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We consider a new topological feauturization of d-dimensional images, obtained by convolving images with various filters before computing persistence. Viewing a convolution filter as a motif within an image, the persistence diagram of the resulting convolution describes the way the motif is distributed throughout that image. This pipeline, which we call convolutional persistence, extends the capacity of topology to observe patterns in image data. Indeed, we prove that (generically speaking) forarXiv:2208.02107v1 fatcat:b5szau3dtfcfzf3kgfr2k7fure