# Explicit Spatial Encoding for Deep Local Descriptors

## TL;DR

This paper introduces a kernelized deep local descriptor that explicitly encodes spatial information using Cartesian and polar parametrizations, improving robustness and outperforming existing methods on benchmarks.

## Contribution

It presents a novel explicit spatial encoding method for deep local descriptors, enhancing robustness to patch misalignment and outperforming prior approaches.

## Key findings

- Outperforms all other methods on standard benchmarks
- Model parameters are independent of patch resolution
- Both Cartesian and polar encodings improve robustness

## Abstract

We propose a kernelized deep local-patch descriptor based on efficient match kernels of neural network activations. Response of each receptive field is encoded together with its spatial location using explicit feature maps. Two location parametrizations, Cartesian and polar, are used to provide robustness to a different types of canonical patch misalignment. Additionally, we analyze how the conventional architecture, i.e. a fully connected layer attached after the convolutional part, encodes responses in a spatially variant way. In contrary, explicit spatial encoding is used in our descriptor, whose potential applications are not limited to local-patches. We evaluate the descriptor on standard benchmarks. Both versions, encoding 32x32 or 64x64 patches, consistently outperform all other methods on all benchmarks. The number of parameters of the model is independent of the input patch resolution.