We develop a process of image-plane self-calibration for interferometric imaging data. The process is based on shape-orientation-size (SOS) conservation for the principal triangle in an image generated from the three fringes made from a triad of receiving elements, in situations where interferometric phase errors can be factorized into element-based terms. The basis of the SOS conservation principle is that, for a three-element array, the only possible image corruption due to an element-based phase screen is a tilt of the aperture plane, leading to a shift in the image plane. Thus, an image made from any three-element interferometer represents a true image of the source brightness, modulo an unknown translation. Image-plane self-calibration entails deriving the unknown translations for each triad image via cross-correlation of the observed triad image with a model image of the source brightness. After correcting for these independent shifts, and summing the aligned triad images, a good image of the source brightness is generated from the full array, recovering source structure at diffraction-limited resolution. The process is iterative, using improved source models based on previous iterations. We demonstrate the technique in a high signal-to-noise context, and include a configuration based on radio astronomical facilities, and simple models of double sources. We show that the process converges for the simple models considered, although convergence is slower than for aperture-plane self-calibration for large-N arrays. As currently implemented, the process is most relevant for arrays with a small number of elements. More generally, the technique provides geometric insight into closure phase and the self-calibration process. The technique is generalizable to non-astronomical interferometric imaging applications across the electromagnetic spectrum.