This paper introduces Motion History Volumes (MHV) as a free-viewpoint representation for human action recognition using multiple calibrated, background-subtracted video cameras. The authors propose a method to compute, align, and compare MHVs of different actions performed by different people in various viewpoints. Alignment and comparison are efficiently performed using Fourier transforms in cylindrical coordinates around the vertical axis. The results show that this representation can be used to learn and recognize basic human action classes, independent of gender, body size, and viewpoint. The paper discusses the use of motion history volumes to represent human actions in a view-invariant manner. It introduces a representation based on Fourier analysis of motion history volumes in cylindrical coordinates. The method involves computing visual hulls and accumulating them into motion history volumes, then transforming the MHVs into cylindrical coordinates and extracting view-invariant features in Fourier space. This representation fits well within the framework of Marr's 3D model, which has been advocated by linguist Jackendoff as a useful tool for representing action categories in natural language. The paper presents efficient descriptors for matching and aligning MHVs, and classification results using these descriptors. The authors show that using invariant Fourier descriptors of binary motion volumes and key frames is suitable for motion recognition. However, the use of additional motion information, as present in the motion history volumes, improves the recognition. The paper also compares the performance of MHVs with other methods such as motion energy volumes and key frames, showing that MHVs provide better performance in distinguishing actions on more detailed scales. The authors test their method on the IXMAS dataset, which contains 11 actions performed by 10 actors. The results show that the method achieves a high classification rate, with an average of 93.33% accuracy using leave-one-out cross validation. The method is also tested on video sequences, showing that it can recognize actions in realistic situations. The experiments demonstrate the ability of MHVs to work with large amounts of data and under realistic situations. The paper concludes that the proposed method is effective for free-viewpoint action recognition and that further research is needed to address the challenges of recognizing complex actions.This paper introduces Motion History Volumes (MHV) as a free-viewpoint representation for human action recognition using multiple calibrated, background-subtracted video cameras. The authors propose a method to compute, align, and compare MHVs of different actions performed by different people in various viewpoints. Alignment and comparison are efficiently performed using Fourier transforms in cylindrical coordinates around the vertical axis. The results show that this representation can be used to learn and recognize basic human action classes, independent of gender, body size, and viewpoint. The paper discusses the use of motion history volumes to represent human actions in a view-invariant manner. It introduces a representation based on Fourier analysis of motion history volumes in cylindrical coordinates. The method involves computing visual hulls and accumulating them into motion history volumes, then transforming the MHVs into cylindrical coordinates and extracting view-invariant features in Fourier space. This representation fits well within the framework of Marr's 3D model, which has been advocated by linguist Jackendoff as a useful tool for representing action categories in natural language. The paper presents efficient descriptors for matching and aligning MHVs, and classification results using these descriptors. The authors show that using invariant Fourier descriptors of binary motion volumes and key frames is suitable for motion recognition. However, the use of additional motion information, as present in the motion history volumes, improves the recognition. The paper also compares the performance of MHVs with other methods such as motion energy volumes and key frames, showing that MHVs provide better performance in distinguishing actions on more detailed scales. The authors test their method on the IXMAS dataset, which contains 11 actions performed by 10 actors. The results show that the method achieves a high classification rate, with an average of 93.33% accuracy using leave-one-out cross validation. The method is also tested on video sequences, showing that it can recognize actions in realistic situations. The experiments demonstrate the ability of MHVs to work with large amounts of data and under realistic situations. The paper concludes that the proposed method is effective for free-viewpoint action recognition and that further research is needed to address the challenges of recognizing complex actions.