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Significant advancements in imaging technology and the dramatic increase in computer power over the last few years broke the ground for the construction of anatomically realistic models of the heart at an unprecedented level of detail. To effectively make use of high-resolution imaging datasets for modeling purposes, the imaged objects have to be discretized. This procedure is trivial for structured grids. However, to develop generally applicable heart models, unstructured grids are much preferable. In this study, a novel image-based unstructured mesh generation technique is proposed. It uses the dual mesh of an octree applied directly to segmented 3-D image stacks. The method produces conformal, boundary-fitted, and hexahedra-dominant meshes. The algorithm operates fully automatically with no requirements for interactivity and generates accurate volume-preserving representations of arbitrarily complex geometries with smooth surfaces. The method is very well suited for cardiac electrophysiological simulations. In the myocardium, the algorithm minimizes variations in element size, whereas in the surrounding medium, the element size is grown larger with the distance to the myocardial surfaces to reduce the computational burden. The numerical feasibility of the approach is demonstrated by discretizing and solving the monodomain and bidomain equations on the generated grids for two preparations of high experimental relevance, a left ventricular wedge preparation, and a papillary muscle.