Retrieve the details of shear angle, horizontal scale and vertical scale.

First question: How’s your math?

(Personally I forgot all mine decades ago, and even those who know geometry think Adobe’s is weird, so caveat emptor, E&OE, etc.)

Anyway, welcome to the `matrix` property:

var image = app.activeDocument.placedItems[0]

var matrix = image.matrix

This will give you information on the transformation that’s currently applied to the image†. Everything after this will give you a headache.

Here’s a good overview:

http://www.senocular.com/flash/tutorials/transformmatrix/

It talks about Flash but the principles are the same. To summarize, a matrix object has 4 properties describing how the image is transformed (plus an extra 2 that can be used to move it around which aren’t relevant here):

mValueA: x scale
mValueB: y skew
mValueC: x skew
mValueD: y scale

Second question: for what purposes do you need this information?

e.g. To remove all transformations from an image:

var matrix = new Matrix()

matrix.mValueA = 1.0
matrix.mValueB = 0.0
matrix.mValueC = 0.0
matrix.mValueD = 1.0

image.matrix = matrix

Or to de-rotate the image while leaving its scale and skew unchanged:

var image = app.activeDocument.rasterItems[0]

var matrix = image.matrix

var angle = Math.atan2(matrix.mValueB, matrix.mValueA)

var angleInDegrees = angle / Math.PI * 180

image.rotate(-angleInDegrees)

Or to remove all skew (which also effectively removes the rotation, since one is the product of the other):

var matrix = image.matrix
matrix.mValueB = 0
matrix.mValueC = 0
image.matrix = matrix

And so on. If you want to copy the image’s transformation matrix to other objects, or apply further transforms, you can do that too. See the Matrix object in Illustrator’s Scripting Reference, and the various matrix math commands on the app object.

OTOH, if you wish to know precisely what x scale, y scale, x skew, y skew, and rotation values the artist originally applied to the image, you will have to ask them that. It’s impossible to convert the 4 matrix values (A,B,C,D) back to those original 5‡, as any one transformation may be produced from any number of different combinations of scale, skew, and rotation numbers.

But anyway, that’s enough of that. Hope it helps, and pass the asprin.

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† Use `rasterItems[n]` if the image is embedded instead of linked (`placedItems[n]`). Or just `pageItems[n]` if you don’t care.

‡ Simultaneous equations are an implacable mistress. You’ll have to pin down values for 2 of the variables before you can calculate the rest.