Origami is the art of paper folding that allows a single flat piece of paper to assume different 3D shapes depending on the fold patterns and the sequence of folding. Using the principles of origami along with computation imaging technique the authors demonstrate a versatile shape-morphing microwave imaging array with reconfigurable field-of-view and scene-adaptive imaging capability. Microwave/millimeter-wave based array imaging systems are expected to be the workhorse for sensory perception of future autonomous intelligent systems. The imaging capability of a planar array-based systems operating in complex scattering conditions have limited field-of-view and lack the ability to adaptively reconfigure resolution. To overcome this, here, deviations from planarity and isometry are allowed, and a shape-morphing computational imaging system is demonstrated. Implemented on a reconfigurable Waterbomb origami surface with 22 active metasurface panels that radiate near-orthogonal modes across 17-27 GHz, capability to image complex 3D objects in full details minimizing the effects of specular reflections in diffraction-limited sparse imaging with scene adaptability, reconfigurable cross-range resolution, and field-of-view is demonstrated. Such electromagnetic origami surfaces, through simultaneous surface shape-morphing ability (potentially with shape-shifting electronic materials) and electromagnetic field programmability, opens up new avenues for intelligent and robust sensing and imaging systems for a wide range of applications.