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Evaluating cylindricity is a very important application in metrology. In this paper, we focus on cylindricity evaluation based on radial form measurements. The standard characterization of cylindricity is the notion of zone cylinder, i.e. the cylindrical crown contained between two coaxial cylinders with minimum radial separation and containing all the data points. Unfortunately, the construction of the zone cylinder is a very complex geometric problem, which can be formulated as a nonlinear optimization. Recently a new method (referred to here as the hyperboloid method) has been discussed, which avoids the direct construction of the zone cylinder of a point set, but approximates it with guaranteed accuracy through a computationally very efficient iterative process based on a linearization of the underlying problem. The iterations can be viewed as the construction of a sequence of "zone hyperboloids" tending to the desired "zone cylinder." An important requirement of the method, however, is that the initial position of the cylindrical specimen axis be nearly vertical, since significant deviations from this condition essentially invalidate the process. It is the purpose of this paper to remove this shortcoming of the hyperboloid technique by providing a simple procedure for appropriately initializing the data (axis estimation). Axis estimation and the hyperboloid technique constitute an integrated methodology for cylindricity evaluation, which is currently the most effective. The theoretical foundations of the method are reviewed from a viewpoint that highlights its essential features and intuitively explains its effectiveness. The analytical discussion is complemented by experimental data concerning a few significant samples.

Precise craniotomy localization is essential in neurosurgical procedures, especially during the preoperative planning. The mainstream craniotomy localization method utilizing image-guided neurosurgery system (IGNS) or augmented reality (AR) navigation system require experienced neurosurgeons to point out the lesion margin by probe and draw the craniotomy manually on the patient's head according to cranial anatomy. However, improper manual operation and dither from the AR model will bring in errors about craniotomy localization. In addition, there is no specific standard to evaluate the accuracy of craniotomy. This paper attempts to propose a standardized interactive 3D method using orthogonal transformation to map the lesion onto the scalp model and generate a conformal virtual incision in real time. Considering clinical requirements, the incision can be amended by 3D interaction and margin modification. According to the IGNS and the virtual incision, an actual craniotomy will be located on the patient's head and the movement path of the probe will be recorded and evaluated by an indicator, which is presented as an evaluated standard to measure the error between virtual and actual craniotomies. After the experiment, an incision is drawn on a 3D printing phantom based on the generated virtual one. The results show that the proposed method can generate a lesion-consistent craniotomy according to the size of the lesion and the mapping angle and delineate the incision on the patient's head precisely under the IGNS.

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