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## that occurring during the final pose.

### that occurring during the final pose.

### Contribution in AR for Oral and Maxillofacial surgeries Current Solution (State of Art) Basic and theories Proposed Solution Current Method: Levenberg Marquardt method Purpose of this Method: to reduce the geometric error that occurring during the final pose refinement ð¸= (ð‘‹0,â€¦,ð‘‹ð‘˜âˆ’1)= Î£(ð‘ð‘–2 (ð‘‹0,â€¦,ð‘‹ð‘˜âˆ’1))ð‘âˆ’1ð‘–=0 X = Sub-pixel edge-point of 2D image, Z = Geometric error, N = Normal point for the matched i, k = Number of iterations Rotational matrix is simply a basic rotation from any one of the axes of the coordinate system in three dimension Rotational matrix (22) will be calculated using the following formula. rt =(cosÃ¸ âˆ’sinÃ¸ð‘ ð‘–ð‘›Ã¸ cosÃ¸) (Xð‘Œ) (4) where rt is rotational matrix and Ã¸ is represents the angle to rotate. By taking into consideration of this vector details rotation will be applied to the image untill it clears from the translation vector . 1) The required rotation that helps to rectify the improper image rotation will be determined by multiplying the rotational matrix with the co-ordinate system X and the identified geometric error. ð‘Ÿð‘¡(ð‘‹ð‘–Ã—ð‘ð‘–) 2) The required point that needs to be move in a given direction will be calculated using. ð‘‰.ð‘ð‘– Finally, the error is minimized using the Proposed Enhanced Equation:, ð¸= Î£((ð‘‹ð‘–âˆ’ ð‘Œð‘–)Ã— ð‘ð‘– +ð‘Ÿð‘¡ (ð‘‹ð‘– Ã—ð‘ð‘–) +ð‘‰.ð‘ð‘–)ð‘˜ð‘–=1 Ã— ((ð‘‹ð‘– âˆ’ ð‘Œð‘–) Ã— ð‘ð‘– +ð‘Ÿð‘¡(ð‘‹ð‘–Ã—ð‘ð‘–) + ð‘‰.ð‘ð‘–) where rt is the rotation matrix and v is the translation vector where rt is the rotation matrix and v is the translation vector The ICP refines the best pose with a number of iterations. The initial pose alignment from Ulrich method is identified as (R0, t0) and (X, Y) in the sub-pixel edge-point of the 2D image. The initial pose alignment from Ulrich method is identified as (R0, t0) and (X, Y) in the sub-pixel edge-point of the 2D image. X & Y = Sub-pixel edge-point of 2D image R & t = Initial pose alignment (ð‘‹ð‘–ð‘˜âˆ’1,ð‘Œð‘–ð‘˜âˆ’1,ð‘ð‘–ð‘˜âˆ’1)ð‘(ð‘˜âˆ’1) â†’ (ð‘…ð‘˜,ð‘¡ð‘˜) X & Y = Sub-pixel edge-point of 2D image, R & t = Initial pose alignment, Z = Geometric error, N = Normal point for the matched i, k = Number of iterations. Translation vector is the data that contains how much the image is wrongly overlayed or registered. Translation vector (22) will be calculated using the following formula. V =(1 0 0 ð‘£ð‘¥0 1 0 ð‘£ð‘¦0 0 1 ð‘£ð‘§0 0 0 1) (5) where V is rotational matrix and v is representing the translation object vector.

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