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 𝐸= (𝑋0,…,𝑋𝑘−1)= Σ(𝑍𝑖2 (𝑋0,…,𝑋𝑘−1))𝑁−1𝑖=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 =(cosø −sinø𝑠𝑖𝑛ø cosø) (X𝑌) (4) where rt is rotational matrix and ø 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. 𝑟𝑡(𝑋𝑖×𝑍𝑖) 2) The required point that needs to be move in a given direction will be calculated using. 𝑉.𝑍𝑖 Finally, the error is minimized using the Proposed Enhanced Equation:, 𝐸= Σ((𝑋𝑖− 𝑌𝑖)× 𝑍𝑖 +𝑟𝑡 (𝑋𝑖 ×𝑍𝑖) +𝑉.𝑍𝑖)𝑘𝑖=1 × ((𝑋𝑖 − 𝑌𝑖) × 𝑍𝑖 +𝑟𝑡(𝑋𝑖×𝑍𝑖) + 𝑉.𝑍𝑖) 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 (𝑋𝑖𝑘−1,𝑌𝑖𝑘−1,𝑍𝑖𝑘−1)𝑁(𝑘−1) → (𝑅𝑘,𝑡𝑘) 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 𝑣𝑥0 1 0 𝑣𝑦0 0 1 𝑣𝑧0 0 0 1) (5) where V is rotational matrix and v is representing the translation object vector.

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