The earlier layers of CNNs are similar to Gabor filters [1], [29].

[1] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification
with deep convolutional neural networks,” in Advances in neural information processing systems, 2012, pp. 1097–1105.
[29]A. Coates, A. Ng, and H. Lee, “An analysis of single-layer networks
in unsupervised feature learning,” in Proceedings of the fourteenth
international conference on artificial intelligence and statistics, 2011,
pp. 215–223.

Gabor filters can be used as pre-processing of the input data [30]-[32]
[30] H. Yao, L. Chuyi, H. Dan, and Y. Weiyu, “Gabor feature based
convolutional neural network for object recognition in natural scene,” in
2016 3rd International Conference on Information Science and Control
Engineering (ICISCE). IEEE, 2016, pp. 386–390
[31]A. Calderon, S. Roa, and J. Victorino, “Handwritten digit recognition ´
using convolutional neural networks and gabor filters,” Proc. Int. Congr.
Comput. Intell, 2003.
[32]B. Kwolek, “Face detection using convolutional neural networks and
gabor filters,” in International Conference on Artificial Neural Networks.
Springer, 2005, pp. 551–556.

or initialization [33]
[33]S.-Y. Chang and N. Morgan, “Robust cnn-based speech recognition with
gabor filter kernels,” in Fifteenth annual conference of the international
speech communication association, 2014.

[34] uses fixed Gabor filters for the first or the second layer to reduce training complexity.
[34]S. S. Sarwar, P. Panda, and K. Roy, “Gabor filter assisted energy efficient
fast learning convolutional neural networks,” in 2017 IEEE/ACM International Symposium on Low Power Electronics and Design (ISLPED).
IEEE, 2017, pp. 1–6.

[35] incorporated selected Gabor orientation filters to each layer to improve the robustness of the networks.
[35] S. Luan, C. Chen, B. Zhang, J. Han, and J. Liu, “Gabor convolutional
networks,” IEEE Transactions on Image Processing, vol. 27, no. 9, pp.
4357–4366, 2018.

[36] uses Gabor filters for the interpretability of the networks in applying person re-identification.
[36]4357–4366, 2018.
[36] Y. Yuan, J. Zhang, and Q. Wang, “Deep gabor convolution network for
person re-identification,” Neurocomputing, vol. 378, pp. 387–398, 2020.

How to incorpate in CNN?

The Gabor wavelets (kernels, filters) can be defined as follows:

where \(\mu\) and \(v\) define the orientation and scale of the Gabor kernels
\(z=(x,y)\)
\(||·||\) denotes the norm operator
and the wave vector \(k_{u,v}\) is defined as

The Gabor kernels in (1) are all self-similar since they can be generated from one filter, the mother wavelet, by scaling and rotation via the wave vector \(k_{u,v}\).

Each kernel is a product of a Gaussian envelope and a complex plane wave, while the first term in the square brackets in (1) determines the oscillatory part of the kernel and the second term compensates for the DC value.
每个核都是高斯包络和复平面波的乘积，而(1)中方括号中的第一项决定了核的振荡部分，第二项补偿了DC值。

The effect of the DC term becomes negligible when the parameter \(\sigma\), which determines the ratio of the Gaussian window width to wavelength, has sufficiently large values.
当决定高斯窗宽与波长之比的参数o具有足够大的值时，DC项的影响变得可以忽略不计。

In most cases one would use Gabor wavelets of five different scales
and eight orientations

Fig 1 shows t