# definitions and usages of options such as “Count” ,”Area”, “ConvexCount”, and “ConvexArea”

I would like to use ComponentMeasurements to do image analysis on porus materials. However definitions andusages of options such as “Count” ,”Area”, “ConvexCount”, and “ConvexArea” are not well documented. I tried to use these options in a simple case. I made a testimage by using EXCELL and Photoshop.
(TEST1)

    <<ComputationalGeometry
data1=Import[“test image3.jpg”];
data1a=Binarize[data1];
data3=ImageData[data1a];
Dimensions[data3]
{700,700}
data5=Table[{i,j,data3[[i,j]]},{i,1,700},{j,1,700}];
data6=Flatten[data5,1];
data7=Select[data6,#[[3]]0&];(*counting number of black element*)
data8=Map[{#[[1]],#[[2]]}&,data7];
Dimensions[data8]
{50197,2}


(Therefore area fraction of black elements with repect to entire image elements is 50197/490000=0.102442857.This is comparable to 0.102040816)

(TEST2)

data9=ConvexHull[data8];
data10=PlanarGraphPlot[data8,data9,LabelPoints®False]


(*This consits of 25 blocks and 5 of them are black. Area fraction of black blocks with repect to the entire ConvexHull is 5/25=0.2. *)

data11=ConvexHullArea[data8](*area of the ConvexHull*)
249498


(Therefore area fraction of black elements with repect to entire CovexHull is 50197/249498=0.201191993. This is comparable to 0.2)

(TEST3*) I think that we can do same things by using ComponentMeasurements with options such as “Count” ,”Area”,“ConvexCount”, and “ConvexArea.”

data12a=ComponentMeasurements[data8,”Count”];(*number of element*)
data13a=ComponentMeasurements[data8,”Area”];(*area of element*)
data14a=Map[{#[[1]],#[[2]]}&,data12a];(*number of element*)
data15a=Map[{#[[1]],#[[2]]}&,data13a];(*area of element*)
data16a=Apply[Plus,Map[#[[2]]&,data15a]](*total number of element*)
112944
data17a=Apply[Plus,Map[#[[2]]&,data16a]](*total area of element*)
112944
data12b=ComponentMeasurements[data8,”ConvexCount”];(*number of element in convex hull polygon*)
data13b=ComponentMeasurements[data8,”ConvexArea”];(*area of element in convex hull polygon*)
data14b=Map[{#[[1]],#[[2]]}&,data12b];(*number of element in convex hull polygon*)
data15b=Map[{#[[1]],#[[2]]}&,data13b];(**area of element in convex hull polygon**)
data16b=Apply[Plus,Map[#[[2]]&,data15b]](*total number of element in convex hull polygon*)
1.64599 ´ 107
data17b=Apply[Plus,Map[#[[2]]&,data16b]](**total area of element in convex hull polygon**)
1.64599 ´ 107


However, definitions and usages of these options are not well documented. I could not get simillar results shown in TEST 1&2. Please give me your advices. Thanks in advance.

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• I think this question can be improved by providing minimal examples and clear questions. – bobthechemist Nov 17 '14 at 17:01

ComponentMeasurements[] counts WHITE components:

img = Import@"http://i.stack.imgur.com/OLjyi.jpg";
data8 = ColorNegate@Binarize@img;

data12a = ComponentMeasurements[data8, "Count"]
data13a = ComponentMeasurements[data8, "Area"]
data12b = ComponentMeasurements[data8, "ConvexCount"]
data13b = ComponentMeasurements[data8, "ConvexArea"]
Range@5 /. data12a // Total

(*
{1 -> 10000, 2 -> 10000, 3 -> 10000, 4 -> 10099, 5 -> 10098}
{1 -> 10049.5, 2 -> 10049.5, 3 -> 10049.5, 4 -> 10148.6, 5 -> 10147.3}
{1 -> 10000, 2 -> 10000, 3 -> 10000, 4 -> 10099, 5 -> 10098}
{1 -> 10000., 2 -> 10000., 3 -> 10000., 4 -> 10099.5, 5 -> 10099.}

50197
*)
`