As medical image data are acquired at higher spatial, gray-scale, and temporal resolution, with increasing image dimensionality and vectorial components per image element, the need to be able to compress them becomes increasingly important, especially for the practical utilization of PACS. Further, a compression method that allows an efficient in-memory representation would be very useful for those processing situations in which the non-compressed data are beyond RAM resources. Consider an n-dimensional (nD) scene intensity function (m- valued) as a digital surface in an (n plus m)D space as described below. The approach leads to a spectrum of lossless and lossy compression methods. For a 2D, scalar valued (m equals 1) scene S, for example, the 3D digital surface representing S is simply the graph of the scene intensity function. The first two coordinates of points on the surface represent the coordinates of a pixel in S and the third coordinate represents the pixel's intensity. In this example, if m equals 2, then the third and the fourth coordinates of the points in the 4D surface represent the two pixel values. The digital surfaces obtained from scenes via this process (referred to as lifting as described below) have certain distinct topological properties not shared by general digital surfaces (for example, they do not enclose holes). These properties allow us to encode them elegantly. For example, the entire surface (for any finite n greater than 0, m greater than 0) can be represented by a Hamiltonian path of surface elements in the graph representing the surface. This path is chain-encoded facilitated by the small number of possible configurations and orientations of adjacent surface elements. Our (very) preliminary results indicate lossless compression ratios of 4.6:1 for CT slices and 1.7:1 for CR scalar-valued scenes (n equals 2, m equals 1) representing 2D scenes. Our preliminary implementation uses simple chain codes that do not exploit the repetitive patterns in the Hamiltonian path. When this is done, and the implementation is extended to scenes with n plus m greater than 3, we expect a higher degree of compression due to the full exploitation of the spatio-temporal and vectorial component coherence. This paper opens a new direction for data compression not taken in previous research. It seems to capture regional information about the uniformity of the intensity distribution better than other methods. It also extends the current shape-based methods used in image interpolation to include compression.