# Enhancing CNNs Performance on Object Recognition Tasks with Gabor Initialization

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## Abstract

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## 1. Introduction

- By incorporating Gabor filters into the CNN, we have observed an improvement in the performance of object classification tasks, as evidenced by increased accuracy, area under the curve (AUC), and a loss reduction.
- Our findings indicate that a random configuration of Gabor filters in the receptive layer leads to the superior performance of the CNN, especially when dealing with complex datasets.
- Our research demonstrates that including Gabor filters in the receptive layers results in the enhanced performance of the CNN in a shorter time frame.

## 2. Background

#### 2.1. Gabor Filters

#### 2.2. CNNs and Gabor Filters

#### 2.3. A Formal Approach for AI-Based Technique Verification

## 3. Methodology

#### 3.1. Gabor Initialization and Control Group

- Random weight initialization (control groups);
- Random weight initialization with a Gabor filter applied to each channel;
- The application of a fixed Gabor filter across all channels.

#### 3.1.1. Random Weight Initialization

#### 3.1.2. Weight Initialization with a Random Gabor Filter on Each Channel

#### 3.1.3. Weight Initialization with a Random Gabor Filter Fixed across Channels

#### 3.2. Datasets

#### 3.3. Architectures

#### 3.4. Evaluation

#### 3.5. Experiments on Data

## 4. Experimental Results

#### 4.1. Performance Analysis

#### 4.2. Statistical Analysis

#### 4.3. Closely Related Work

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Gabor Filter Examples

## Appendix B. Statistical Analysis

## Appendix C. Additional Experiments

**Table A1.**Improvement in maximum accuracy of epoch-constrained Gabor-initialized CNN with respect to traditional CNN when training period was constrained to maximum accuracy epoch of traditional CNN. Bold numbers indicate top results.

Dataset | Base Maximum Accuracy | Random Gabor Filter | Repeated Gabor Filter | |||
---|---|---|---|---|---|---|

Mean | Stdev | Mean | Stdev | Mean | Stdev | |

Cats vs. Dogs | 0.8839 | 0.004 | +0.0212 | 0.007 | +0.0253 | 0.006 |

CIFAR-10 | 0.8024 | 0.004 | +0.0197 | 0.003 | +0.0212 | 0.005 |

CIFAR-100 | 0.7132 | 0.003 | +0.0054 | 0.005 | +0.0053 | 0.005 |

Caltech 256 | 0.5085 | 0.007 | +0.0131 | 0.008 | +0.0163 | 0.010 |

Stanford Cars | 0.2326 | 0.070 | +0.1200 | 0.065 | +0.1576 | 0.068 |

Tiny Imagenet | 0.5175 | 0.004 | +0.0128 | 0.003 | −0.0008 | 0.007 |

Average | 0.6097 | 0.015 | +0.0320 | 0.015 | +0.0375 | 0.017 |

**Table A2.**Improvement in AUC at maximum accuracy of epoch-constrained Gabor-initialized CNN with respect to traditional CNN when training period was constrained to maximum accuracy epoch of traditional CNN. Bold numbers indicate top results.

Dataset | Base AUC | Random Gabor Filter | Repeated Gabor Filter | |||
---|---|---|---|---|---|---|

Mean | Stdev | Mean | Stdev | Mean | Stdev | |

Cats vs. Dogs | 0.9515 | 0.003 | +0.0129 | 0.004 | +0.0164 | 0.004 |

CIFAR-10 | 0.9719 | 0.001 | +0.0033 | 0.001 | +0.0026 | 0.001 |

CIFAR-100 | 0.9621 | 0.002 | +0.0013 | 0.002 | +0.0022 | 0.002 |

Caltech 256 | 0.8885 | 0.004 | +0.0086 | 0.004 | +0.0062 | 0.005 |

Stanford Cars | 0.8077 | 0.026 | +0.0552 | 0.022 | +0.0645 | 0.026 |

Tiny Imagenet | 0.9370 | 0.003 | +0.0023 | 0.004 | −0.0010 | 0.003 |

Average | 0.9198 | 0.006 | +0.0134 | 0.006 | +0.0151 | 0.007 |

**Table A3.**Improvement in minimum loss of Gabor-initialized CNN with respect to traditional CNN when training period was constrained to minimum loss epoch of traditional CNN. Bold numbers indicate top results.

Dataset | Base Minimum Loss | Random Gabor Filter | Repeated Gabor Filter | |||
---|---|---|---|---|---|---|

Mean | Stdev | Mean | Stdev | Mean | Stdev | |

Cats vs. Dogs | 0.2960 | 0.012 | −0.0406 | 0.015 | −0.0553 | 0.013 |

CIFAR-10 | 0.6555 | 0.013 | −0.0517 | 0.015 | −0.0567 | 0.013 |

CIFAR-100 | 1.1823 | 0.020 | −0.0150 | 0.038 | −0.0192 | 0.029 |

Caltech 256 | 2.6428 | 0.067 | −0.0908 | 0.038 | −0.0192 | 0.029 |

Stanford Cars | 4.1857 | 0.356 | −0.6513 | 0.231 | −0.8913 | 0.264 |

Tiny Imagenet | 2.7390 | 0.014 | −0.0522 | 0.024 | −0.0027 | 0.028 |

**Table A4.**Improvement in minimum loss epoch of Gabor-initialized CNN with respect to traditional CNN when training period constrained to minimum loss epoch of traditional CNN. Bold numbers indicate top results.

Dataset | Base Epoch | Random Gabor Filter | Repeated Gabor Filter | |||
---|---|---|---|---|---|---|

Mean | Stdev | Mean | Stdev | Mean | Stdev | |

Cats vs. Dogs | 70.6 | 13.5 | −7 | 5.4 | −14 | 9.8 |

CIFAR-10 | 40.1 | 5.5 | −8.6 | 8.1 | −10 | 7.4 |

CIFAR-100 | 70.2 | 6.5 | −6.2 | 3.3 | −8.8 | 7.7 |

Caltech 256 | 42.1 | 5.1 | −3.5 | 2.7 | −5.2 | 3.5 |

Stanford Cars | 74.0 | 14.9 | −5.1 | 4.4 | −6.4 | 3.9 |

Tiny Imagenet | 32.2 | 4.6 | −5.2 | 5.6 | −5.9 | 6.1 |

**Table A5.**Improvement in maximum accuracy of Gabor-initialized CNN (frozen receptive convolutional layer variant) with respect to traditional CNN. Bold numbers indicate top results.

Dataset | Base Maximum Accuracy | Random Gabor Filter | Repeated Gabor Filter | |||
---|---|---|---|---|---|---|

Mean | Stdev | Mean | Stdev | Mean | Stdev | |

Cats vs. Dogs | 0.8839 | 0.004 | +0.0029 | 0.009 | +0.0183 | 0.005 |

CIFAR-10 | 0.8024 | 0.004 | +0.0086 | 0.005 | −0.0075 | 0.007 |

CIFAR-100 | 0.7132 | 0.003 | +0.0022 | 0.004 | −0.0559 | 0.007 |

Caltech 256 | 0.5085 | 0.007 | +0.0079 | 0.011 | +0.0012 | 0.012 |

Stanford Cars | 0.2326 | 0.070 | +0.0924 | 0.096 | +0.1662 | 0.086 |

Tiny Imagenet | 0.5175 | 0.004 | +0.0045 | 0.009 | −0.0391 | 0.004 |

Average | 0.6097 | 0.015 | +0.0197 | 0.022 | +0.0139 | 0.020 |

**Table A6.**Improvement in AUC of Gabor-initialized CNN (frozen receptive convolutional layer variant) with respect to traditional CNN. Bold numbers indicate top results.

Dataset | Base AUC | Random Gabor Filter | Repeated Gabor Filter | |||
---|---|---|---|---|---|---|

Mean | Stdev | Mean | Stdev | Mean | Stdev | |

Cats vs. Dogs | 0.9515 | 0.003 | +0.0020 | 0.006 | +0.0133 | 0.002 |

CIFAR-10 | 0.9719 | 0.001 | +0.0012 | 0.001 | −0.0017 | 0.002 |

CIFAR-100 | 0.9621 | 0.002 | −0.0003 | 0.003 | −0.0095 | 0.002 |

Caltech 256 | 0.8885 | 0.004 | +0.0052 | 0.007 | +0.0048 | 0.006 |

Stanford Cars | 0.8077 | 0.026 | +0.0408 | 0.035 | +0.0684 | 0.032 |

Tiny Imagenet | 0.9370 | 0.003 | +0.0012 | 0.004 | −0.0081 | 0.003 |

Average | 0.9198 | 0.006 | +0.0083 | 0.009 | +0.0112 | 0.008 |

**Table A7.**Improvement in minimum loss of Gabor-initialized CNN (frozen receptive convolutional layer variant) with respect to traditional CNN. Bold numbers indicate top results.

Dataset | Base Minimum Loss | Random Gabor Filter | Repeated Gabor Filter | |||
---|---|---|---|---|---|---|

Mean | Stdev | Mean | Stdev | Mean | Stdev | |

Cats vs. Dogs | 0.2960 | 0.012 | −0.0100 | 0.018 | −0.0475 | 0.010 |

CIFAR-10 | 0.6555 | 0.013 | −0.0352 | 0.019 | +0.0086 | 0.022 |

CIFAR-100 | 1.1823 | 0.020 | −0.0099 | 0.035 | +0.2437 | 0.037 |

Caltech 256 | 2.6428 | 0.067 | −0.0794 | 0.091 | −0.0466 | 0.068 |

Stanford Cars | 4.1857 | 0.356 | −0.6217 | 0.502 | −1.0837 | 0.487 |

Tiny Imagenet | 2.7390 | 0.014 | −0.240 | 0.027 | +0.1628 | 0.019 |

**Table A8.**Improvement in maximum accuracy on Cats vs. Dogs dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.8261 | 0.8303 | 0.8165 | 0.8143 | 0.8035 | 0.8037 | 0.7869 |

Random Gabor ($\Delta $) | −0.0202 | −0.0389 | −0.0114 | +0.0036 | +0.0120 | +0.0044 | +0.0094 | |

Repeated Gabor ($\Delta $) | −0.0258 | −0.0174 | −0.0170 | −0.0120 | −0.0174 | −0.0020 | +0.0090 | |

64 × 64 | Traditional CNN (Base) | 0.8015 | 0.8403 | 0.8381 | 0.8297 | 0.8425 | 0.8315 | 0.8279 |

Random Gabor ($\Delta $) | −0.0168 | +0.0038 | +0.0100 | +0.0132 | +0.0022 | +0.0128 | +0.0058 | |

Repeated Gabor ($\Delta $) | +0.0126 | −0.0070 | +0.0204 | +0.0162 | +0.0044 | +0.0116 | +0.0180 | |

128 × 128 | Traditional CNN (Base) | 0.8672 | 0.9026 | 0.8948 | 0.9022 | 0.8992 | 0.8804 | 0.8952 |

Random Gabor ($\Delta $) | +0.0062 | −0.0138 | −0.0022 | +0.0114 | +0.0150 | +0.0242 | +0.0150 | |

Repeated Gabor ($\Delta $) | +0.0134 | +0.0120 | +0.0228 | +0.0144 | +0.0160 | +0.0341 | +0.0216 | |

256 × 256 | Traditional CNN (Base) | 0.8932 | 0.8892 | 0.8926 | 0.8862 | 0.8924 | 0.8916 | 0.8870 |

Random Gabor ($\Delta $) | −0.0170 | −0.0058 | −0.0078 | +0.0076 | +0.0156 | +0.0214 | +0.0142 | |

Repeated Gabor ($\Delta $) | −0.0214 | +0.0120 | +0.0142 | +0.0264 | +0.0136 | +0.0170 | +0.0240 |

**Table A9.**Improvement in AUC at maximum accuracy on Cats vs. Dogs dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.9028 | 0.9092 | 0.8947 | 0.8946 | 0.8789 | 0.8809 | 0.8650 |

Random Gabor ($\Delta $) | −0.0161 | −0.0391 | −0.0076 | −0.0012 | +0.0137 | +0.0024 | +0.0107 | |

Repeated Gabor ($\Delta $) | −0.0208 | −0.0149 | −0.0110 | −0.0081 | −0.0110 | +0.0008 | +0.0095 | |

64 × 64 | Traditional CNN (Base) | 0.8900 | 0.9232 | 0.9213 | 0.9077 | 0.9214 | 0.9127 | 0.9097 |

Random Gabor ($\Delta $) | −0.0179 | +0.0027 | +0.0053 | +0.0103 | +0.0022 | +0.0113 | +0.0081 | |

Repeated Gabor ($\Delta $) | +0.0090 | −0.0066 | +0.0127 | +0.0146 | +0.0037 | +0.0116 | +0.0139 | |

128 × 128 | Traditional CNN (Base) | 0.9461 | 0.9690 | 0.9641 | 0.9670 | 0.9651 | 0.9557 | 0.9638 |

Random Gabor ($\Delta $) | +0.0032 | −0.0094 | −0.0028 | +0.0071 | +0.0093 | +0.0148 | +0.0094 | |

Repeated Gabor ($\Delta $) | +0.0068 | +0.0044 | +0.0118 | +0.0089 | +0.0097 | +0.0188 | +0.0103 | |

256 × 256 | Traditional CNN (Base) | 0.9586 | 0.9565 | 0.9602 | 0.9531 | 0.9570 | 0.9565 | 0.9541 |

Random Gabor ($\Delta $) | −0.0099 | −0.0016 | −0.0056 | +0.0072 | +0.0086 | +0.0139 | +0.0087 | |

Repeated Gabor ($\Delta $) | −0.0129 | +0.0054 | +0.0086 | +0.0178 | +0.0085 | +0.0121 | +0.0141 |

**Table A10.**Improvement in minimum loss on Cats vs. Dogs dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.7039 | 1.0208 | 1.3793 | 0.8991 | 0.8574 | 0.9765 | 1.0263 |

Random Gabor ($\Delta $) | −0.0630 | −0.3510 | −0.7026 | −0.2184 | −0.1522 | −0.1801 | +0.1596 | |

Repeated Gabor ($\Delta $) | −0.0696 | −0.3772 | −0.6521 | −0.2515 | −0.1687 | −0.1927 | −0.1891 | |

64 × 64 | Traditional CNN (Base) | 0.8884 | 0.9717 | 0.8448 | 0.9905 | 1.2597 | 1.3066 | 1.4466 |

Random Gabor ($\Delta $) | −0.1744 | −0.2768 | −0.1251 | −0.3048 | −0.5674 | −0.4398 | −0.6611 | |

Repeated Gabor ($\Delta $) | −0.2145 | −0.2895 | −0.1689 | −0.3397 | −0.5842 | −0.6421 | −0.6685 | |

128 × 128 | Traditional CNN (Base) | 1.0480 | 0.8813 | 1.1060 | 0.7639 | 0.8840 | 1.0305 | 1.3318 |

Random Gabor ($\Delta $) | −0.3270 | −0.0753 | −0.3405 | −0.0858 | −0.1525 | −0.3765 | −0.5583 | |

Repeated Gabor ($\Delta $) | −0.4209 | −0.2144 | −0.4912 | −0.2167 | −0.2957 | −0.3765 | −0.7697 | |

256 × 256 | Traditional CNN (Base) | 1.1261 | 0.6374 | 0.7055 | 0.7233 | 1.1426 | 0.8459 | 0.8025 |

Random Gabor ($\Delta $) | −0.4575 | −0.0646 | −0.0882 | −0.0916 | −0.5824 | −0.2015 | −0.2225 | |

Repeated Gabor ($\Delta $) | −0.4516 | −0.0561 | +0.0252 | −0.0221 | −0.5944 | −0.0720 | −0.1276 |

**Table A11.**Improvement in maximum accuracy on CIFAR-10 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.7818 | 0.7896 | 0.7929 | 0.7712 | 0.7713 | 0.7744 | 0.7654 |

Random Gabor ($\Delta $) | −0.0049 | −0.0090 | −0.0122 | +0.0143 | +0.0124 | +0.0089 | +0.0101 | |

Repeated Gabor ($\Delta $) | −0.0037 | −0.0028 | −0.0087 | +0.0283 | +0.0164 | +0.0234 | +0.0155 | |

64 × 64 | Traditional CNN (Base) | 0.7086 | 0.7257 | 0.7199 | 0.7207 | 0.7115 | 0.7203 | 0.7219 |

Random Gabor ($\Delta $) | −0.0076 | −0.0129 | +0.0077 | +0.0143 | +0.0279 | +0.0393 | +0.0403 | |

Repeated Gabor ($\Delta $) | −0.0098 | −0.0107 | +0.0206 | +0.0348 | +0.0466 | +0.0416 | +0.0394 | |

128 × 128 | Traditional CNN (Base) | 0.7936 | 0.7988 | 0.8007 | 0.7930 | 0.7989 | 0.8004 | 0.8067 |

Random Gabor ($\Delta $) | +0.0086 | +0.0073 | +0.0146 | +0.0258 | +0.0228 | +0.0271 | +0.0177 | |

Repeated Gabor ($\Delta $) | +0.0093 | +0.0113 | +0.0134 | +0.0273 | +0.0281 | +0.0199 | +0.0142 |

**Table A12.**Improvement in AUC at maximum accuracy on CIFAR-10 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.9759 | 0.9773 | 0.9777 | 0.9744 | 0.9734 | 0.9737 | 0.9722 |

Random Gabor ($\Delta $) | −0.0011 | −0.0011 | −0.0027 | +0.0018 | +0.0023 | +0.0019 | +0.0018 | |

Repeated Gabor ($\Delta $) | −0.0010 | −0.0006 | −0.0019 | +0.0036 | +0.0037 | +0.0034 | +0.0021 | |

64 × 64 | Traditional CNN (Base) | 0.9575 | 0.9615 | 0.9606 | 0.9614 | 0.9598 | 0.9621 | 0.9623 |

Random Gabor ($\Delta $) | −0.0026 | −0.0019 | +0.0020 | +0.0032 | +0.0069 | +0.0073 | +0.0081 | |

Repeated Gabor ($\Delta $) | −0.0018 | −0.0006 | +0.0050 | +0.0080 | +0.0104 | +0.0086 | +0.0076 | |

128 × 128 | Traditional CNN (Base) | 0.9730 | 0.9724 | 0.9734 | 0.9725 | 0.9737 | 0.9733 | 0.9746 |

Random Gabor ($\Delta $) | +0.0008 | +0.0017 | +0.0011 | +0.0023 | +0.0023 | +0.0047 | +0.0033 | |

Repeated Gabor ($\Delta $) | +0.0005 | +0.0029 | +0.0021 | +0.0044 | +0.0031 | +0.0023 | +0.0015 |

**Table A13.**Improvement in minimum loss on CIFAR-10 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 1.4764 | 1.5682 | 1.9694 | 1.9144 | 1.6672 | 1.5935 | 2.1591 |

Random Gabor ($\Delta $) | −0.1391 | −0.2193 | −0.5082 | −0.5611 | −0.1535 | −0.1015 | −0.6806 | |

Repeated Gabor ($\Delta $) | −0.0672 | −0.1756 | −0.6604 | −0.6354 | −0.0718 | −0.1837 | −0.8144 | |

64 × 64 | Traditional CNN (Base) | 1.6460 | 1.9160 | 2.3001 | 1.6342 | 1.6378 | 1.8921 | 2.0575 |

Random Gabor ($\Delta $) | −0.0266 | −0.3585 | −0.6622 | −0.0978 | −0.1412 | −0.2156 | −0.4911 | |

Repeated Gabor ($\Delta $) | +0.0670 | −0.3258 | −0.7804 | −0.0624 | −0.1956 | +0.3132 | −0.3499 | |

128 × 128 | Traditional CNN (Base) | 1.4920 | 2.2684 | 1.2744 | 1.3457 | 1.3687 | 1.7287 | 1.4233 |

Random Gabor ($\Delta $) | −0.2609 | −1.1010 | −0.0477 | −0.1184 | −0.1824 | −0.3236 | −0.0045 | |

Repeated Gabor ($\Delta $) | −0.2781 | −1.0944 | +0.2863 | −0.1774 | −0.2432 | −0.1496 | −0.0947 |

**Table A14.**Improvement in maximum accuracy on CIFAR-100 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.5842 | 0.5740 | 0.5854 | 0.5488 | 0.5605 | 0.5678 | 0.5590 |

Random Gabor ($\Delta $) | −0.0237 | +0.0114 | −0.0281 | +0.0192 | +0.0201 | −0.0139 | +0.0081 | |

Repeated Gabor ($\Delta $) | −0.0189 | +0.0003 | −0.0021 | +0.0023 | +0.0004 | −0.0086 | −0.0029 | |

64 × 64 | Traditional CNN (Base) | 0.6803 | 0.6869 | 0.6807 | 0.6866 | 0.6898 | 0.6886 | 0.6867 |

Random Gabor ($\Delta $) | +0.0007 | +0.0025 | −0.0007 | −0.0015 | −0.0087 | −0.0094 | −0.0015 | |

Repeated Gabor ($\Delta $) | +0.0039 | +0.0018 | +0.0027 | −0.0028 | −0.0080 | −0.0010 | −0.0006 | |

128 × 128 | Traditional CNN (Base) | 0.7144 | 0.7065 | 0.7162 | 0.7164 | 0.7138 | 0.7123 | 0.7112 |

Random Gabor ($\Delta $) | −0.0060 | +0.0037 | +0.0018 | +0.0002 | +0.0012 | +0.0073 | 0.0059 | |

Repeated Gabor ($\Delta $) | +0.0017 | +0.0106 | −0.0070 | −0.0041 | +0.0040 | +0.0086 | +0.0145 |

**Table A15.**Improvement in AUC at maximum accuracy on CIFAR-100 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.9550 | 0.9503 | 0.9530 | 0.9525 | 0.9511 | 0.9514 | 0.9512 |

Random Gabor ($\Delta $) | −0.0025 | +0.0035 | +0.0003 | −0.0028 | +0.0023 | −0.0007 | −0.0004 | |

Repeated Gabor ($\Delta $) | −0.0036 | +0.0018 | −0.0006 | +0.0025 | −0.0019 | +0.0020 | −0.0006 | |

64 × 64 | Traditional CNN (Base) | 0.9636 | 0.9652 | 0.9659 | 0.9628 | 0.9655 | 0.9643 | 0.9652 |

Random Gabor ($\Delta $) | +0.0008 | +0.0002 | −0.0009 | +0.0030 | −0.0006 | +0.0025 | +0.0007 | |

Repeated Gabor ($\Delta $) | −0.0004 | −0.0004 | −0.0007 | +0.0027 | −0.0012 | +0.0021 | +0.0006 | |

128 × 128 | Traditional CNN (Base) | 0.9694 | 0.9686 | 0.9684 | 0.9690 | 0.9682 | 0.9691 | 0.9682 |

Random Gabor ($\Delta $) | +0.0008 | +0.0002 | +0.0010 | +0.0021 | +0.0028 | +0.0000 | +0.0016 | |

Repeated Gabor ($\Delta $) | +0.0002 | +0.0011 | +0.0030 | +0.0013 | +0.0010 | +0.0007 | +0.0029 |

**Table A16.**Improvement in minimum loss on CIFAR-100 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 4.3399 | 4.5608 | 4.0880 | 5.9439 | 4.1416 | 4.2599 | 5.1038 |

Random Gabor ($\Delta $) | +0.1598 | −0.6657 | −0.0989 | −1.7213 | +0.1809 | −0.2785 | +2.1429 | |

Repeated Gabor ($\Delta $) | +0.4380 | −0.4634 | +0.7734 | −1.5532 | +0.5421 | +0.2966 | −1.1574 | |

64 × 64 | Traditional CNN (Base) | 3.6348 | 3.7467 | 3.5715 | 3.8046 | 3.8158 | 4.0575 | 4.0832 |

Random Gabor ($\Delta $) | +0.1774 | −0.0744 | +0.0242 | −0.3521 | +0.2289 | +0.1263 | +0.2179 | |

Repeated Gabor ($\Delta $) | +0.5789 | +0.3015 | +1.7995 | −0.0274 | +0.1685 | +0.8609 | +0.1275 | |

128 × 128 | Traditional CNN (Base) | 3.4936 | 4.1385 | 4.1666 | 5.1151 | 3.7694 | 3.5885 | 4.0887 |

Random Gabor ($\Delta $) | +0.2320 | −0.2233 | −0.6036 | −1.3428 | +0.9635 | +0.0513 | −0.0090 | |

Repeated Gabor ($\Delta $) | +0.4857 | −0.2240 | −0.1239 | −0.6645 | +0.0184 | −0.0016 | +0.1811 |

**Table A17.**Improvement in maximum accuracy on Caltech 256 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.3086 | 0.3084 | 0.3022 | 0.3096 | 0.3061 | 0.3099 | 0.2978 |

Random Gabor ($\Delta $) | −0.0007 | +0.0002 | +0.0195 | +0.0106 | +0.0064 | +0.0010 | +0.0008 | |

Repeated Gabor ($\Delta $) | +0.0123 | +0.0020 | +0.0146 | +0.0115 | +0.0056 | +0.0008 | −0.0005 | |

64 × 64 | Traditional CNN (Base) | 0.4296 | 0.4388 | 0.4375 | 0.4404 | 0.4403 | 0.4380 | 0.4313 |

Random Gabor ($\Delta $) | −0.0090 | −0.0028 | +0.0113 | +0.0025 | −0.0116 | +0.0119 | +0.0214 | |

Repeated Gabor ($\Delta $) | +0.0039 | −0.0054 | +0.0082 | +0.0072 | +0.0113 | +0.0059 | +0.0059 | |

128 × 128 | Traditional CNN (Base) | 0.5028 | 0.5025 | 0.5350 | 0.5200 | 0.5113 | 0.5195 | 0.5092 |

Random Gabor ($\Delta $) | +0.0151 | +0.0208 | +0.0008 | +0.0026 | +0.0211 | +0.0061 | +0.0041 | |

Repeated Gabor ($\Delta $) | +0.0195 | +0.0128 | −0.0043 | +0.0036 | +0.0188 | +0.0051 | +0.0198 |

**Table A18.**Improvement in AUC at maximum accuracy on Caltech 256 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.8481 | 0.8419 | 0.8513 | 0.8574 | 0.8454 | 0.8474 | 0.8392 |

Random Gabor ($\Delta $) | −0.0021 | +0.0162 | +0.0019 | −0.0027 | +0.0050 | +0.0003 | +0.0057 | |

Repeated Gabor ($\Delta $) | +0.0055 | +0.0095 | −0.0030 | +0.0005 | +0.0131 | +0.0037 | +0.0069 | |

64 × 64 | Traditional CNN (Base) | 0.8741 | 0.8853 | 0.8846 | 0.8853 | 0.8837 | 0.8848 | 0.8840 |

Random Gabor ($\Delta $) | +0.0026 | −0.0037 | +0.0036 | +0.0033 | −0.0010 | +0.0060 | −0.0001 | |

Repeated Gabor ($\Delta $) | +0.0037 | −0.0028 | −0.0007 | +0.0050 | +0.0114 | +0.0034 | +0.0041 | |

128 × 128 | Traditional CNN (Base) | 0.9034 | 0.9097 | 0.9062 | 0.9036 | 0.9046 | 0.9049 | 0.9021 |

Random Gabor ($\Delta $) | +0.0053 | −0.0004 | +0.0072 | +0.0020 | +0.0006 | −0.0059 | +0.0036 | |

Repeated Gabor ($\Delta $) | +0.0050 | +0.0002 | +0.0010 | +0.0028 | +0.0045 | +0.0044 | +0.0054 |

**Table A19.**Improvement in minimum loss on Caltech 256 dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 8.1892 | 6.2550 | 7.0410 | 7.8705 | 8.5046 | 11.1519 | 5.8391 |

Random Gabor ($\Delta $) | −2.5809 | +0.6026 | −1.6581 | −2.3008 | +0.8493 | −0.4026 | −0.3982 | |

Repeated Gabor ($\Delta $) | −1.6821 | +1.8756 | −1.0074 | −1.6438 | −0.5016 | −5.2436 | +2.1425 | |

64 × 64 | Traditional CNN (Base) | 6.3774 | 8.1425 | 6.8721 | 6.7314 | 7.0304 | 8.6386 | 5.2090 |

Random Gabor ($\Delta $) | −0.8742 | −3.0356 | −1.2754 | −1.3800 | −1.0103 | −2.7627 | +0.8800 | |

Repeated Gabor ($\Delta $) | −1.1548 | −2.6945 | +3.0506 | −0.1708 | +5.0498 | −2.1193 | +0.7651 | |

128 × 128 | Traditional CNN (Base) | 4.9090 | 5.1978 | 13.0624 | 6.8160 | 6.3426 | 7.1236 | 7.1915 |

Random Gabor ($\Delta $) | +0.3547 | +0.1951 | −8.0269 | −1.6014 | −1.3128 | −1.7678 | −1.8235 | |

Repeated Gabor ($\Delta $) | +0.7467 | +0.3598 | −7.7013 | −0.7981 | −0.6349 | +1.1454 | −1.4903 |

**Table A20.**Improvement in maximum accuracy on Stanford Cars dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.0493 | 0.0426 | 0.0442 | 0.0425 | 0.0304 | 0.0334 | 0.0300 |

Random Gabor ($\Delta $) | −0.0088 | +0.0090 | −0.0002 | +0.0060 | +0.0133 | +0.0076 | +0.0009 | |

Repeated Gabor ($\Delta $) | +0.0051 | +0.0024 | +0.0004 | +0.0059 | +0.0152 | +0.0115 | +0.0139 | |

64 × 64 | Traditional CNN (Base) | 0.1774 | 0.1602 | 0.1498 | 0.1350 | 0.1386 | 0.0818 | 0.1143 |

Random Gabor ($\Delta $) | −0.0330 | +0.0081 | +0.0015 | +0.0019 | −0.0162 | +0.0436 | −0.0009 | |

Repeated Gabor ($\Delta $) | −0.0339 | +0.0117 | +0.0326 | +0.0281 | −0.0092 | +0.0524 | +0.0410 | |

128 × 128 | Traditional CNN (Base) | 0.4103 | 0.3879 | 0.4180 | 0.3598 | 0.3010 | 0.3102 | 0.3517 |

Random Gabor ($\Delta $) | −0.0151 | +0.0396 | +0.0157 | +0.0802 | +0.1398 | +0.1930 | +0.0600 | |

Repeated Gabor ($\Delta $) | −0.0818 | +0.0274 | +0.0005 | +0.0029 | +0.1313 | +0.0788 | +0.0648 |

**Table A21.**Improvement in AUC at maximum accuracy on Stanford Cars dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.7107 | 0.6970 | 0.7114 | 0.6907 | 0.6290 | 0.6427 | 0.6325 |

Random Gabor ($\Delta $) | −0.0198 | +0.0019 | −0.0198 | +0.0009 | +0.0526 | +0.0292 | +0.0041 | |

Repeated Gabor ($\Delta $) | +0.0111 | −0.0038 | −0.0106 | +0.0173 | +0.0705 | +0.0448 | +0.0568 | |

64 × 64 | Traditional CNN (Base) | 0.8211 | 0.8046 | 0.7911 | 0.7815 | 0.7713 | 0.7255 | 0.7472 |

Random Gabor ($\Delta $) | −0.0173 | −0.0063 | +0.0018 | +0.0030 | −0.0056 | +0.0358 | +0.0146 | |

Repeated Gabor ($\Delta $) | −0.0150 | −0.0046 | +0.0154 | +0.0165 | +0.0045 | +0.0528 | +0.0388 | |

128 × 128 | Traditional CNN (Base) | 0.8736 | 0.8831 | 0.8723 | 0.8808 | 0.8369 | 0.8344 | 0.8811 |

Random Gabor ($\Delta $) | +0.0020 | +0.0020 | +0.0180 | +0.0033 | +0.0455 | +0.0458 | +0.0032 | |

Repeated Gabor ($\Delta $) | +0.0063 | +0.0017 | +0.0028 | +0.0030 | +0.0515 | +0.0278 | +0.0035 |

**Table A22.**Improvement in minimum loss on Stanford Cars dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 7.3203 | 47.5599 | 8.8750 | 9.2702 | 22.8231 | 7.1648 | 9.1182 |

Random Gabor ($\Delta $) | +12.3424 | −37.8715 | +3.6937 | +3.4808 | −15.7108 | +0.3171 | +0.4810 | |

Repeated Gabor ($\Delta $) | +7.1468 | −37.3148 | −2.6179 | +6.2107 | −4.7338 | +5.3186 | +7.1548 | |

64 × 64 | Traditional CNN (Base) | 24.1874 | 7.3460 | 14.2081 | 10.4780 | 16.0974 | 17.0614 | 20.6991 |

Random Gabor ($\Delta $) | −13.0682 | +1.0896 | −6.3144 | +1.3075 | −3.0181 | −4.1803 | −0.5565 | |

Repeated Gabor ($\Delta $) | −16.0293 | +13.3526 | +13.5375 | +2.7611 | −1.1857 | −0.2307 | −3.6890 | |

128 × 128 | Traditional CNN (Base) | 18.8136 | 36.2230 | 18.1727 | 6.6971 | 6.5915 | 73.8066 | 6.7081 |

Random Gabor ($\Delta $) | −1.3699 | −26.1808 | −9.9487 | +9.0980 | +4.3474 | −66.8044 | +7.0920 | |

Repeated Gabor ($\Delta $) | −4.3315 | −23.0504 | −9.2398 | +4.6752 | +34.7256 | −62.0934 | +4.2712 |

**Table A23.**Improvement in maximum accuracy on Tiny Imagenet dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.3921 | 0.3950 | 0.3832 | 0.3712 | 0.3671 | 0.3649 | 0.3543 |

Random Gabor ($\Delta $) | −0.0077 | −0.0029 | −0.0419 | −0.0223 | −0.0294 | −0.0340 | −0.0083 | |

Repeated Gabor ($\Delta $) | −0.0050 | −0.0465 | −0.0462 | −0.0453 | −0.0401 | −0.0612 | −0.0410 | |

64 × 64 | Traditional CNN (Base) | 0.4806 | 0.4824 | 0.4739 | 0.4699 | 0.4659 | 0.4662 | 0.4562 |

Random Gabor ($\Delta $) | +0.0102 | −0.0021 | −0.0041 | −0.0072 | −0.0102 | +0.0002 | +0.0152 | |

Repeated Gabor ($\Delta $) | −0.0037 | −0.0390 | −0.0186 | +0.0004 | −0.0244 | −0.0229 | −0.0021 | |

128 × 128 | Traditional CNN (Base) | 0.5199 | 0.5233 | 0.5241 | 0.5216 | 0.5229 | 0.5218 | 0.5104 |

Random Gabor ($\Delta $) | +0.0113 | +0.0056 | +0.0081 | −0.0031 | −0.0018 | +0.0056 | +0.0170 | |

Repeated Gabor ($\Delta $) | −0.0066 | −0.0153 | −0.0411 | −0.0126 | −0.0142 | −0.0099 | +0.0060 |

**Table A24.**Improvement in AUC at maximum accuracy on Tiny Imagenet dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 0.9109 | 0.9113 | 0.9062 | 0.9056 | 0.9011 | 0.8991 | 0.8979 |

Random Gabor ($\Delta $) | −0.0002 | −0.0054 | −0.0118 | −0.0109 | −0.0079 | −0.0098 | −0.0006 | |

Repeated Gabor ($\Delta $) | −0.0038 | −0.0181 | −0.0082 | −0.0163 | −0.0103 | −0.0172 | −0.0175 | |

64 × 64 | Traditional CNN (Base) | 0.9361 | 0.9319 | 0.9333 | 0.9312 | 0.9308 | 0.9294 | 0.9262 |

Random Gabor ($\Delta $) | −0.0031 | +0.0008 | −0.0026 | +0.0002 | −0.0033 | −0.0006 | +0.0037 | |

Repeated Gabor ($\Delta $) | −0.0093 | −0.0050 | −0.0094 | −0.0021 | −0.0039 | −0.0078 | −0.0018 | |

128 × 128 | Traditional CNN (Base) | 0.9435 | 0.9418 | 0.9438 | 0.9432 | 0.9439 | 0.9428 | 0.9427 |

Random Gabor ($\Delta $) | −0.0006 | +0.0011 | −0.0013 | −0.0017 | −0.0014 | −0.0009 | +0.0013 | |

Repeated Gabor ($\Delta $) | −0.0065 | −0.0068 | −0.0091 | −0.0089 | −0.0061 | −0.0056 | −0.0023 |

**Table A25.**Improvement in minimum loss on Tiny Imagenet dataset with different kernel sizes and image sizes. Bold numbers indicate top results.

Image Size | Gabor Configuration | Kernel Size | ||||||
---|---|---|---|---|---|---|---|---|

3 × 3 | 5 × 5 | 7 × 7 | 9 × 9 | 11 × 11 | 13 × 13 | 15 × 15 | ||

32 × 32 | Traditional CNN (Base) | 5.2912 | 5.2273 | 5.2322 | 5.1488 | 5.1689 | 5.2050 | 5.1729 |

Random Gabor ($\Delta $) | −0.2901 | −0.2618 | −0.2595 | −0.2248 | −0.1753 | −0.1808 | −0.1660 | |

Repeated Gabor ($\Delta $) | −0.0636 | −0.0202 | −0.0505 | −0.0025 | −0.0429 | −0.0107 | −0.0384 | |

64 × 64 | Traditional CNN (Base) | 5.1014 | 5.1428 | 5.1198 | 5.1246 | 5.0847 | 5.1234 | 5.0616 |

Random Gabor ($\Delta $) | −0.2692 | −0.2719 | −0.2538 | −0.2102 | −0.2546 | −0.1730 | −0.1027 | |

Repeated Gabor ($\Delta $) | +0.1317 | +0.0625 | −0.0146 | −0.0464 | +0.0509 | −0.0955 | −0.0103 | |

128 × 128 | Traditional CNN (Base) | 5.0659 | 5.0616 | 5.0584 | 5.0257 | 5.0092 | 5.0673 | 5.2985 |

Random Gabor ($\Delta $) | −0.2046 | −0.2492 | −0.3288 | −0.1116 | +0.0950 | −0.0409 | −0.5205 | |

Repeated Gabor ($\Delta $) | +0.1017 | +0.0927 | +0.0865 | +0.0545 | +0.0739 | −0.0492 | −0.3941 |

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**Figure 1.**Learned convolutional filters in the receptive field for general-purpose object recognition networks (

**a**–

**c**). (

**d**) Gabor filters produced with different values for $\lambda ,\theta $, and $\gamma $; the values for the parameters on each row are $\gamma =0.1,\theta =0,$ and $\lambda =1$, unless otherwise specified. There are similarities between the learned filters by different popular CNNs and Gabor filters; these similarities suggest that, perhaps, initializing CNNs with Gabor filters could accelerate convergence to an optimal set of convolutional filters. Specifically: (

**a**) is a ResNet50 subset of learned filters [30]. (

**b**) is a ResNet152V2 subset of learned filters [31]. (

**c**) is a DenseNet121 subset of learned filters [32]. (

**d**) are Gabor filters with different parameters [29].

**Figure 2.**This is the CNN architecture used for the Tiny Imagenet dataset. The architectures for the rest of the datasets only change the input layers in direct proportion to the input image sizes. This kind of architecture resembles the classic AlexNet [19], a very successful general-purpose architecture.

**Figure 3.**Comparison of all classifiers against each other with the Nemenyi test. Classifiers that are not significantly different at $\alpha =0.10$ or $\alpha =0.5$ are connected. Note that at least one Gabor-based method is always significantly different than the baseline. This suggests that the proposed methodology can offer performance and convergence advantages with statistical significance.

**Table 1.**Summary of the main properties of the datasets considered in our experiments. These include binary and multiclass datasets with and without balance across various domains.

Dataset | Classes | Distribution | Dimension | Training | Testing | Reference |
---|---|---|---|---|---|---|

Cats vs. Dogs Version 1.0 | 2 | Balanced | 256 × 256 | 20,000 | 5000 | [65] |

CIFAR-10 Version 3.0.2 | 10 | Balanced | 128 × 128 | 50,000 | 10,000 | [66] |

CIFAR-100 Version 3.0.2 | 100 | Balanced | 128 × 128 | 50,000 | 10,000 | [66] |

Caltech 256 Version 2.0 | 257 | Imbalanced | 128 × 128 | 24,485 | 6122 | [67] |

Stanford Cars Version 2.0 | 196 | Imbalanced | 128 × 128 | 8144 | 8041 | [68] |

Tiny Imagenet | 200 | Balanced | 128 × 128 | 100,000 | 10,000 | [69] |

**Table 2.**Critical values for the Nemenyi test, which is conducted following the Friedman test, with two-tailed results.

#Classifiers | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|

${q}_{\alpha =0.05}$ | $1.960$ | $2.343$ | $2.569$ | $2.728$ | $2.850$ |

${q}_{\alpha =0.10}$ | $1.645$ | $2.052$ | $2.291$ | $2.459$ | $2.589$ |

**Table 3.**Improvement in maximum accuracy of Gabor-configured CNN with respect to traditional CNN. The proposed methodology displays accuracy-based advantages with statistical confidence. The highest accuracies are shown in bold.

Dataset | Baseline Glorot N. | Baseline Glorot U. | Random Gabor Filter | Repeated Gabor Filter | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | |

Cats vs. Dogs | 0.8937 | 0.005 | (3) | 0.8839 | 0.004 | (4) | 0.9072 | 0.007 | (2) | 0.9102 | 0.006 | (1) |

CIFAR-10 | 0.8023 | 0.004 | (4) | 0.8024 | 0.004 | (3) | 0.8229 | 0.004 | (2) | 0.8238 | 0.005 | (1) |

CIFAR-100 | 0.7130 | 0.004 | (4) | 0.7132 | 0.003 | (3) | 0.7198 | 0.005 | (2) | 0.7206 | 0.005 | (1) |

Caltech 256 | 0.5084 | 0.007 | (4) | 0.5085 | 0.007 | (3) | 0.5232 | 0.009 | (2) | 0.5273 | 0.011 | (1) |

Stanford Cars | 0.2331 | 0.074 | (3) | 0.2326 | 0.070 | (4) | 0.3620 | 0.072 | (2) | 0.3952 | 0.072 | (1) |

Tiny Imagenet | 0.5174 | 0.005 | (4) | 0.5175 | 0.004 | (3) | 0.5307 | 0.003 | (1) | 0.5178 | 0.007 | (2) |

Average | 0.6113 | 0.017 | (3.66) | 0.6097 | 0.015 | (3.33) | 0.6443 | 0.017 | (1.83) | 0.6492 | 0.018 | (1.16) |

**Table 4.**Improvement in AUC at the maximum accuracy of Gabor-configured CNN with respect to traditional CNN. The proposed methodology displays AUC-based performance advantages with statistical confidence. The highest AUCs are shown in bold.

Dataset | Baseline Glorot N. | Baseline Glorot U. | Random Gabor Filter | Repeated Gabor Filter | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | |

Cats vs. Dogs | 0.9514 | 0.004 | (4) | 0.9515 | 0.003 | (3) | 0.9651 | 0.004 | (2) | 0.9684 | 0.004 | (1) |

CIFAR-10 | 0.9717 | 0.002 | (4) | 0.9719 | 0.001 | (3) | 0.9749 | 0.001 | (1) | 0.9744 | 0.001 | (2) |

CIFAR-100 | 0.9620 | 0.002 | (4) | 0.9621 | 0.002 | (3) | 0.9634 | 0.002 | (2) | 0.9637 | 0.002 | (1) |

Caltech 256 | 0.8887 | 0.004 | (3) | 0.8885 | 0.004 | (4) | 0.8962 | 0.005 | (1) | 0.8925 | 0.005 | (2) |

Stanford Cars | 0.8074 | 0.026 | (4) | 0.8077 | 0.026 | (3) | 0.8584 | 0.021 | (2) | 0.8703 | 0.025 | (1) |

Tiny Imagenet | 0.9367 | 0.004 | (3) | 0.9370 | 0.003 | (2) | 0.9394 | 0.004 | (1) | 0.9358 | 0.007 | (4) |

Average | 0.9197 | 0.007 | (3.66) | 0.9198 | 0.006 | (3) | 0.9329 | 0.006 | (1.5) | 0.9342 | 0.007 | (1.83) |

**Table 5.**Improvement in minimum loss of Gabor-configured CNN with respect to traditional CNN. The proposed methodology displays optimization advantages with statistical confidence, reaching a lower minimum value in comparison to the standard methodology. The smallest loss is shown in bold.

Dataset | Baseline Glorot N. | Baseline Glorot U. | Random Gabor Filter | Repeated Gabor Filter | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | |

Cats vs. Dogs | 0.2981 | 0.019 | (4) | 0.2960 | 0.012 | (3) | 0.2524 | 0.017 | (2) | 0.2399 | 0.012 | (1) |

CIFAR-10 | 0.6443 | 0.014 | (3) | 0.6555 | 0.013 | (4) | 0.6011 | 0.015 | (2) | 0.5985 | 0.017 | (1) |

CIFAR-100 | 1.1805 | 0.021 | (3) | 1.1823 | 0.020 | (4) | 1.1578 | 0.018 | (2) | 1.1509 | 0.020 | (1) |

Caltech 256 | 2.6357 | 0.066 | (3) | 2.6428 | 0.067 | (4) | 2.5388 | 0.078 | (1) | 2.5399 | 0.065 | (2) |

Stanford Cars | 4.2337 | 0.323 | (4) | 4.1857 | 0.356 | (3) | 3.4045 | 0.291 | (2) | 3.1459 | 0.360 | (1) |

Tiny Imagenet | 2.7357 | 0.022 | (3) | 2.7390 | 0.014 | (4) | 2.6863 | 0.024 | (1) | 2.7353 | 0.027 | (2) |

Average | (3.33) | (3.66) | (1.66) | (1.33) |

**Table 6.**Improvement in maximum accuracy epoch of epoch-constrained Gabor-initialized CNN with respect to traditional CNN when training period was constrained to maximum accuracy epoch of traditional CNN. The proposed methodology displays optimization advantages with statistical confidence, reaching the best accuracy in a smaller number of epochs than the standard methodology. The smallest number of epochs are shown in bold.

Dataset | Baseline Glorot N. | Baseline Glorot U. | Random Gabor Filter | Repeated Gabor Filter | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | Mean | Stdev | Rk. | |

Cats vs. Dogs | 87.1 | 12.1 | (3) | 88.4 | 13.8 | (4) | 83.2 | 5.4 | (2) | 70.8 | 15.2 | (1) |

CIFAR-10 | 66.3 | 5.7 | (3) | 67.9 | 5.6 | (4) | 59.0 | 6.1 | (1) | 61.3 | 3.6 | (2) |

CIFAR-100 | 99.5 | 3.8 | (4) | 99.3 | 6.4 | (3) | 95.0 | 2.9 | (2) | 92.8 | 6.2 | (1) |

Caltech 256 | 74.1 | 4.9 | (4) | 73.3 | 5.4 | (3) | 69.1 | 4.4 | (2) | 67.6 | 4.0 | (1) |

Stanford Cars | 104.3 | 8.3 | (4) | 103.6 | 13.2 | (3) | 97.9 | 5.1 | (2) | 97.7 | 5.4 | (1) |

Tiny Imagenet | 36.8 | 7.1 | (3) | 37.3 | 6.6 | (4) | 32.2 | 5.7 | (1) | 32.6 | 5.7 | (2) |

Average | (3.5) | (3.5) | (1.66) | (1.33) |

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Rivas, P.; Rai, M.
Enhancing CNNs Performance on Object Recognition Tasks with Gabor Initialization. *Electronics* **2023**, *12*, 4072.
https://doi.org/10.3390/electronics12194072

**AMA Style**

Rivas P, Rai M.
Enhancing CNNs Performance on Object Recognition Tasks with Gabor Initialization. *Electronics*. 2023; 12(19):4072.
https://doi.org/10.3390/electronics12194072

**Chicago/Turabian Style**

Rivas, Pablo, and Mehang Rai.
2023. "Enhancing CNNs Performance on Object Recognition Tasks with Gabor Initialization" *Electronics* 12, no. 19: 4072.
https://doi.org/10.3390/electronics12194072