Problem 852. Index of neighbor pixel with steepest gradient

Wolfgang Schwanghart

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Unlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient of a digital elevation model (DEM) is usually returned as the steepest gradient. The steepest gradient is the largest downward slope of a pixel to one of its eight neighbors.
In this problem, your task will be to return the linear index of the steepest neighbor for each pixel in a gridded DEM. Pixels that don't have downward neighbors should receive the index value zero.
An example should help. The DEM is
dem = [1 5 9; ...
       4 5 6; ...
       8 7 3];
The result should be
IX  = [0 1 4; ...
       1 1 9; ...
       2 9 0];
The results may not be unique, but the test cases have been built so that this is not a problem. The spatial resolution of the dem is dx=1 and dy=1. Note that the diagonal distance is hypot(dx,dy).

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Last Solution submitted on Apr 17, 2026

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Dishant Arora on 2 Aug 2012

I'v developed the code using padarray and ordfilt2, which satisfies the test suite on my system, but seems like cody doesn't support padarray, is this so??

Wolfgang Schwanghart on 2 Aug 2012

Hi Dishant, I thought the IPT is available, too, but apparently Cody does not support toolboxes at this time. see box on the right hand side: http://www.mathworks.de/matlabcentral/about/cody/

Jean-Marie Sainthillier on 19 Aug 2014

More difficult thant expected...

Rafael S.T. Vieira on 8 Jun 2020

Pay attention. The problem is asking for the index and not the value of the steepest gradient. And gradients on diagonals directions must be divided by sqrt(2).

Dyuman Joshi on 22 Dec 2022

Test cases have been added and solutions have been rescored.

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