# Neutrosophic Hough Transform

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## Abstract

**:**

## 1. Introduction

## 2. Previous Works

#### 2.1. Hough Transform

_{HT}.

#### 2.2. Fuzzy Hough Transform

## 3. Proposed Method

#### 3.1. Neutrosophic Hough Space Image

_{i}is $\left\{\mathrm{T}\left({A}_{i}\right),\text{}\mathrm{I}\left({A}_{i}\right),\mathrm{F}\left({A}_{i}\right)\right\}/{A}_{i}$, where $\mathrm{T}\left({A}_{i}\right)$, $\mathrm{I}\left({A}_{i}\right)$, and $\mathrm{F}\left({A}_{i}\right)$ are the membership values to the true, indeterminate, and false set.

_{HT}is mapped into neutrosophic set domain, denoted as I

_{NHT}, which is interpreted using T

_{HT}, I

_{HT}, and F

_{HT}. Given a pixel $P\left(\rho ,\theta \right)$ in I

_{HT}, it is interpreted as ${P}_{\mathrm{NHT}}\left(\rho ,\theta \right)=\left\{{T}_{\mathrm{HT}}\left(\rho ,\theta \right),{I}_{\mathrm{HT}}\left(\rho ,\theta \right),\text{}{F}_{\mathrm{HT}}\left(\rho ,\theta \right)\text{}\right\}$. ${T}_{\mathrm{HT}}\left(\rho ,\theta \right)$, ${I}_{\mathrm{HT}}\left(\rho ,\theta \right)$, and ${F}_{\mathrm{HT}}\left(\rho ,\theta \right)$ represent the memberships belonging to foreground, indeterminate set, and background, respectively [20,21,22,23,24,25,26,27].

_{NHT}.

#### 3.2. Indeterminacy Filtering

#### 3.3. Thresholding Based on Histogram in Neutrosophic Hough Image

## 4. Experimental Results

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Application of the neutrosophic Hough transform (NHT) on a synthetic image, (

**a**) input synthetic image; (

**b**) neutrosophy (NS) Hough space; (

**c**) Detected peaks in NS Hough space; and, (

**d**) Detected lines.

**Figure 3.**Application of the NHT on a noisy synthetic image, (

**a**) input noisy synthetic image; (

**b**) NS Hough space; (

**c**) Detected peaks in NS Hough space; and, (

**d**) Detected lines.

**Figure 4.**Application of the NHT on a noisy synthetic image, (

**a**) input noisy and noise-free synthetic image; (

**b**) Detected lines with proposed NHT.

**Figure 6.**Comparison of NHT with Hough transform (HT) and FHT on noisy images (

**a**) HT results; (

**b**) FHT results and (

**c**) NHT results.

**Figure 7.**Comparison of NHT with HT and FHT on noisy images (

**a**) HT results; (

**b**) FHT results; and, (

**c**) NHT results.

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**MDPI and ACS Style**

Budak, Ü.; Guo, Y.; Şengür, A.; Smarandache, F. Neutrosophic Hough Transform. *Axioms* **2017**, *6*, 35.
https://doi.org/10.3390/axioms6040035

**AMA Style**

Budak Ü, Guo Y, Şengür A, Smarandache F. Neutrosophic Hough Transform. *Axioms*. 2017; 6(4):35.
https://doi.org/10.3390/axioms6040035

**Chicago/Turabian Style**

Budak, Ümit, Yanhui Guo, Abdulkadir Şengür, and Florentin Smarandache. 2017. "Neutrosophic Hough Transform" *Axioms* 6, no. 4: 35.
https://doi.org/10.3390/axioms6040035