The tree of shapes (ToS) is a self-dual and contrast invariant hierarchical representation of images, making it highly suitable for various image processing tasks such as filtering, segmentation, and object detection. The existing linear algorithm for computing the ToS is effective for low-quantized images, but exhibits increased complexity for high-quantized images due to the reliance on data structures like red-black trees, which have logarithmic complexity for insertion and deletion operations. This paper introduces a novel algorithm based on the fast marching method to compute a distance map from which the ToS is extracted. This method takes advantage of the distribution of the gradient values of the image pixels to make use of an efficient priority queue structure that lowers the computational complexity of the ToS on high-dynamic range images.