y-coordinate

Obviously, initially this result will be the y-coordinate of the chosen pixel.

Dewarping pages « The Half-Baked Maker 2010

The y-coordinate is not transformed because we are only straightening the image based on the tilt of the left and right margins.

Dewarping pages « The Half-Baked Maker 2010

This simply involves finding the minimum and maximum x-coordinate and minimum and maximum y-coordinate of each pixel in a given component.

Dewarping pages « The Half-Baked Maker 2010

Set up a new array of 30 y-values, and initialize each element to the y-coordinate of the chosen pixel.

Dewarping pages « The Half-Baked Maker 2010

For every line, compute the topmost (smallest) y-coordinate (topY) and bottommost (largest) y-coordinate (botY).

Dewarping pages « The Half-Baked Maker 2010

I settled on an ArcForm expression whose arguments are the list of y-coordinate values of the connection points, and lists of endpoint indices for the left and right arcs.

Wolfram Blog : Minimum Inventory, Maximum Diversity 2009

For each connected component, and for each x-coordinate in its box, determine the average y-coordinate, and put a black pixel in the new image at the (x, average y) point.

Dewarping pages « The Half-Baked Maker 2010

Order the lines in the array by their first y-coordinate (lowest first).

Dewarping pages « The Half-Baked Maker 2010

Then the length of the vertical side is simply the y-coordinate of its endpoint, A, and the length of the horizontal side is the x-coordinate of its endpoint, B.

Euclid’s Window Leonard Mlodinow 2001

Mathematicians attach a minus sign to the x-coordinates of all the points to the left of the y-axis (i.e., the “east side”), and to the y-coordinate of all points which lie below the x-axis (i.e., the “south side”).

Euclid’s Window Leonard Mlodinow 2001