Accuracy of linear measurement using cone-beam computed tomography at different reconstruction angles

Purpose: This study was performed to evaluate the effect of changing the orientation of a reconstructed image on the accuracy of linear measurements using cone-beam computed tomography (CBCT). Materials and Methods: Forty-two titanium pins were inserted in seven dry sheep mandibles. The length of these pins was measured using a digital caliper with readability of 0.01 mm. Mandibles were radiographed using a CBCT device. When the CBCT images were reconstructed, the orientation of slices was adjusted to parallel (i.e., 0°), +10°, +12°, -12°, and -10° with respect to the occlusal plane. The length of the pins was measured by three radiologists, and the accuracy of these measurements was reported using descriptive statistics and one-way analysis of variance (ANOVA); p<0.05 was considered statistically significant. Results: The differences in radiographic measurements ranged from -0.64 to +0.06 at the orientation of -12°, -0.66 to -0.11 at -10°, -0.51 to +0.19 at 0°, -0.64 to +0.08 at +10°, and -0.64 to +0.1 at +12°. The mean absolute values of the errors were greater at negative orientations than at the parallel position or at positive orientations. The observers underestimated most of the variables by 0.5-0.1 mm (83.6%). In the second set of observations, the reproducibility at all orientations was greater than 0.9. Conclusion: Changing the slice orientation in the range of -12°to +12°reduced the accuracy of linear measurements obtained using CBCT. However, the error value was smaller than 0.5 mm and was, therefore, clinically acceptable. © 2014 by Korean Academy of Oral and Maxillofacial Radiology

Evaluation of the accuracy of linear and angular measurements on panoramic radiographs taken at different positions

Purpose: This study assessed the accuracy of linear and angular measurements on panoramic radiographs taken at different positions in vitro. Materials and Methods: Two acrylic models were fabricated from a cast with normal occlusion. Straight and 75° mesially and lingually angulated pins were placed, and standardized panoramic radiographs were taken at standard position, at an 8° downward tilt of the occlusal plane compared to the standard position, at an 8° upward tilt of the anterior occlusal plane, and at a 10° downward tilt of the right and left sides of the model. On the radiographs, the length of the pins above (crown) and below (root) the occlusal plane, total pin length, crown-to-root ratio, and angulation of pins relative to the occlusal plane were calculated. The data were subjected to repeated measures ANOVA and LSD multiple comparisons tests. Results: Significant differences were noted between the radiographic measurements and true values in different positions on both models with linear (P<0.001) and those with angulated pins (P<0.005). No statistically significant differences were observed between the angular measurements and baselines of the natural head posture at different positions for the linear and angulated pins. Conclusion: Angular measurements on panoramic radiographs were sufficiently accurate and changes in the position of the occlusal plane equal to or less than 10° had no significant effect on them. Some variations could exist in the pin positioning (head positioning), and they were tolerable while taking panoramic radiographs. Linear measurements showed the least errors in the standard position and 8° upward tilt of the anterior part of the occlusal plane compared to other positions. © 2013 by Korean Academy of Oral and Maxillofacial Radiology

An Efficient Approach to Lattice-based Fixed-rate Entropy-coded Vector Quantization

In the absence of channel noise, variable-length quantizers perform better than fixed rate Lloyd-Max quantizers for any source with a non-uniform density function. However, channel errors can lead to a loss of synchronization resulting in a propagation of error. To avoid having variable rate, one can use a vector quantizer selected as a subset of high probability points in the Cartesian product of a set of scalar quantizers and represent its elements with binary code-words of the same length (quantizer shaping). We choose these elements from a lattice resulting in a higher quantization gain in comparison to simply using the Cartesian product of a set of scalar quantizers. We introduce a class of lattices which have a low encoding complexity, and at the same time result in a noticeable quantization gain. We combine the procedure of lattice encoding with that of quantizer shaping using hierarchical dynamic programming. In addition, by devising appropriate partitioning and merging rules, we obtain sub-optimum schemes of low complexity and small performance degradation. The proposed methods show a substantial improvement in performance and/or a reduction in the complexity with respect to the best known results

A Low Complexity Method for Fixed-rate Entropy-coded Vector Quantization based on Integer Programming

This paper describes a new approach to Fixed-rate Entropy-coded Vector Quantization (FEVQ) for stationary memoryless sources where the structure of code-words are derived from a variable-length scalar quantizer. We formulate the quantization search operation as a zero-one integer optimization problem [1], and show that the resulting integer program can be closely approximated by solving a simple linear program. The result is a Lagrangian formulation which adjoins the constraint on the entropy (codeword length) to the distortion. Unlike the previously known methods with a fixed Lagrangian multiplier (fixed-slope, and variable rate output), we use an iterative algorithm to optimize the underlying objective function while updating the Lagrange multiplier until the constraint on the overall rate is satisfied (ensured to be fixed-rate). This results in a chain of improving solutions which moves towards the optimum point as fast as possible (in the sense that the changes in the objective function value at each step is maximized). In order to achieve some packing gain, we combine the process of Trellis Coded Quantization (TCQ) with that of FEVQ. This results in an iterative application of the Viterbi algorithm on the underlying trellis for optimizing the Lagrangian multiplier. Numerical results are presented demonstrating substantial improvement in comparison with the alternative methods reported in the literature