Thread Subject: find the maximum, minimum & inflection points on a curve

How does one find these points on a curve - maximum, minimum
& inflection points along both x & y directions.
The curve is a 2D, represented as (x,y). we know all the
values of (x,y) of the curve. The data points are integer
values(pixel values in grayscale).
The curve is a smooth curve, without any noise.

In article <flrgkq$73u$1@fred.mathworks.com>,
rakesh sepuri <rakeshsepuri.nospam@mathworks.com> wrote:
>How does one find these points on a curve - maximum, minimum
>& inflection points along both x & y directions.
>The curve is a 2D, represented as (x,y). we know all the
>values of (x,y) of the curve. The data points are integer
>values(pixel values in grayscale).
>The curve is a smooth curve, without any noise.

If the coordinates are integer values, then the curve is not
a smooth curve. Consider the point set

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

Where are the minima and maxima and inflection points for that?
The answer is that they *all* fall into one of those categories.

The end-points are obviously minima and maxima respectively, but
because pixels are rectangular (square), you get "the staircase effect"

    +-+
    | |
  +-+-+
  | |
+-+-+
| |
+-+

Every corner marked with + is a local minima or maxima (or both)

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