# Effective Image Retrieval Using Texture Elements and Color Fuzzy Correlogram

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. The Proposed Feature Extraction Methods

#### 3.1. Color Layer-Based Texture Elements Histogram

#### 3.1.1. Texture Elements Definition

#### 3.1.2. Feature Extraction

**Step 1**. Convert the original RGB image to the corresponding HSV image and quantize it using Equations (1)–(3).

**Step 2**. Traverse every color layer using the texture elements in Figure 1 according to the order of top to bottom and left to right. The moving step length is 2 pixels. An example is given in Figure 2, taking the three color layers quantized from the component saturation.

**Step 3**. For every color layer, count the number of each kind of texture element to obtain a 16-dimensional statistical histogram, and normalize it using the following equation:

**Step 4**. Reassemble the histograms of all of the color layers to obtain the required feature vector. The final feature vector of the example in Figure 2 is:

#### 3.2. Color Fuzzy Correlogram

#### 3.2.1. The Calculation of Color Fuzzy Correlogram

**Step 1**. Quantify the given image I into the range of $\left[{I}_{\mathrm{min}},{I}_{\mathrm{max}}\right]$. Take any pixel $a$ as the central pixel. $x$ is a surrounding pixel of $a$ and it is not more than $d$ pixels away from $a$. Figure 3 shows how to determine the surrounding pixels of a given pixel $a$ for different distance $d$. Here, the colored pixels are the surrounding pixels $x$. The fuzziness ${\varphi}_{d}\left(a,x\right)$ between $a$ and $x$ can be computed as:

**Step 2**. Add all of the fuzziness ${\varphi}_{d}\left(a,x\right)$ together to get the fuzzy correlation value of the central pixel $a$. The fuzzy correlation value ${\psi}_{d}\left(a\right)$ can be easily computed as:

**Step 3**. For pixels with the same color value, add up their fuzzy correlation values as follows:

**Step 4**. Express the color fuzzy correlogram of image I − $CF{C}_{d}\left(I\right)$, as follows:

#### 3.2.2. Color Feature Extraction

**Step 1**. Divide I into multiple non-overlapping image blocks of size $m\times n$. Let $\mathrm{{\rm B}}=\left\{b(i,j)|\text{}i=1,2,\cdots ,\frac{\mathrm{{\rm M}}}{m};\text{}j=1,2,\cdots ,\frac{\mathrm{{\rm N}}}{n}\right\}$ be the set of all of these image blocks.

**Step 2**. Replace image block $b(i,j)$ with a pixel ${p}_{\mathrm{max}}\left(i,j\right)$ which is defined as :

**Step 3**. Replace image block $b(i,j)$ with a pixel ${p}_{\mathrm{min}}\left(i,j\right)$, which is defined as:

**Step 4**. Quantize the two shrunken images max-image and min-image to 72 bins using Equations (12) and (13) based on Equations (1)–(3):

**Step 5**. Set up distance $d$ in Chapter 3.2.1 successively as the values in set $D=\left\{1,3,5,7\right\}$. Since the image was quantized to 72 bins, for each value in D, we can obtain a 72-dimensional color fuzzy correlogram vector. Perform normalization on it using the following formula:

**Step 6**. Apply Step 5 to max-image and min-image separately to obtain two 288-dimensional vectors. Integrate them into the 576-dimensional final color feature descriptor.

## 4. Experiments

#### 4.1. Similarity Measurement between Images

#### 4.2. Performance Evaluation

#### 4.3. Experimental Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Example of traversing color layers with the proposed texture elements. (

**a**) Quantized saturation in the image; (

**b**), (

**c**), and (

**d**) are traversing the color layer of quantized values 0, 1, and 2, respectively.

**Figure 3.**Determination of surrounding pixels $x$ for a given pixel $a$ when $d$ is set as d = 1, d = 2, and d = 3, separately.

**Figure 5.**The comparison of average retrieval performance of different algorithms on different image databases: (

**a**) Corel-1k; (

**b**) Corel-10k; and (

**c**) USPTex1.0.

**Figure 7.**Examples of the top 10 retrieved images for each class in Corel-1k with $\left\{{\lambda}_{1}=1,\text{}{\lambda}_{2}=1\right\}$.

**Table 1.**Retrieval precision of different block sizes on the database Corel-1k with $\left\{{\lambda}_{1}=1,\text{}{\lambda}_{2}=0\right\}$.

Different Block Sizes | Recall Rates | |||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | |

No block | 0.6505 | 0.5694 | 0.5162 | 0.4701 | 0.4312 | 0.3850 |

2 × 2 | 0.6922 | 0.6075 | 0.5535 | 0.5088 | 0.4655 | 0.4202 |

4 × 4 | 0.6912 | 0.6070 | 0.5529 | 0.5109 | 0.4708 | 0.4306 |

8 × 8 | 0.6610 | 0.5750 | 0.5219 | 0.4777 | 0.4380 | 0.3997 |

**Table 2.**Retrieval precision on the database Corel-1k with $\left\{{\lambda}_{1}=0,\text{}{\lambda}_{2}=1\right\}$.

Recall Rates | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 |
---|---|---|---|---|---|---|

Precision Rates | 0.6949 | 0.6313 | 0.5891 | 0.5510 | 0.5143 | 0.4795 |

**Table 3.**Retrieval precision of different block sizes on the database Corel-1k with $\left\{{\lambda}_{1}=1,\text{}{\lambda}_{2}=1\right\}$.

Different Block Sizes | Recall Rates | |||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | |

No block | 0.7404 | 0.6683 | 0.6229 | 0.5817 | 0.5420 | 0.5041 |

2 × 2 | 0.7512 | 0.6834 | 0.6359 | 0.6005 | 0.5643 | 0.5250 |

4 × 4 | 0.7539 | 0.6848 | 0.6373 | 0.5993 | 0.5612 | 0.5228 |

8 × 8 | 0.7422 | 0.6726 | 0.6263 | 0.5854 | 0.5473 | 0.5084 |

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Yang, F.-p.; Hao, M.-l.
Effective Image Retrieval Using Texture Elements and Color Fuzzy Correlogram. *Information* **2017**, *8*, 27.
https://doi.org/10.3390/info8010027

**AMA Style**

Yang F-p, Hao M-l.
Effective Image Retrieval Using Texture Elements and Color Fuzzy Correlogram. *Information*. 2017; 8(1):27.
https://doi.org/10.3390/info8010027

**Chicago/Turabian Style**

Yang, Fu-ping, and Mei-li Hao.
2017. "Effective Image Retrieval Using Texture Elements and Color Fuzzy Correlogram" *Information* 8, no. 1: 27.
https://doi.org/10.3390/info8010027