[?] Calculate area of a maple leaf image?

Questions
,
1

Hi,

I want to calculate the area of the maple leaf in cm^2.

maple.jpg
maple.jpg512×512 54.8 KB

I have tried this

img = Binarize@
    Import["http://i37.ltalk.ru/22/85/298522/92/9427492/leave2.png"]~
   Erosion~1;
(m = MorphologicalComponents[img]) // Colorize

linecount = 
  2 /. (Binarize@
        Import["http://i37.ltalk.ru/22/85/298522/92/9427492/leave2.\
png"] // ColorNegate // Thinning // 
     ComponentMeasurements[#, "PerimeterCount"] &);
areacount = 
  2 /. ComponentMeasurements[MorphologicalComponents[img], "Count"];
areacount/linecount^2 // N

but I’m not sure which region is calculated and the unit given.

Can somebody help me? Thank you.

2

The way your image is displayed is misleading. It has an alpha channel. This is why the results from Binarize are weird.

Check this:

im = Import["http://i37.ltalk.ru/22/85/298522/92/9427492/leave2.png"]
ColorSeparate[im]

From the output it is clear that the alpha channel is already a good mask of the leaf.

To compute the area, use

comp = Binarize@AlphaChannel[im]

ComponentMeasurements[comp, "Area"]
(* {1 -> 82093.4} *)

As we’re working with an image, the units are pixels.

To get the result in \mathrm{cm}^2, we would need to know the dimensions of the image or the leaf in centimetres. If you have the actual leaf, you could measure it with a ruler, then use that information to calculate the pixel/cm ratio.

3

Thank you for your great help! :slight_smile:

4

very useful. if you can plot an area, then you can obtain the area without complex integral - assuming you do not need a perfect accuracy, which in the real world is (often)