pdf

NEIGH-CONN.pdf

NEIGH-CONN.pdf

Solved

Posted on 2009-04-30

Please find the attached pdf on image processing and neighbours of a pixel.

"Each of them are at Euclidean distance of

1.414 from P"

What does this mean? What is Eucildean distance?

thanks in advance

"Each of them are at Euclidean distance of

1.414 from P"

What does this mean? What is Eucildean distance?

thanks in advance

4 Comments

pdf

NEIGH-CONN.pdf

NEIGH-CONN.pdf

1.414 is close to sqrt(2). When one point is at (x,y) and another point is at (x+1, y+1) the distance is ((x+1 - x)^2 + (y+1 - y)^2) = sqrt(1 + 1) = sqrt(2) ~= 1.414.

Yes I see the formulae for the line but why do they bother to call it Euclidean distance. What does this mean?

It used to be that the geometry taught in Elements was just referred to as Geometry. But as mathematicians discovered that there can be other types of geometries besides the one that we see in our everyday life, they realized that "geometry" should be a more abstract term, and the geometry described in Euclid's Elements should specifically be called Euclidean Geometry. Thus, the distance formula from Euclidean Geometry is called euclidean distance.

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