Described are anatomically specified conformation computed tomography (ASC-CT) systems, which are fully tomographic x-ray imaging systems configured to conform to the contour of the anatomy of interest and perform a near scatter-free image acquisition, thereby providing an enhanced contrast resolution in the reconstructed CT image volume. The apparatus comprises independently controlled, yet synchronized, x-ray generation and detection assemblies configured to perform a tomographic image acquisition. The method of image acquisition entails adjusting the layout of the x-ray panels within the detector assembly based on the shape of the anatomy, followed by capturing a collimated, narrow x-ray beam composed of primary photons while sweeping a circular trajectory around the anatomy placed in the field of view, resulting in a conforming sinogram of the anatomy.