来拟合出通道系数[r,g,b],求解过程采用Levenberg-Marquarelt算法。Assuming that the roughness and specular reflection coefficient of all points in the whole image are consistent, use all points in the image to fit the channel coefficients [r, g, b], and the solution process adopts the Levenberg-Marquarelt algorithm.

5.基于聚类的方法确定相似像素点的位置并采用逐步迭代细化确定最终的聚类类数。5. The clustering-based method determines the positions of similar pixels and adopts step-by-step iterative refinement to determine the final number of clusters.

5.1使用聚类方法判断相似点位置。将环境光图I1作为判定像素点类别的基准图像,为了更好衡量颜色的距离,将图片从RGB颜色空间转到CIE 1976L*a*b*颜色空间。5.1 Use the clustering method to determine the location of similar points. The ambient light image I 1 is used as the benchmark image for determining the category of pixel points. In order to better measure the distance of the color, the image is transferred from the RGB color space to the CIE 1976L*a*b* color space.

5.2使用K-means聚类方式,质心初始化方式使用了K-means++,为提高运算速度,使用了基于三角不等式的聚类加速算法。5.2 The K-means clustering method is used, and the centroid initialization method uses K-means++. In order to improve the operation speed, a clustering acceleration algorithm based on triangular inequality is used.

5.3确定聚类类别。首先初始时将图像中的类别分成较少的类别k=[3:10],然后逐步迭代细化,并将父类结果作为子类的初始值,直到不再满足继续细分的条件,为每类中的点赋予相同反射参数。可以继续细分需要的要求为:5.3 Determine the clustering category. First, the categories in the image are initially divided into fewer categories k=[3:10], and then iteratively refined step by step, and the parent category result is used as the initial value of the subcategory until the conditions for continued subcategory are no longer satisfied, which is Points in each class are assigned the same reflection parameters. The requirements that can be further subdivided are:

Ni>λ1·(w·h),λ1∈(0.05,0.2)N i1 ·(w·h), λ 1 ∈(0.05, 0.2)

Di>λ2·min(w,h),λ2∈(0.2,0.5)D i2 ·min(w, h), λ 2 ∈(0.2, 0.5)

其中,Ni表示第i簇中像素的数量,Di表示第i簇中每一个点到簇中所有点空间分布质心位置的平均距离,w和h分别为图像的宽和高,λ1和λ2为控制系数。Among them, Ni represents the number of pixels in the i-th cluster, D i represents the average distance from each point in the i-th cluster to the centroid of the spatial distribution of all points in the cluster, w and h are the width and height of the image, respectively, λ 1 and λ 2 is the control coefficient.

实施例1Example 1

本实施例主要对比现有方法(具体参见【Deschaintre,Valentin,et al."Single-image svbrdf capture with a rendering-aware deep network."ACM Transactions onGraphics(ToG)37(4),1-15,2018.】)和本发明的方法在现实材质中的估计结果进行比较。图2为在环境光和闪光灯下采集的4种材质图片。图3为本发明和现有方法的比较,可以发现,本发明方法没有现有方法中普遍存在的伪影现象,而且本方法估计出来的高光贴图和粗糙度贴图更加符合客观实际,从图4的渲染结果来看,本方法重新渲染的图像和现有方法相比更加接近实际采集的图像。This embodiment mainly compares the existing method (for details, see [Deschaintre, Valentin, et al. "Single-image svbrdf capture with a rendering-aware deep network." ACM Transactions onGraphics (ToG) 37(4), 1-15, 2018 .]) and the estimation results of the method of the present invention in real materials are compared. Figure 2 shows images of four materials collected under ambient light and flash. Fig. 3 is a comparison between the present invention and the existing method. It can be found that the method of the present invention does not have the common artifacts in the existing method, and the specular map and roughness map estimated by the method are more in line with the objective reality. From Fig. 4 Compared with the existing method, the image re-rendered by this method is closer to the actual collected image.

以上所述的具体实施方式对本发明的技术方案和有益效果进行了详细说明,应理解的是以上所述仅为本发明的优选实施例子,并不用于限制本发明,凡在本发明的原则范围内所做的任何修改、补充和等同替换等,均应包含在本发明的保护范围之内。The specific embodiments described above describe in detail the technical solutions and beneficial effects of the present invention. It should be understood that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Anything within the scope of the principles of the present invention Any modifications, additions and equivalent substitutions made within the scope of the present invention shall be included in the protection scope of the present invention.

Claims (1)

1.一种基于便携式设备采集图像估计材质反射参数的方法,其特征在于,通过拍摄一张闪光灯图和环境光图来估计材质的SVBRDF,该方法步骤如下:1. a method for estimating material reflection parameters based on portable equipment collection image, is characterized in that, by taking a flash light map and ambient light map to estimate the SVBRDF of material, the method steps are as follows: (1)根据环境光图估计材质的粗糙度、镜面反射系数、漫反射系数和法向贴图;逐像素标定闪光灯图和环境光图到相机和光源的方向、距离和真实辐照度;(1) Estimate the roughness, specular reflection coefficient, diffuse reflection coefficient and normal map of the material according to the ambient light map; calibrate the direction, distance and true irradiance from the flash map and ambient light map to the camera and light source pixel by pixel; (2)求解环境光图和闪光灯图之间颜色通道校正向量;(2) Solve the color channel correction vector between the ambient light map and the flash map; (3)基于聚类的方法确定相似像素点的位置并采用逐步迭代细化的方式确定最终的聚类类数,为每类中的点赋予相同反射参数;(3) The method based on clustering determines the position of similar pixel points and adopts the method of gradual iterative refinement to determine the final number of clustering classes, and assigns the same reflection parameters to the points in each class; 所述的步骤(2)中:采用拟合方法对环境光图和闪光灯图之间颜色通道校正向量进行求解,在拟合过程中给漫反射项三个颜色通道加入控制比例的参数,使得环境光图漫反射部分色调和闪光灯图漫反射部分色调保持一致;In the described step (2): a fitting method is used to solve the color channel correction vector between the ambient light image and the flash image, and in the fitting process, parameters for controlling the ratio are added to the three color channels of the diffuse reflection item, so that the environment The color tone of the diffuse reflection part of the light map is consistent with that of the diffuse reflection part of the flash map; 所述步骤(3)具体为:初始时只将图像中像素点的类别分成较少的类别,然后逐步迭代细化,并将父类的结果作为子类的初始值,直到不再满足继续细分的条件,为每类中的点赋予相同反射参数;The step (3) is specifically as follows: at the beginning, only the categories of the pixel points in the image are divided into fewer categories, and then iteratively refines step by step, and the result of the parent category is used as the initial value of the subcategory, until it is no longer satisfied to continue the refinement. The conditions of the points are assigned the same reflection parameters to the points in each category; 其中,继续细分的条件为:Among them, the conditions for continued subdivision are: Ni>λ1·(w·h),λ1∈(0.05,0.2)N i1 ·(w·h), λ 1 ∈(0.05, 0.2) Di>λ2·min(w,h),λ2∈(0.2,0.5)D i2 ·min(w, h), λ 2 ∈(0.2, 0.5) 其中,Ni表示第i簇中像素的数量,Di表示第i簇中每一个点到簇中所有点空间分布质心位置的平均距离,ω和h分别为图像的宽和高,λ1和λ2为控制系数。Among them, Ni represents the number of pixels in the i-th cluster, D i represents the average distance from each point in the i-th cluster to the centroid position of the spatial distribution of all points in the cluster, ω and h are the width and height of the image, λ 1 and λ 2 is the control coefficient.
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