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I do have DICOMs (Digital Images and COmmunications in Medicine) from several CT volumes where most volumes miss the SliceThickness and SliceLocation attribute.

Is there another attribute usually contained in a DICOM which tells me something about the length or height of the total scan?

The goal is to approximate the SLiceThickness - any means are much appreciated!

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The slice location can be easily computed by looking at the (0020, 0032) ImagePosition tag.

This tag is described in the DICOM Documentation Part 3 (page 561) and it's a type 1 attribute, i.e. it's required to be in the SOP (Service-Object Pair) Instance and must have a valid value, so you will always find this value within your DICOM sets.

For your convenience I copy-paste here a table from the documentation above: enter image description here

So the ImagePosition attribute gives you the x, y, and z coordinates of the upper left hand corner of the image, in mm. To compute the distance between two slices just compute the difference between the z coordinates of two contiguous images. Similarly, compute the difference between the z coordinates of the first and last slice to get the total height of the image set.

Note that sometimes you can have an image set with variable slice spacing.

Regarding the thickness, usually you can have overlapping slices, so the slice thickness and slice increment will be different as you can see in the image below (courtesy of Materialise): enter image description here

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