In the first phase of the study, the in vitro phase, quantitative measurements were calculated on 40 extracted teeth which were then replanted in dry mandibular sockets to undergo periapical imaging . In the second phase, the in vivo phase, digital panoramic radiographs of 5 volunteers, in Dental School of Isfahan University of medical sciences were used as standard references and the patients kindly accepted and signed consent forms which let us taking an extra periapical image in our proposed setup.
Extracted tooth replanted in a dry mandibular socket
The measurements on real teeth were performed by a caliper. The widest part of the tooth was measured for horizontal measurement and the distance from end to end was evaluated to represent the vertical length. Knowing the resolution of imaging device, the measured values were calculated in pixels and were used as gold standards in error estimation. For the second phase of study, measurements on digital panoramic images were simply done by getting the cursor's location through mouse clicks of the expert.
In order to remove the image distortions, a new method based on embedded landmarks aligned by an external frame was applied. For this purpose, we designed a radiolucent frame covered with a rectangular network. The proposed width for comprising lines is 0.2 mm and the side length for parallelograms is suggested to be 2 mm.  The most important shortness of our previous method[6
] was the superimposition of the embedded square mesh with the region of interest (periapical zone), which could cause misdiagnosis . To solve this problem, a special frame with an empty area in lower part of the frame was designed to be used instead of a full cover of squares . Furthermore, we used smaller mesh compared with our first experiment to improve the accuracy of the method.
(a) Intersecting vertical and horizontal radio-opaque lines (square mesh) on the frame with smaller squares on the upper part of the frame. (b) Old frame with bigger squares on the whole area
The frame was mounted on the top of the radiographic cone without any intrusion on the patient . The proposed imaging technique for periapical radiography is a combination of parallel and bisecting periapical image acquisition methods.[7
] To clear up, the angle between tooth and sensor is similar to bisecting method, however, the angle between the cone and the tooth is like parallel imaging. In standard geometry (parallel frame with the sensor, and both parallel with the teeth), the squares on the frame would appear with a same size in the acquired image. However, if the parallelization is not provided, the squares would be distorted and skewed and would appear in a shape of rectangles or trapezoids.
The frame installed on the top of the radiographic cone
At this stage, by calculating the imposed distortion on squares, the overall image distortion can be estimated and corrected. In this method, after applying noise removal in preprocessing step, the proposed image processing algorithms are applied to find specific points (Landmarks) on each image[8
Some image processing algorithms applied in order to find specific points
The locations of the detected points (depicted by green markers in ) were compared to corresponding positions in the case of standard geometry (depicted by red markers in ). The respective coordinates are then utilized to correct the distortion (magnification, translation and rotation) by a projective transform, which needs at least four points for estimation of the transform (four corners of one square are proposed to be used in this step). The basic formulas of a projective transform are like[9
A sample in vitro image. Green points indicate the detected points and the red Points are the ones which should be found in the case of standard geometry
An example of the corrected image is demonstrated in , where the incorrect magnification, translation and rotation are all removed and the squares are in the accurate size of squares in standard geometry. Therefore, we can expect the dental structures to have the right size, similar to what was expected in an ideal case of imaging (parallel frame with the sensor, both parallel with the teeth).