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2. Es werden f¨ ur jede Messung patientenspezifischen Schallgeschwindigkeitswerte bestimmt und den Messungen entsprechend korrigiert. Um diese patientenspezifischen Schallgeschwindigkeitswerte zu bestimmen, ist eine Differenzierung zwischen den unterschiedlichen Gewebearten n¨otig. Diese kann dadurch erfolgen, dass vor der eigentlichen Messung Ultraschall-HF-Daten von Zielbereich akquiriert werden. In diesen Daten werden nun gewebespezifische Parameter, wie die frequenzabh¨ angige D¨ ampfung [7, 8, 9] oder die R¨ uckstreuung [10, 11] in Abh¨ angigkeit der Eindringtiefe betrachtet.

I−1 Ai , where the origin oi is found in the 4th column.. Equation 1 lists first the column of the manipulator Jacobian for a Interactive Guidance System for C-Arm Repositioning Without Radiation 23 prismatic joint (like length and height of the C-arm) and second for a revolute joint (like wigwag, angular and orbital movement). 1 zi 0 ; ji = zi × (o5 − oi ) zi (1) Visual Servoing At the desired position F ∗ , a 3D point X is projected on a virtual plane perpendicular to the optical axis of the camera into a 2D point m∗ : m∗ = (x∗ , y ∗ , 1) ∝ I3×3 03×1 X (2) The same 3D point X is projected into a 2D point m in the current camera position F: m = (x, y, 1) ∝ R t X where R is the rotation matrix and t is the translation vector between the two coordinate systems F and F ∗ .

The needle should be set in the direction where these two lines meet. One problem with this view is the need of mouse interaction, which is usually not practical. – Needle view: The user can see the needle and the target, in the direction of the needle. This is especially intuitive for directing the needle. – Augmented camera view: This view includes a camera video. The camera, like the US probe and the needle, is tracked and calibrated, so it is possible to superimpose the virtual models on top of the video.

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A 3/2-approximation algorithm for the jump number of interval orders by Ageev A.A.

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