Title: Learning from multiscale wavelet superpixels using GNN with spatially heterogeneous pooling. Abstract: Neural networks have become the standard for image classification tasks. On one hand, convolutional neural networks (CNNs) achieve state-of-the-art performance by learning from a regular grid representation of images. On the other hand, graph neural networks (GNNs) have shown promise in learning image classification from an embedded superpixel graph. However, in the latter, studies have been restricted to SLIC superpixels, where 1) a single target number of superpixels is arbitrarily defined for an entire dataset irrespective of differences across images and 2) the superpixels in a given image are of similar size despite intrinsic multiscale structure. In this study, we investigate learning from a new principled representation in which individual images are represented by an image-specific number of multiscale superpixels. We propose WaveMesh, a wavelet-based superpixeling algorithm, where the number and sizes of superpixels in an image are systematically computed based on the image content. We also present WavePool, a spatially heterogeneous pooling scheme tailored to WaveMesh superpixels. We study the feasibility of learning from the WaveMesh superpixel representation using SplineCNN, a state-of-the-art network for image graph classification. We show that under the same network architecture and training settings, SplineCNN with original Graclus-based pooling learns from WaveMesh superpixels on-par with SLIC superpixels. Additionally, we observe that the best performance is achieved when replacing Graclus-based pooling with WavePool while using WaveMesh superpixels.