Devise an efficient algorithm to compute the distance transform. The algorithm should take a binary image and return at each pixel the city block distance to the nearest nonzero element of the...

1. 
   

   
   Devise an efficient algorithm to compute the distance transform. The algorithm should take a binary image and return at each pixel the city block distance to the nearest nonzero element of the
   
   <sup>original
   
   
   
   
   image.
   
   
   
   
   The
   
   
   
   
   city
   
   
   
   
   block
   
   
   
   
   distance
   
   
   
   
   
   d
   
   
   
   
   
   
   
   between
   
   
   
   
   pixels
   
   
   
   
   (
   
   
   
   x</sup>
   
   
   1
   
   
   <sup>,
   
   
   
   
   
   
   
   
   y</sup>
   
   
   1
   
   <sup>)
   
   
   
   
   and
   
   
   
   
   pixel
   
   
   
   
   (
   
   
   
   x</sup>
   
   
   2
   
   
   <sup>,
   
   
   
   
   
   
   
   
   y</sup>
   
   
   2
   
   <sup>)
   
   
   
   
   is
   
   
   
   
   defined
   
   
   
   
   as</sup>
   
   

   
   

<sup>d







=





|




x</sup>


1


<sup>−








x</sup>


2


<sup>|







+





|




y</sup>


1


<sup>−








y</sup>


2


<sup>|




.</sup>