be computed in a once-off, offline step. The second term, $\mathrm{Tr}(\mathbf{A} (\mathbf{P} \mathbf{E}^T))$, has a computational complexity which grows with the number of pixels used, $n$, but is independent of the number of sample warps, $m$. As $m \gg n$, this term is computationally cheap. To find out how (\[eq:expected\_sq\_err\]) is derived, we refer the reader to the supplementary material.

Experimental Results {#sec:exp_results}
====================

We evaluate our approach against the IC-LK and ESM methods in Sec. \[sec:energy\], and the Linear Predictors in Sec. \[sec:lin\_predictors\]. Tracking by detection methods such as [@Henriques2015; @Zimmermann2014] are not evaluated as they are usually used for tracking a single, large patch and they do not account for affine warp models.

#### Experimental Settings

All methods were implemented in C++ in order to enable a fair comparison. We have also implemented a CUDA version of our approach, whereby the pre-computation step is done using a GPU (NVIDIA 1080).

#### Notation

Throughout this section, “jd" represents the method of Jurie and Dhome, “dct-r" denotes the DCT method with $r$ number of retained coefficients, “hp" denotes the re-formulation approach, and “hpdct-r" denotes the hybrid approach. Further, “sym" denotes our proposed approach, and “symdct-r" represents a combination of our 