# Cross-Correlation and Fractal Analysis in the Images Diatoms Symmetry

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Diatom Images

#### 2.2. Fractal Dimension Analysis

^{®}[36], and it was applied to the different diatoms images used in this study.

#### 2.3. Power Spectra Analysis

^{®}, the FFT function computes the Fourier transform using a fast Fourier transform algorithm. Use FFT to compute the discrete Fourier transform of the signal. y = fft(x); plot the power spectrum as a function of frequency.

#### 2.4. Two-Dimensional Cross-Correlation

#### 2.5. Software

## 3. Results and Discussion

#### 3.1. Self-Similarity and Symmetry

#### 3.2. Power Spectrum in the Self-Similarity and Symmetry

#### 3.3. CC between Diatoms

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Diatom images for each species taken by optical microscopy from ADIAC diatoms image database.

**Figure 3.**Calculated 2D cross-correlation and preprocessing steps using symmetry operations from the (

**a**) imagen I3 and (

**b**) imagen I34. The red lines are the CCauto.

**Figure 4.**Polar plot for all the diatom images where the radius is Nf and the angle is the projection for each symmetry operation (

**a**) PSv, (

**b**) R180, (

**c**) PSo and (

**d**) score plot PC 1 vs. PC2 for all diatoms images using Nf, and projection parameters.

**Figure 6.**(

**a**) Projection for each symmetry operation (

**b**) score plot PC 1 vs. PC2 for all diatoms images using Nf, and projections parameters, inset: loading plot of PC1 vs. PC2.

Cod | Name | Cod | Name | Cod | Name | Cod | Name | Cod | Name |
---|---|---|---|---|---|---|---|---|---|

I1 | Actinoptychus senarius | I11 | Achnanthes | I21 | Martyana martyi | I31 | Brachysira brebissonii | I41 | Neidium affine |

I2 | Auliscus sculptus | I12 | Caloneis amphisbaena | I22 | Melosira nummuloides | I32 | Craticula ambigua | I42 | Nitzschia amphibia |

I3 | Cyclostephanos dubius | I13 | Denticula subtilis | I23 | Opephora marina | I33 | Ctenophora pulchella | I43 | Plagiotropis tayrecta |

I4 | Cyclotella radiosa | I14 | Didymosphenia geminata | I24 | Parlibellus berkeleyi | I34 | Cymbella cornuta | I44 | Staurophora amphioxys |

I5 | Hyalodiscus scoticus | I15 | Dimeregramma minor | I25 | Plagiogramma staurophorum | I35 | Encyonopsis microcephala | I45 | Stenopterobia densestriata |

I6 | Cavinula jaernefeltii | I16 | Tryblionella coarctata | I26 | Pseudostaurosira brevistriata | I36 | Eunotia bilunaris | I46 | Surirella angusta |

I7 | Delphineis surirella | I17 | Diploneis boldtiana | I27 | Stauroforma inermis | I37 | Eunotia incisa | I47 | Meridion circulare |

I8 | Luticola mutica | I18 | Encyonema elginense | I28 | Thalassionema nitzschioides | I38 | Gyrosigma acuminatum | I48 | Odontella aurita |

I9 | Psammodiscus nitidus | I19 | Epithemia sorex | I29 | Amphora acutiuscula | I39 | Hannaea arcus | I49 | Stauroneis legumen |

I10 | Rhaphoneis amphiceros | I20 | Lyrella abrupta | I30 | Berkeleya rutilans | I40 | Licmophora oedipus | I50 | Tabellaria flocculosa |

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**MDPI and ACS Style**

Pestana-Nobles, R.; Villarreal-González, R.; Galan-Freyle, N.J.; Aranguren-Díaz, Y.; Machado-Sierra, E.; Yime-Rodríguez, E.; Pacheco-Londoño, L.C.
Cross-Correlation and Fractal Analysis in the Images Diatoms Symmetry. *Appl. Sci.* **2023**, *13*, 4909.
https://doi.org/10.3390/app13084909

**AMA Style**

Pestana-Nobles R, Villarreal-González R, Galan-Freyle NJ, Aranguren-Díaz Y, Machado-Sierra E, Yime-Rodríguez E, Pacheco-Londoño LC.
Cross-Correlation and Fractal Analysis in the Images Diatoms Symmetry. *Applied Sciences*. 2023; 13(8):4909.
https://doi.org/10.3390/app13084909

**Chicago/Turabian Style**

Pestana-Nobles, Roberto, Reynaldo Villarreal-González, Nataly J. Galan-Freyle, Yani Aranguren-Díaz, Elwi Machado-Sierra, Eugenio Yime-Rodríguez, and Leonardo C. Pacheco-Londoño.
2023. "Cross-Correlation and Fractal Analysis in the Images Diatoms Symmetry" *Applied Sciences* 13, no. 8: 4909.
https://doi.org/10.3390/app13084909