X-Corner Point Localization of Surgical Tools in Surgical Navigation System

In visible light surgical navigation systems, precise localization of the X-corner point of surgical tools is critical. This paper presents a novel X-corner point extraction algorithm that overcomes challenges posed by defocusing blur, perspective distortions due to rotation angles, and occlusion by stains. The proposed method tackles situations where candidate points deviate from the precise corner positions by utilizing a simplified hyperbolic tangent function to readjust these points to their accurate locations. This adjustment recalculates the positional distance among four grayscale mutations, extracting the X-corner points. Additionally, an affine-transform-based hyperbolic tangent function model is introduced for fitting non-central areas of the X-corner neighborhood, enabling sub-pixel level coordinate refinement. Experimental validation on synthetic and natural images demonstrates the robustness and high accuracy of the proposed X-corner point extraction and sub-pixel refinement algorithm. We computed the fiducial localization error, fiducial registration error, and target registration error. Experimental results reveal that the proposed X-corner localization algorithm achieves a fiducial localization error of 0.09mm, a fiducial registration error of 0.11mm, and a target registration error of 0.74mm, meeting the localization requirements for surgical navigation.