Question

Pixel $(x,y)$ indicates a pixel at location $x,y$ in the image coordinate system. Which of the following statement(s) is/are CORRECT?

• A. Pixels $(x+1,y)$ and $(x,y+1)$ are the adjacent horizontal and vertical neighbors of pixel $(x,y)$, respectively
• B. The digital number at pixel $(x,y)$ will always be the average of the digital numbers of pixels $(x-1,y)$ and $(x+1,y)$
• C. Pixel $(x-1,y-1)$ is not an adjacent neighbor of pixel $(x+1,y+1)$
• D. Pixel $(x,y)$ has only four diagonal adjacent neighbors

Hint:

On a square grid: 4-neighbors $\to$ $(x\!\pm\!1,y)$, $(x,y\!\pm\!1)$; Diagonal neighbors $\to$ $(x\!\pm\!1,y\!\pm\!1)$; 8-neighbors $=$ union of both sets.

Answer 1

The Correct Option is A

(A) True. By definition of 4-/8-neighborhoods on the image grid, $(x\!\pm\!1,y)$ are the horizontal neighbors and $(x,y\!\pm\!1)$ are the vertical neighbors of $(x,y)$.
(B) False. A pixel value (DN) equals the average of left and right neighbors only if a specific 1D smoothing/averaging filter has been applied. In general images, $I(x,y)$ is independent and need not equal $\tfrac{1}{2}\{I(x-1,y)+I(x+1,y)\}$.
(C) True. $(x-1,y-1)$ and $(x+1,y+1)$ are separated by $\Delta x=\Delta y=2$; they are two pixels apart diagonally and not adjacent (neither 4- nor 8-neighbors).
(D) True. In the 8-neighborhood of $(x,y)$ there are exactly four diagonal neighbors: $(x\!\pm\!1,y\!\pm\!1)$. (The other four are the horizontal/vertical ones.)