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So, welcome everybody to the lecture of Diagnostic Metical Image Processing.

So my name is Eva Kolloz for those of you who don't know me.

So last week we talked about projection models and homogeneous coordinates.

A short overview of the big picture.

You know this, so this is usually the first question in the exam.

So what you all did in the lecture.

So first you talk about modalities and about SVD and so on.

Then you had acquisition specific preprocessing.

So last week we discussed there about MRI and homogeneities.

And yeah, we had the definition of what a gain field or a bias field is.

We learned about different methods, how we can correct for the inhomogeneities.

So for example, we had the homomorphic filtering, the homomorphic unsharp masking,

polynomial surface fitting, there was the link to the distortion chapter you already discussed.

Then the Kuybak-Liebler divergence where we had the link to the mutual information.

And the FASC means clustering where we start with the K-means clustering.

Then we go on with the 3D reconstruction.

So next week Andreas Meyer or tomorrow Andreas Meyer will start with the reconstruction.

Therefore we need some information about the projection models,

homogeneous coordinates, extrinsic and intrinsic camera parameters, and camera calibration.

Okay, so to give a short repetition what we learned last week.

So the motivation is, for example, you have your X-ray system or you have a CT scanner.

You have your optical center here.

Then you acquire some X-ray images here on your detector plane.

And you can see here your 3D object, what you were scanning.

So this is only one image, but if your CT scanner rotates around the patient,

you will get multiple images and you want to reconstruct the object.

So this is the main goal.

To understand the different coordinate systems,

so because we talked about homogeneous coordinates and projection models and so on,

this is just a short picture to give you an intuition.

So we have a 3D world coordinate system here.

Then we have a 3D camera coordinate system and a 2D image coordinate system.

So the 3D object coordinate system we don't consider here.

To come from the 3D camera coordinates to the 2D image coordinates,

we learned something about projection models.

So we have here four different types.

So maybe someone can shortly explain the projection models we learned last week.

So what are the differences or what is the simplest one?

So, okay, last week I started from the left, so maybe this time from the right.

Or somebody.

Nobody has an idea.

Okay.

So orthographic projection was the simplest one.

We just project onto the image plane, so you skip the set coordinate.

Then perspective model is also, we consider always the perspective model,

and weak perspective and power perspective were some subtypes, so to say,

because you first do a projection on a virtual plane and do then a perspective projection.

Okay.

We introduced the homogeneous coordinates.