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Computed tomography images of the human bone system are essential for evaluation of abnormalities and disease detection. Structural and anatomical information can be assessed with computer tomography with the aim of performing diagnosis, planning and treatment evolution. Automatic segmentation can provide a fast, objective evaluation and quantification of the bone conditions. In this work, we propose a segmentation technique consisting of a region growing method implemented in the Hermite transform domain. The Hermite transform provides a powerful mathematical tool which is useful for extraction of the image features. These are obtained through a set of Hermite coefficients. A seed or a pre-segmentation is used to initialize the region growing approach and coefficients of the Hermite transform are posteriorly employed to grow the initial shape. We have used Hermite coefficients up to second order. Edge, gray level and zero crossing information obtained with the Hermite transform are configured for the growing criterion. Several computer tomography images were used for evaluation. Different metrics were employed for performance assessment and we have compared results of the proposed method against the manual segmentation. The obtained results demonstrate that the HT substantially improves the texture classification which is directly reflected into a better segmentation of the bone tissues. The region growing algorithm presents a better performance if it is applied to Hermite coefficients compared to the original method which is performed on the original image space.

Image fusion is an interesting processing task that has reached great significance for medical image analysis. In general, the combination of medical images coming from different modalities is a common practice that significantly helps in the process of diagnosis and detection of several diseases. In this work, we present a novel method for image fusion based on the Hermite transform which consists of a powerful tool that projects an input image into the space defined by the Hermite polynomials. The proposed approach is performed in three main stages. 1) The HT is applied to the input images, 2) The resulting coefficients are fused using the maximum and average intensity rules, and 3) The inverse HT is performed to obtain the final fused image. The method is applied and evaluated using several single photon emission computed tomography and computed tomography studies taken for bone structures. Typical metrics were used to assess the proposed framework. We demonstrate that this methodology is able to efficiently fuse images coming from different modalities, particularly, nuclear medicine and x-ray tomographic techniques. With the Hermite transform, image features are successfully extracted which becomes fundamental in the process of image fusing.

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