Nowadays there are many efforts to develop image matching applications exploiting a large number of images stored in smart devices such as smartphones, smart pads, and smart cameras. Boundary image matching converts boundary images to time-series and identifies similar boundary images using time-series matching on those time-series. In boundary image matching, computing the rotation-invariant distance between image time-series is a very time-consuming process since it requires a lot of Euclidean distance computations for all possible rotations. To support the boundary image matching in smart devices, we need to devise a simple but fast computation mechanism for rotation-invariant distances. For this purpose, in this paper we propose a novel rotation-invariant matching solution that significantly reduces the number of distance computations using the triangular inequality. To this end, we first present the notion of self-rotation distance and formally show that the self-rotation distance with the triangular inequality produces a tight lower bound and prunes many unnecessary distance computations. Using the self-rotation distance, we then propose a triangular inequality-based solution to rotation-invariant image matching. We next present the concept of k-self rotation distance as a generalized version of the self-rotation distance and formally show that this -self rotation distance produces a tighter lower bound and prunes more unnecessary distance computations. Using the -self rotation distance we also propose an advanced triangular inequality-based solution to rotation-invariant image matching. Experimental results show that our self-rotation distance-based algorithms significantly outperform the existing algorithms by up to one or two orders of magnitude, and we believe that this performance improvement makes our algorithms very suitable for smart devices.