Estimation of the interpolation error of a three-step rotation algorithm using recorded images with rotated test pattern as ground truth

Abstract

Abstract Nowadays, the surgical microscope is the goldstandard for microsurgical procedures. Additional functionalities such as surgical navigation, data injection or imageoverlay are providing additional valuable information to the surgeon. For substituting the conventional optical system by a fully-digital multi-camera setup the three dimensional (3D) reconstruction of the scenery in the field of view is required. However, for in camera-based systems, an exact alignment of the cameras is a challenging task. Therefore, a final adjustment through a digital image rotation becomes necessary. Even though the digital rotation is a commonly used procedure, it leads to unavoidable errors because of the discretized grid of the image. Previous research reported in literature has demonstrated that the method of digitally rotating the images combined with the Fourier interpolation delivers the results of best quality. Nevertheless, the performance evaluation of this algorithm was carried out rotating an image in multiple threestep rotations to a total of 90 or 180 degrees and comparing it to the original image rotated in one step. This is a valid approach because a rotation of 90 or 180 degrees does not produce rotation artifacts. In this research project, we verify the performance of the three-step rotation algorithm using recorded images for which the test pattern was rotated as ground truth. A series of photographs with a rotation angle of 3 to 45 degrees was created. The advantage of this setup is that the result of the digital rotation can be directly compared to the recorded image. In addition, with the knowledge obtained about the interpolation error, we can improve pixel matching in the further triangulation used for 3D reconstruction. By doing so, the estimation of the interpolation error helps to reduce the triangulation error.