Question

For the image in Fig. 2 where pixels are designated as 1s on a background of 0s, determine the area the minimum aspect ratio the centroid Compactness Choose the origin (0, 0) of the image coordinates in the upper left-handed corner

Edit: The matrix at the bottom is the figure.

Answer 1

a)To find area of an image which is represented in binary format ,we need to consider number of pixels that are "on" implies number of bits that are 1.

Therefore,no of bits represented as 1=77

Hence ,area=77

b)To find minimum aspect ratio which is represented as x:y where x represents width and y represents height.

Which we can represent width as 14 since 1st Column and last columns are only 0's. We can exclude and can count remaining columns for width.

Height is 8 because 1st and last rows represents 0 .

Therefore, minimum aspect ratio=14:8

c)To find centroid ,we need consider the rows and columns where the pixel value is 1.

Let's consider row values,row=[4-6,4-6,4-6,4-9,2-9,2-8,2-8,2-9,2-9,4-9,4-9,4-9,5-7,5-7]

Columns=[6-10,6-10,2-13,2-15,2-15,5-15,5-13,5,6,9-13]

Now we will find the mean of rows and coloumns.

Row mean=total sum/number of pixels represented as 1

=439/77

=5.7

Columns mean= 665/77

=8.63

d) Compactness:It is the square of the perimeter to its area.lets find the perimeter of the matrix.

We need to find equidistant between each and every pair of rows and columns using formula sqrt((x2-x1)²+(y2-y1)²)

We need to do between all the row column pairs which we got in b) .

Compactness=sqrt(resulting perimeter from above) /area

=Sqrt(perimeter)/77

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