Background: DICOM standard does not have modules that provide the possibilities of two-dimensional Presentation States to three-dimensional (3D). Once the final 3D rendering is obtained, only video/image exporting or snapshots can be used. To increase the utility of 3D Presentation States in clinical practice and teleradiology, the storing and transferring the segmentation results, obtained after tedious procedures, can be very effective. Purpose: To propose a strategy for preserving interaction and mobility of visualizations for teleradiology by storing and transferring only binary segmented data, which is effectively compressed by modern adaptive and context-based reversible methods. Material and Methods: A diverse set of segmented data, which include four abdominal organs (liver, spleen, right, and left kidneys) from 20 T1-DUAL and 20 T2-SPIR MRI, liver from 20 CT, and abdominal aorta with aneurysms (AAA) from 19 computed tomography-angiography datasets, are collected. Each organ is segmented manually by expert physicians, and binary volumes are created. The well-established reversible binary compression methods PNG, JPEG-LS, JPEG-XR, CCITT-G4, LZW, JBIG2, and ZIP are applied to medical datasets. Recently proposed context-based (3D-RLE) and adaptive (ABIC) algorithms are also employed. The performance assessment has been presented in terms of the compression ratio that is a universal compression metric. Results: Reversible compression of binary volumes results with substantial decreases in file size such as 254 to 2.14 MB for CT-AAA, 56.7 to 0.3 MB for CT-liver. Moreover, compared to the performance of well-established methods (i.e., mean 76.14%), CR is observed to be increased significantly for all segmented organs from both CT and MRI datasets when ABIC (95.49%) and 3D-RLE (94.98%) are utilized. The hypothesis is that morphological coherence of scanning procedure and adaptation between the segmented organs, that is, bi-level images, contributes to compression performance. Although the performance of well-established techniques is satisfactory, the sensitivity of ABIC to modality type and the advantage of 3D-RLE when the spatial coherence between the adjacent slices are high results with up to 10 times more CR performance. Conclusion: Adaptive and context-based compression strategies allow effective storage and transfer of segmented binary data, which can be used to re-produce visualizations for better teleradiology practices preserving all interaction mechanisms.