# The effect of structure on image classification using signatures

Original Article

First Online:

Received:

Accepted:

- 24 Downloads

## Abstract

Humans recognize transformed images from a very small number of samples. Inspired by this idea, we evaluate a classification method that requires only one sample per class, while providing invariance to image transformations generated by a compact group. This method is based on signatures computed for images. We test and illustrate this theory through simulations that highlight the role of image structure and sampling density, as well as how the signatures are constructed. We extend the existing theory to account for variations in recognition accuracy due to image structure.

## Keywords

Image classification Invariance Signature## References

- Anselmi F, Leibo J, Rosasco L, Mutch J, Tacchetti A, Poggio T (2014) Unsupervised learning of invariant representations with low sample complexity. CBMM Memo No. 001, March 12Google Scholar
- Cucker F, Smale S (2001) On the mathematical foundations of learning. Am Math Soc 39(1):1–49CrossRefGoogle Scholar
- Dow DM, Snyder AZ, Vautin RG, Bauer R (1981) Magnification factor and receptive field size in foveal striate cortex of the monkey. Exp Brain Res 44:213–228CrossRefPubMedCentralPubMedGoogle Scholar
- Downing P, Jiang Y (2001) A cortical area selective for visual processing of the human body. Science 293(5539):2470–2473CrossRefPubMedGoogle Scholar
- Foldiak P (1991) Learning invariance from transformation sequences. Neural Comput 3(2):194–200CrossRefGoogle Scholar
- Fukushima K (1980) Neocognitron: a self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biol Cybern 36:193–202CrossRefPubMedCentralPubMedGoogle Scholar
- Grill-Spector K, Knouf N, Kanwisher N (2004) The fusiform face area subserves face perception, not generic within-category identification. Nat Neurosci 7(5):555–562CrossRefPubMedCentralPubMedGoogle Scholar
- Kanwisher N (2017) The quest for the FFA and where it led. J Neurosci 37(5):1056–1061CrossRefPubMedCentralPubMedGoogle Scholar
- Kanwisher N, McDermott J, Chun M (1997) The fusiform face area: a module in human extrastriate cortex specialized for face perception. J Neurosci 17(11):4302–4311CrossRefPubMedGoogle Scholar
- Liao Q, Leibo JZ, Poggio T (2013) Learning invariant representations and applications to face verification. In: Proceedings of advances in neural information processing systems (NIPS 2013), Lake Tahoe, NVGoogle Scholar
- Tsao D, Freiwald W, Tootell R, Livingstone M (2006) A cortical region consisting entirely of face-selective cells. Science 311(5761):670–674CrossRefPubMedCentralPubMedGoogle Scholar

## Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018