Matrix of eight nearest neighbors

Hi all,

 This matrix

 neigb=[-1 0; 1 0; 0 -1; 0 1];

 represents the four nearest neighbors.

 How is the matrix of eight neighbors?

Answer 1

[Titus Edelhofer]

Hi Marlene,

this should not be that difficult, I guess? One of the next four neighbors you would get by adding the line [-1 -1] to your variable neigb.

Titus

Answer 2

[Image Analyst]

I don't understand that in an image processing context. In image processing a four-connected structuring element would look like

0 1 0
1 x 1
0 1 0

while an 8-connected one would be

1 1 1
1 x 1
1 1 1

You gave

-1  0
 1  0
 0 -1
 0  1

[Titus Edelhofer]

I understand this as follows: -1 0 means one to the left on the same y (this would correspond to index (2,1) of your first matrix).

[Image Analyst]

I know it's used in the form I listed in all of the image processing routines in the Image Processing Toolbox. Where is the form you and Marlene used?

[Titus Edelhofer]

I know this from numerical analysis, when you implement e.g. finite differences (in 1D the central difference is f(x+h)-f(x-h), so it would be the neighbors [-1; 1]. The discrete laplacian uses (often) the four neighbors Marlene used, i.e., f(x+h, y+h), f(x+h, y-h), f(x-h, y+h), f(x-h, y-h). Starting from x=[x,y] you add the neighbors matrix.

[Sean de Wolski]

Yes it's a five point stencil:

http://en.wikipedia.org/wiki/Five-point_stencil

Answer 3

[Marlene]

% Neighbor locations (footprint)

 neigb= conndef(2,'maximal');

 OR

neigb= [-1 0; 1 0; 0 -1;0 1;-1 -1;-1 1;1 -1;1 1];

[Titus Edelhofer]

Yepp, that's what I thought it should be when writing my answer above ... ;-).