Hyperdimensional Computing (HDC), also known as Vector-Symbolic Architectures (VSA), is an approach that has been proposed to combine the advantages of distributed vector representations and symbolic structured data representations in Artificial Intelligence, Machine Learning, and Pattern Recognition problems. HDC/VSA operate with hypervectors, i.e., brain-like distributed representations of large fixed dimension. The key problem of HDC/VSA is how to transform data of various types into hypervectors. In this paper, we propose a novel approach for the formation of hypervectors of spatial objects, such as images, that provides both an equivariance with respect to the shift of objects and preserves the similarity of objects described by similar features at nearby positions. In contrast to known hypervector formation methods, we represent the features by compositional hypervectors and exploit permutations of hypervectors for representing the position of features. We experimentally explored the proposed approach in some tasks that exploit various descriptions of two-dimensional (2D) images. In terms of standard accuracy measures such as error rate or mean average precision, our results are on a par or better than those of other methods and are obtained without feature learning. The proposed techniques were designed for the HDC/VSA model known as Sparse Binary Distributed Representations. However, they can be adapted to hypervectors in formats of other HDC/VSA models, as well as for representing spatial objects other than 2D images.