基于统计复杂性测度、多重分形谱等方法的柑橘品质分级

基于统计复杂性测度、多重分形谱等方法的柑橘品质分级

曹乐平1, 温芝元2*

(1.湖南生物机电职业技术学院科研处,长沙410127;2.湖南农业大学理学院,长沙410128)

摘要为精确地度量柑橘品质分级,研究了病虫害为害状冰糖橙缺陷果实复杂性测度机器识别、脐橙果实周长-面积分形维数与分段色调单位坐标化多重分形谱高度/宽度的形状和颜色分级及糖酸度无损检测。对冰糖橙生理性缺硼、锈壁虱、油胞凹陷病3种常见病虫害果实为害状缺陷在0°—50°主色调区域实施长度为1°的分段,统计各分段色调区间像素分布概率,并计算统计复杂性测度C(Y)与Shannon信息熵H(Y),以C(Y)与H(Y)为检索词计算机查询果实病虫害检索表来进行病虫害缺陷果机器识别,平均正确识别率为93.33%。对脐橙果实果梗面与侧面在相垂直的2个投影面上的图像进行去背景与边界轮廓提取操作,计算边界轮廓周长-面积分形维数,以此为指标检索果实信息字典进行脐橙形状分级,正确率100%。以脐橙果实相对的2个侧面图像为研究对象,去其背景,将30°—120°主色调区域进行30°—50°、50°—70°、70°—90°和90°—120°的区间分割,生成4幅色调图像,计算此图像多重分形谱质心坐标、高度与宽度,对该高度与宽度进行单位质心坐标化处理,一方面以单位质心坐标化多重分形谱高度与宽度为指标检索果实信息字典进行脐橙颜色分级,正确率98%;另一方面以单位质心坐标化多重分形谱高度与宽度为参数通过糖酸度偏最小二乘模型映射果实糖酸度,糖度与酸度标准差分别在0.77及0.36以内,与实际值的相关系数分别在0.8及0.7以上。试验结果表明：统计复杂性测度、周长-面积分形维数、单位质心坐标化多重分形谱高度与宽度较精确地反映了柑橘分级中需识别的冰糖橙果实病虫害缺陷的特征、脐橙果实形状与颜色特性及内部糖酸度无损检测映射参数特点。

关键词冰糖橙与脐橙; 复杂性测度; 分形维数; 多重分形谱; 病虫害缺陷果机器识别; 形状与颜色机器分级; 糖酸度无损检测

中图分类号S 126; S 666.4文献标志码A

Citrus quality grading based on statistical complexity measurement and multifractal spectrum method. Journal of ZhejiangUniversity (Agric. & LifeSci.), 2015,41(3)：309-319

Cao Leping1, Wen Zhiyuan2*(1.ScientificResearchDepartment,HunanBiologicalandElectromechanicalPolytechnic,Changsha410127,China; 2.CollegeofScience,HunanAgriculturalUniversity,Changsha410128,China)

SummaryCitrus quality grading can raise the observability degree and grade degree of citrus, improving the product level and increasing market competitiveness. It can also make huge economic and social benefits and increase farmers income and agricultural productivity so as to promote the sustained and healthy development of the citrus industry.

For the purpose of precise measurement of citrus quality grading, the complexity measurement of Bingtang orange defective fruit damaged by diseases and insect pest patterns were studied by machine recognition, along with the navel orange fruit perimeter-area fractal dimension and the shape, color grading and sugar acid nondestructive detection of section tone unit coordinates multifractal spectrum height and width.

Physiological boron deficiency,Eriophyesoleivorusand rind oil spotting disease were very common in Bingtang orange fruits. The 0°—50° main tone region of these diseases and insect pests damage pattern were augmented into the length of 1°, and pixel distribution probability of each segment tone, complexity measurementC(Y) and Shannon entropyH(Y) were calculated.C(Y) andH(Y) were set as the features to identify fruit diseases and insect pests by machine recognition. The background and extracting boundary contour from the two projection images formed by navel orange fruits’ stalk surface and side perpendicular were removed, and then perimeter-area fractal dimension was calculated. The result was used as index to retrieve fruit information and navel orange shape grading. The two side images where navel oranges were relative were set as the research object, and then the background was extracted, and the main tone region 30°—120°of two images were segmented into 30°—50°, 50°—70°, 70°—90° and 90°—120°, and four tone images were created. Its multifractal spectrum barycentric coordinate, height and width were calculated. The height and width were transformed into the unit barycentric coordinate. On one hand, multifractal spectrum height and width of the unit barycentric coordinate were set as the index and were retrieved in fruit information dictionary to grade navel oranges by color; on the other hand, multifractal spectrum height and width of the unit barycentric coordinate were set as parameters and reflected the degree of fruit sugar and acidity by sugar and acidity partial least square mode.

The average correct recognition rate of Bingtang orange disease and insect pest defect fruit was 93.33%. The correct rate of navel orange fruit shape grading was 100%. The correct rate of navel orange color grading was 98%. The standard deviations of sugar and acidity in navel orange were within 0.77 and 0.36, separately. And the correlation coefficients with the true value were above 0.8 and 0.7.

The above results show that calculating complexity measurement, perimeter-area fractal dimension, unit barycentric coordinate multifractal spectrum height and width can better reflect the characteristics of Bingtang orange fruits with disease and insect pest defects which need to grade citrus fruit quality, and can also reflect navel oranges fruit shape, color characteristics and internal sugar and acidity level which are nondestructive detection mapping parameter features.

Key wordsBingtang orange and navel orange; complexity measurement; fractal dimension; multifractal spectrum; machine recognition of defective fruits with diseases and insect pests; machine grading for shape and color; nondestructive detection of sugar acidity

复杂性本身复杂多样,至今复杂性科学的发展还处于萌芽阶段,缺少对复杂性统一的定义[1-3].Seth Lloyd总结的复杂性就有分形维、重分形、熵、计算复杂性等31条定义,也正是因为复杂性定义的多样性,对不同定义下复杂性的刻画方法也就各不相同。如何刻画复杂性问题的复杂性是20世纪科学前沿与研究热点,岩石的海水与油饱和特性[4]、社会公众部门的业务流程问题[5]、软件调整的规模问题[6]就是复杂性测度的应用尝试。

柑橘作为一生物体,其生长过程受众多因素的影响使其形状、颜色、内部品质及病虫害为害状呈现复杂性,部分学者对此类问题进行了复杂性量测的研究。用果梗面和侧面柑橘轮廓盒维数作为形状特征值,0°—100° 5个等分色调区间色调盒维数作为颜色特征值进行柑橘形状与颜色分级,平均正确分级率95.83%[7];以脐橙果实病虫害为害状轮廓分形维数作为特征值之一,结合为害状红色、绿色、蓝色3个颜色参数识别其病虫害,平均正确识别率为85.51%[8];用病虫害为害状多重分形谱特征值识别柑橘果实病虫害,平均正确识别率分别为83.12%和92.67%[9-10]。形状与颜色的盒维数刻画只计盒子数,未考虑盒子内像素数使其形状与颜色的描述粗糙,影响分级正确率;以为害状区域颜色分量均值和为害状边界分形维数作为病虫害识别特征形状表达较充分,但识别病虫害的典型小色斑信息因调和而被弱化,影响病虫害正确识别率;以为害状多重分形谱参数作为病虫害识别特征,虽结合了为害状的形状与颜色信息,但计算过程较为复杂,计算机消耗大。有鉴于此,本文运用周长-面积分形维数、多重分形、熵、统计复杂性测度理论,分别研究脐橙果实形状与颜色计算机分级、糖酸度无损检测及冰糖橙果实病虫害计算机识别的柑橘实际问题。

1试验设备、软件与样本

1.1试验设备与图像分析软件

纽荷尔脐橙果实及冰糖橙果实病虫害图像拍摄像机为索尼DSC-H20,焦距38～380 mm,对焦范围25 mm～∞,镜头f=6.3～63 mm,最高分辨率3 648～2 736像素,快门速度1/4～1/1 600 s。计算机Lenovo PⅣ2.13 GHz CPU,内存512 MB。图像分析软件Matlab R2010a及ACDSee 10。

1.2试验样本

2013年10月上旬与11月中旬先后2次分别在湖南省永州市蓝山县与怀化市麻阳县进行健康脐橙果实和冰糖橙病虫害果实采样采摘,红黄色、黄色、绿黄色、黄绿色、绿色健康脐橙果实各色学习样本与检验样本均采样100个;生理性缺硼(physiological deficient boron)[11]、锈壁虱(Eriophyesoleivorus)、油胞凹陷病(rind oil spotting disease)[12]3种常见的病虫害冰糖橙果实学习样本与检验样本采样100个。洗净2类果实样本的果面,并晾干。用白纸衬底在自然光照条件下拍摄冰糖橙果实病虫害为害状图像及健康脐橙果实果梗面与相对2侧面图像。所采集的果实图像用ACDSee 10软件进行512像素×512像素裁切,备后续图像分析用。

2试验理论与方法

复杂性问题一般具有非线性、多样性、多层次性、自相似性等多种复杂特征[13-15],周长-面积分形维数、多重分形、信息熵与统计复杂性测度(statistical complexity measurement)就是解决这类具有复杂特征问题的理论方法。

2.1周长-面积分形维数

分形维数是刻画非规则曲线特征差异的重要理论工具,Mandelbrot提出封闭的粗糙曲线周长Q与面积A满足Q∝A0.5D关系,将这种关系应用到柑橘果实的分形上有周长-面积分形维数D[16-17].

(1)

2.2多重分形

多重分形考虑了尺度单元中像素数使结果包含了许多被简单分形所忽略的信息,目前已成为研究分形物质的重要手段。定义概率p(δ)的q次方加权和为一配分函数χq(δ)[18-21].

(2)

δτ(q),

(3)

式中τ(q)为质量指数。

依据统计物理方法有

f(α)=αq-τ(q),

(4)

式中:f(α)为多重分形谱;α=dτ(q)/dq为奇异指数。

2.3统计复杂性测度

近年来,随着非线性科学的发展与混沌运动研究的不断深入,系统复杂性的深入研究越来越有必要。复杂性测度是对对象复杂程度的客观度量,大体包含统计复杂度和算法复杂度2大类[22-25],本文引入统计复杂性测度。

在信息熵的基础上,R. Lòpez-Ruiz等定义统计复杂性测度

C(Y)=H(Y)B(Y),

(5)

(6)

(7)

显然,C(Y)反映了系统内在排列无序性及系统结构规则性,可以较方便地表达复杂性的程度。

2.4试验方法

2.4.1形状分级根据周长-面积分形维数理论对脐橙果实按以下步骤进行形状分级.

1)依据亮度直方图双峰分布特性,取谷底亮度作为阈值去除脐橙果实背景,备形状及颜色分级和糖酸度无损检测使用。

2)提取脐橙果实边界,并进行边界跟踪与细化。

3)统计果梗面及一个侧面图像果实边界像素与果实区域像素。

4)作边界像素与区域像素数的最小二乘拟合,根据拟合直线截距计算水果形状因子β。

5)根据式(1)计算脐橙果实果梗面、一个侧面的分形维数,以此作为脐橙果实形状分级的特征值。

6)计算机检索脐橙果实信息字典,进行形状定级。

2.4.2颜色分级及糖酸度无损检测运用多重分形理论对脐橙果实实施下列步骤的颜色分级及糖酸度无损检测.

1)对亮度阈值法去背景的2个侧面脐橙果实图像进行色调-饱和度-亮度(HSI)色空间转换。

2)对脐橙果实图像色调分布范围[30°,120°]进行30°—50°、50°—70°、70°—90°和90°—120°的区间分割,生成4幅色调图。

3)统计δ×δ(δ=21,22,…,29)滑动窗口内及整幅色调图像像素nij及N,计算像素分布概率Pij(δ)=nij/N(i,j=20,21,…,28)。

5)各色调区间多重分形谱位置与形状均存在差异,为便于比较,计算单位坐标化多重分形谱高度η=Δf/f(αc)及单位坐标化多重分形谱宽度μ=Δα/αc来作为脐橙果实颜色特征值。

6)计算机检索脐橙果实信息字典,进行颜色定级与糖酸度映射。

2.4.3脐橙果实信息字典参照《鲜柑橘》(GB/T12947—2008)将脐橙果实外观品质分为优等、一等、二等、等外4个等级,果形用果梗面及1个侧面的2个分形维数作为评价指标,其整体分布区间为(1,2),依据纵横径比果形指数在人工对500个学习样本等级评定的基础上计算果梗面及侧面分形维数的级间界点,以此作为分形维数等级区间的上下限sub与inf。颜色指标依据《柑橘等级规格》(NY/T1190—2006)进行学习样本着色面积的人工评定,再计算等级间单位坐标化多重分形谱高度η及宽度μ来确定infη、infμ、subη、subμ。

脐橙果实糖酸度按照食品卫生检测方法理论部分总则(GB/T5009.1—2003)与食品中总酸的测定方法(GB/T12456—1990)分别用WYT-4型上海有限公司生产的手持糖度计及PHS-2F型南京庚辰科学仪器公司生产的数字pH计,对图像采集后的学习样本与检测样本取果肉榨汁搅拌均匀进行逐个检测,将学习样本检测结果与脐橙果实4个色调区间单位坐标化多重分形谱高度及单位坐标化多重分形谱宽度进行偏最小二乘回归,建立检测样本糖酸度无损检测模型,检测样本糖酸度用于模型评价。

(8)

(9)

用果梗面分形维数、侧面分形维数、侧面单位坐标化多重分形谱高度与宽度、糖度和酸度6个指标,建立脐橙果实信息字典,进行果实机器等级查询定级与糖酸度无损检测(表1),t为1,2,3和4时分别对应优等果、一等果、二等果及等外果,高一等级形状与颜色等级区间上限sub对应低一等级形状与颜色等级区间下限inf,保证整体等级区间连续不间断。

表1　脐橙果实信息字典

2.4.4病虫害缺陷果识别根据统计复杂性测度理论对冰糖橙果实病虫害为害状缺陷进行以下步骤的机器识别：1)在设置亮度阈值去除冰糖橙果实背景的基础上进行彩色图像(RGB空间)至(HSI空间)转换。2)改进型分水岭算法进行果实病虫害为害状边界提取,对过分割的区域实行区域连通合并。3)根据为害状边界提取病虫害为害状,统计其像素M。4)对病虫害为害状色调进行长度为1°的区间分割,统计各分割区间像素mk,计算各分割区间像素分布概率ρk(yk)=mk/M。5)根据式(7)、(6)、(5)分别计算B(Y)、H(Y)、C(Y),依据病虫害果实学习样本确定柑橘生理性缺硼、锈壁虱、油胞凹陷病3种常见病虫害的为害状缺陷C(Y)、H(Y)范围,按检测样本C(Y)和H(Y)值计算机查找其所处范围,进而确定哪类病虫害缺陷果实,如表2所示,对于超检索范围的情形依据数值与检索范围最近的原则进行判别。

表2　冰糖橙果实病虫害检索表

3结果与分析

3.1结果

依据脐橙果实形状、颜色特征值计算机查询信息字典,进行果实形状、颜色单独定级与糖酸度无损检测,特征值超出形状与颜色检索范围的,以与哪个等级区间距离最近评定为哪级的最短距离原则实施等级界定;颜色特征值跨2个等级的以属于哪级指标数多界定为哪级为原则,若出现属于2个等级指标数一致的情形则以2个等级中低的等级进行评定。对比人工等级评定结果,计算机形状分级正确率100%,颜色分级正确率98%,5种颜色共500个检验样本糖度与酸度无损检测相对误差范围分别为-19.79%～30.90%和-19.37%～24.38%。

根据复杂性测度C(Y)、Shannon信息熵H(Y)2个特征识别参数值计算机查询冰糖橙果实病虫害检索表,生理性缺硼、锈壁虱、油胞凹陷病3种病虫害为害状缺陷果各100个检验样本的正确识别率分别为93%、95%和92%,3种病虫害为害状缺陷果平均正确识别率为93.33%。

3.2分析

3.2.1形状分级分析按形状分级试验方法的步骤计算健康果实互相垂直的果梗面及侧面2个投影面分形维数,D1∈[1.010 2,1.017 0],D2∈[1.018 9,1.025 8],标准差s1=0.000 9,s2=0.001 3。脐橙果实果梗面投影接近于圆,分形维数较小,果实侧面投影接近椭圆,分形维数较大。按周长-面积分形维数形状等级区间划分,优等、一等、二等及等外4个等级界定清楚无误.图1为100个检测样本计算形状分级情况,①、②、③、④、⑤和Ⅰ、Ⅱ、Ⅲ、Ⅳ、Ⅴ分别为果梗面及与侧面形状等级区间界点inf和sub,优等为①、②水平线与Ⅰ、Ⅱ铅垂线围成的矩形区域,一等、二等及等外分别为②、③水平线与Ⅱ、Ⅲ铅垂线,③、④水平线与Ⅲ、Ⅳ铅垂线,④、⑤水平线与Ⅳ、Ⅴ铅垂线围成的“7”字形区域,图中优等果7个、一等果18个、二等果39个、等外果36个。2个互相垂直的投影面果实轮廓分形维数较准确地刻画了果实准椭球体的立体形状特征,检测样本计算机形状分级未出现误判,较文献[8]正确分级率高,果实形状表达较以几何参数进行形状度量的文献[26-27]及以傅里叶描述子刻画形状的文献[28]精确与全面,正确分级率高。

3.2.2颜色分级分析脐橙果实颜色表征按其试验方法的步骤分析果实多重分形特征,如图2所示,在δ=26～29范围内配分函数呈近似放射状,该尺度区间可认为具有标度不变性,在该区间研究其多重分形谱特性才有理论依据。图3为红黄、黄色、绿黄、黄绿、绿色各1个检测样本在30°—50°、50°—70°、70°—90°和90°—120° 4个色调区间的多重分形谱线。

图1　检验样本分形维数分布 Fig.1　Fractal dimension of test samples

图2　黄色果实标度 Fig.2　Yellow fruit scales

A:红黄果;B:黄果;C:绿黄果;D:黄绿果;E:绿果. A: Red-yellow fruit; B: Yellow fruit; C: Green-yellow fruit; D: Yellow-green fruit; E: Green fruit. 图3　多重分形谱 Fig.3　Multifractal spectra

由图3可知,分形谱虽有形状的不同,但位置也存在明显差异,对分形谱高度与宽度分别以质心纵横坐标进行单位坐标化处理,一方面降低了颜色表征数据维数,另一方面避免了数据交叉与重叠,充分反映与表达了等级间脐橙果实色泽的差异。图4为图3单位坐标化多重分形谱高度与宽度分布。脐橙果实以4个色调区间单位坐标化多重分形谱高度与宽度8个颜色特征参数进行颜色分级,较以0°—100° 5等分色调区域分形维数为颜色分级参数的文献[1]分级正确率高,较以红色、绿色或蓝色均值为颜色特征值进行果实色泽分级的文献[29-31]颜色描述彻底,分级精度有明显改进。

A: 30°—50°; B: 50°—70°; C: 70°—90°; D: 90°—120°. 图4　多重分形谱高度与宽度分布 Fig.4　Height and width distribution of multifractal spectra

3.2.3糖酸度无损检测分析根据糖酸度偏最小二乘无损检测模型,用30°—50°、50°—70°、70°—90°和90°—120° 4个色调区间的单位坐标化多重分形谱高度与宽度映射脐橙果实糖度与酸度,糖度、有效酸度预测标准差分别为0.765 2和0.358 7,5种颜色共500个检验样本糖度与酸度无损检测值与实际值相关系数r分别在0.8和0.7以上.图5表明了5种颜色各20个检测样本糖酸度无损检测与理化检测的相关程度。以单位坐标化多重分形谱高度与宽度8个颜色特征参数无损检测脐橙果实糖度与酸度,其相对误差较以0°—120° 6等分色调区域分形维数为参数的文献[16]低,糖度与酸度无损检测值与实际值相关系数高。

3.2.4病虫害缺陷果识别分析以改进型分水岭算法进行脐橙病虫害为害状边缘检测存在过分割现象,在此基础上进行检测区域联通与合并生成病虫害为害状边界轮廓,依据此轮廓提取脐橙病虫害为害状,使后续图像分析与特征参数提取不受果面其他区域的影响。图6为3种病虫害缺陷果各1个样本病虫害边界轮廓、病虫害为害状情况。

考察色调0°—50°之间像素,各病虫害为害状在该区域像素占0°—360°色调像素比均在95%以上,该色调区间像素分布不失一般性,同时也减轻了计算工作量.表3给出了检测样本0°—50°色调区间像素分布概率范围及复杂性测度C(Y)、Shannon信息熵H(Y)均值.从中可以看出,不同病虫害果面留下的为害状缺陷其C(Y)、H(Y)2个参数有所不同,较以果面病虫害为害状缺陷红色、绿色、蓝色分量和为害状边界分形维数为特征值的文献[8]平均识别正确率高,较以果面病虫害为害状缺陷多重分形谱高度、宽度为参数的文献[9],及以果面病虫害为害状缺陷傅里叶变换幅度谱图多重分形谱的高度、宽度和质心坐标作为特征值的文献[10]识别方法简单,平均识别正确率稍有提高,说明能用此方法识别病虫害缺陷果。

图5　检验样本糖酸度预测值与实际值相关性 Fig.5　Relationship between prediction and true values sugar content or valid acidity in test samples

A:锈壁虱样本;B:锈壁虱边界轮廓;C:锈壁虱为害状;D:生理性缺硼样本;E:生理性缺硼边界轮廓;F:生理性缺硼为害状;G:油胞凹陷病样本;H：油胞凹陷病边界轮廓;I:油胞凹陷病为害状。 　　A：E. oleivorus sample; B： E. oleivorus boundary; C： E. oleivorus damage pattern; D： Physiological boron deficiency sample; E： Physiological boron deficiency boundary; F： Physiological boron deficiency damage pattern; G： Rind oil spotting disease sample; H： Rind oil spotting disease boundary; I： Rind oil spotting disease damage pattern。 图6　冰糖橙病虫害为害状 Fig.6　Damage patterns of diseases and insect pests in Bingtang orange

检测样本Testsamples锈壁虱E.oleivorus生理性缺硼Physiologicalborondeficiency油胞凹陷病Rindoilspottingdiseaseρ(y)[0,0.1282][0,0.1270][0,0.2357]C(Y)7.19556.83877.4759H(Y)4.23204.32614.1143

4讨论与结论

4.1脐橙果实呈准椭球状,用其投影面轮廓的纵径与横径比表达果实典型形状特征,仅仅是刻画了在轮廓曲线为椭圆的假设前提下长轴与短轴的长度比,其实质是估计果实纵横向大小尺寸关系。若用傅里叶描述子的前几个谐波分量度量果实轮廓形状,虽形状表达细腻程度有所提高,但也仅是在三角度、方形度等形状规则程度上的改进,果实轮廓的局部与整体弯曲信息表达粗糙不彻底。通过互相垂直的果梗面及侧面投影分别提取果实在该2个投影面上轮廓的周长-面积分形维数,一方面单个投影面上果实轮廓曲线形状表达完整,覆盖了轮廓曲线的各个部分;另一方面准椭球状果实立体形状得以刻画,且形状描述数据仅2维,减少了计算机消耗。

4.2脐橙果实生长受光照、气候条件等众多因素的影响,果面着色并非均匀一致,存在色差。以果面颜色分量均值为指标反映果实颜色特征,整体颜色特征得到表达,但影响果实等级的小色块、小疤痕被忽略。将果实主要色调区间等分,用各等分区间色调分形维数度量果实颜色,考虑了果面着色不均匀的情况,在色泽的描述上较颜色分量均值法精细,但还缺少各色调的分布信息。用脐橙果实相对的2个侧面30°—120°的4个色调区间单位坐标化多重分形谱高度、宽度作为果实颜色特征值,一方面考虑了绝大部分果面的着色,避免了因采集果实多幅图像而出现部分果面重复采图与重复计算的现象,另一方面分段色调多重分形过程中像素的累计信息与分布信息得到丈量,覆盖了影响果实等级的小色块、小疤痕情况,颜色度量更为精细彻底。

4.3果实糖酸度无损检测技术较多,近红外光谱、激光、X射线及高光谱图像技术都可应用于果实内部品质的无损检测,且有一定的精度,但机器视觉技术设备简单、成本低、数据量少、计算机消耗小,不失为果实内部品质无损检测的通用方法之一。果面分段色调单位坐标化多重分形谱高度与宽度映射脐橙果实糖酸度因果面颜色刻画精细标准差较低,分别在0.77和0.36以内,与实际值间的相关系数较高,分别在0.80和0.70以上,能基本确定果实糖酸度,表明该方法可用于脐橙果实糖酸度无损检测。

4.4冰糖橙果实病虫害众多,虽各病虫害为害状具备典型特征,但如何用较少的数据以较全面地反映果实病虫害为害状这一缺陷典型特征没有定论。病虫害为害状分形维数反映的是形状信息,若结合为害状的颜色(颜色分量均值)来识别病虫害缺陷果,会因均值计算中为害点状或线状典型特征,被调和近乎忽略而收不到应有的效果。综合了果实病虫害为害状缺陷分段色调像素累计信息与形状信息的多重分形谱方法、复杂性测度法不失为有效方法,尤其是复杂性测度法因色调分段细微(仅为1°),点状、线状缺陷被保留未被大色块调和而展现出优势。

总之,柑橘形状与颜色分级、糖酸度无损检测、病虫害果实缺陷识别等问题,因面对的是柑橘生物体而呈现出复杂性,用统计复杂性测度、分形维数、多重分形谱方法进行复杂性问题的复杂性量测,较精确地反映了冰糖橙果实病虫害缺陷典型特征、脐橙果实形状、颜色特征和糖酸度无损检测的映射参数特点。

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