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We present an analytical method for the estimation of rigid-body motion in three-dimensional SPECT and PET slices. This method utilizes mathematically defined generalized center-of-mass points in images, requiring neither segmentation nor an iterative process. It can be applied to compensation of the rigid-body motion in both SPECT and PET. We generalized the formula for the center-of-mass and obtained a family of points co-moving with the object's rigid-body motion. In calculation of the generalized center-of-mass points and estimation of the rigid-body motion, we optimized a Gaussian smoothing function and chose the best three points, which resulted in the minimum root-mean-square difference between images. The estimated motion was used to generate a summed image, or incorporated in the iterative reconstruction of the motion-present data. To evaluate this method for different noise levels, we performed simulations with the MCAT phantom. We observed that though noise degraded the motion-detection accuracy, this method helped in reducing the motion artifact both visually and quantitatively. We also acquired four sets of the emission and transmission data of the Data Spectrum Anthropomorphic Phantom positioned at four different locations and/or orientations. From these we generated a composite acquisition simulating phantom movements during acquisition. The simulated motion was calculated from the generalized center-of-mass points on the images reconstructed from individual acquisitions. We determined that motion-compensation greatly reduced the motion artifact. Finally, in a simulation with the gated MCAT phantom, an exaggerated rigid-body motion was applied to the end-systolic frame. The motion was estimated from the end-diastolic and end-systolic images, and used to sum them into a summed image without obvious artifact. As an image-driven approach this method assumes angularly complete data sets for each state of motion. We expect this method to be applied in correction of the respiratory motion in respiratory gated SPECT and respiratory or other rigid-body motion in PET.