Four Retouches of One Doorway

A photo of a dark doorway in a pale wall is cropped to a small grayscale grid, $3$ rows by $6$ columns. All three rows are identical:

	c0	c1	c2	c3	c4	c5
each row	40	40	40	180	180	180

An edge detector compares every pixel with its right-hand neighbour and records the size of the change between them, ignoring whether brightness went up or down. Those sizes, laid out as a grid of $3$ rows by $5$ , are the photo's edge map: the edges-only version of the picture.

The photo is then retouched in four different ways. Pixel values are stored from $0$ to $255$ , so any value that would go above $255$ is held at $255$ .

retouch	what happens to every row
Negative	every value $v$ becomes $255 - v$
Halved	every value is divided by $2$
Brightened	$100$ is added to every value
Softened	the pixel in c3 becomes $110$ , so each row reads $40, 40, 40, 110, 180, 180$

Which retouched photo has exactly the same edge map as the original?

Four Retouches of One Doorway

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