There is a notion called the "orthogonal convex hull," or the "digital convex hull," which may be what you seek. For example, in this paper,
Karmakar, Nilanjana, and Arindam Biswas. "Construction of 3D Orthogonal Convex Hull of a Digital Object." In International Workshop on Combinatorial Image Analysis, pp. 125-142. Springer, Cham, 2015. Springer link.
the authors define it this way: "Orthogonal convex hull of a digital object in 3D domain is defined as the minimum volume orthogonal polyhedron enclosing the object such that its intersection with an axis-parallel face plane is either empty or a collection of projection-disjoint convex polygons."
Here's another image, specifically in 2D:
Image from [P. Bhowmick's slides (PDF)](https://cse.iitkgp.ac.in/~pb/convex-hull-talk-nit-dgp-2014a.pdf).
>A. Biswas, P. Bhowmick, M. Sarkar, B. B. Bhattacharya, A linear-time combinatorial algorithm to find the orthogonal hull of an object on the digital plane, *Information Sciences*, 216, pp. 176–195, 2012. [Elsevier link](https://www.sciencedirect.com/science/article/pii/S0020025512004100).