# Hierarchical Coding Vectors for Scene Level Land-Use Classification

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## Abstract

**:**

## 1. Introduction

- We devise the Hierarchical Coding Vectors (HCV) by organizing off-the-shelf coding methods into a hierarchical architecture and evaluate the parameters of HCV for land-use classification on the LU database.
- The HCV achieves excellent performance for land-use classification. Further, combining HCV with standard FV, our method (FV + HCV) outperforms the state-of-the-art performance reported on the LU and RSSCN7 databases.

## 2. Related Work

## 3. Hierarchical Coding Vector

**X**= (x

_{1},x

_{2},...,x

_{k,}…,x

_{K})$\in {\mathbb{R}}^{E\times K}$ from the geographical image to the coding space

**D**= (d

_{1},d

_{2},...,d

_{k}…,d

_{K})$\in {\mathbb{R}}^{M\times K}$ using the K-means codebook

**B**= (b

_{1}_{1},b

_{2},...,b

_{m,}...,b

_{M})$\in {\mathbb{R}}^{E\times M}$. After local pooling and normalization, the semi-local features

**F**= (f

_{1},f

_{2},...f

_{t}…,f

_{T})$\in {\mathbb{R}}^{M\times \mathrm{T}}$ are fed into the Fisher coding layer. With the Gaussian Mixture Model (GMM) codebook

**B**= (b

_{2}_{1},b

_{2},...b

_{n,.}..,b

_{N})$\in {\mathbb{R}}^{M\times N}$, the Hierarchical coding Vector

**HCV**$\in {\mathbb{R}}^{M\times 2N}$ is produced by Fisher vector (FV) coding. Finally, HCV is input into a classifier such as a Support Vector Machine (SVM) for scene-level land use classification. The detailed description of each layer is as follows. The parameters used in this paper are summarized in Table 1.

#### 3.1. The BOVW Coding Layer

**X**$\in {\mathbb{R}}^{E\times K}$ to the semi-local features

**F**$\in {\mathbb{R}}^{M\times \mathrm{T}}$. The pipeline of the BOVW coding layer is shown in Figure 2. Let

**X**be a set of D-dimensional local descriptors extracted from a geographical image

**X**$\in {\mathbb{R}}^{E\times K}$ with densely sampled interest points. Through clustering, a codebook is formed with M entries

**B**$\in {\mathbb{R}}^{E\times M}$. The codebook is used to express each descriptor and to develop the coding result

_{1}**D**$\in {\mathbb{R}}^{M\times K}$. Then, pooling and normalization methods are used to produce the local patch coding representation (i.e., a semi-local features

**F**$\in {\mathbb{R}}^{M\times \mathrm{T}}$). Finally, the features,

**F,**are fed into the next Fisher coding layer as the input.

#### 3.1.1. BOVW Coding

**X**$\in {\mathbb{R}}^{E\times K}$ to the coding result

**D**$\in {\mathbb{R}}^{M\times K}$.

**X**were usually strongly correlated, which created significant challenges in the subsequent codebook generation [12]. The feature pre-processing approach, Whitening, was used to realize the decorrelation. The overcomplete basis vectors (i.e., codebook

**B**$\in {\mathbb{R}}^{E\times M}$) were computed on the training set using the K-means clustering method [21]. To retain spatial information, the dense local descriptors (e.g., Scale Invariant Feature Transformation (SIFT) [8]) were augmented with their normalized x, y location before codebook clustering.

_{1}**F**. The strong sparsity caused great challenges in the next Fisher coding layer. SA chose to activate the entire codebook and used the kernel function of distance as the coding representation:

#### 3.1.2. Spatial Local Pooling

**D**$\in {\mathbb{R}}^{M\times K}$ into the semi-local features

**F**$\in {\mathbb{R}}^{M\times \mathrm{T}}$, thus achieving greater invariance to image transformations and better robustness to noise and clutter. Compared to the regions used in the traditional global pooling, the regions are much smaller and sampled much more densely in our HCV framework. The semi-local feature representation captures more complex image statistics with the spatial local pooling.

_{t}is the tth element in the semi-local features

**F**and the d

_{k}is the coding result. P refers to the local pooling region. The Max-pooling method has demonstrated its effectiveness in many studies [6,13,14,23].

#### 3.1.3. Normalization

_{2}normalization method as a pre-processing step.

**F**and make their distribution smoother, improving the classification performance of HCV (with the experiment on the LU database, we found that the power-normalization can improve the classification accuracy 3%~5%).

**F**were also augmented with their normalized x, y location before they were fed into the next layer.

#### 3.2. The Fisher Coding Layer

**F**$\in {\mathbb{R}}^{M\times \mathrm{T}}$ into the final global representation Hierarchical coding vector

**HCV**$\in {\mathbb{R}}^{M\times 2N}$ using the Fisher vector (FV) coding method. The pipeline of the Fisher coding layer is shown in Figure 3. All the semi-local features were decorrelated using Whitening technology before being fed into the Fisher coding layer.

**F**and then encoding the derivatives of the log-likelihood of the model with respect to its parameters [25]. The GMMs with diagonal covariance are used in our HCV framework, leading to a HCV representation that captures the Gaussian mean (1st) and variance (2nd) differences between the input semi-local features

**F**and each of the GMM centers.

**B**= (b

_{2}_{1},b

_{2},...b

_{n},...,b

_{N})$\in {\mathbb{R}}^{M\times N}$. f

_{t}is one semi-local feature fed into the Fisher coding layer and T is the number of the semi-local features. ${\alpha}_{t}(n)$ is the soft assignment weight of the t-th semi-local features f

_{t}to the n-th Gaussian.

**HCV**$\in {\mathbb{R}}^{M\times 2N}$ is obtained by stacking the first and second differences:

_{2}scheme, and serves as the final scene representation of HCV.

## 4. Experiment

#### 4.1. Experimental Data and Setup

#### 4.2. Experimental Results

#### 4.3. Evaluation of the Parameters in HCV

#### 4.3.1. The Effect of Different Codebook Size

#### 4.3.2. The Key Parameter $\beta $ in the SA Coding Method

**f**$\in {\mathbb{R}}^{M}$ output by the BOVW coding layer, and the remaining part is the visualization of HCV. The visualizations of the semi-local feature

_{t}**f**(output of the BOVW coding layer) for the five different images are quite similar, so we have only displayed one representative of the feature

_{t}**f**for each value of $\beta $ in Figure 8.

_{t}_{k}and codeword b

_{m}. The codebook is almost activated in the same intensity. The BOVW coding layer cannot capture enough discriminable image information, and the HCV is not able to represent the complex semantic structure. We can observe that the BOVW layer output seems to be meaningless and the HCV of the five images are very similar in this situation, as shown in Figure 8. It is easy to cause misclassification. With the increase of $\beta $, the SA coding method can express the distance information $\widehat{e}$ appropriately and the BOVW layer output appears to be undulating. The HCV output by the Fisher coding layer of different images shows the obvious difference and increasing classification performance is expected. When $\beta $ becomes too large, the SA coding response decreases rapidly with the increasing distance $\widehat{e}$. Figure 8 shows that the sparsity of the BOVW layer output increases and the HCV of the five images becomes similar. The increasing sparsity is a challenge for the Fisher vector coding and weakens the discriminability of the HCV.

#### 4.3.3. The Effect of Different Spatial Structures in Local Pooling

_{k}$\in {\mathbb{R}}^{M}$ of the SIFT features x

_{k}$\in {\mathbb{R}}^{D}$ under four scales were aggregated to semi-local feature f

_{t}$\in {\mathbb{R}}^{M}$ using the Max-pooling methods.

#### 4.3.4. The Effect of the Number of Coding Layers

#### 4.4. Comparison with the State-of-the-Art Methods

#### 4.5. Computational Complexity

^{2}) or O(n

^{3}) in the train phase and O(n) in the testing phase, where n is the training size. It implies a poor scalability for the real application. Our method, using a simple linear SVM, reduces the training complexity to O(n), and obtains a constant complexity in testing, while still achieving a superior performance. In the end, we evaluated the computation complexity of our method (HCV + FV) and used the 21-class land-use (LU) database to obtain the processing time. Our codes are all implemented in MATLAB 2014a and were run on a computer with an Inter (R) Xeon (R) CPU E5-2620 v2 @ 2.1GHZ and 32G RAM in a 64-bit Win7 operation system. As observed from our experiment, the train phase takes about 27 min and the average processing time for a test remote sensing image (size of 256 × 256 pixels) is 0.55 ± 0.02 second (including dense local descriptors extraction, HCV, and FV coding to get the final representation).

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

HCV | Hierarchical Coding Vector |

BOVW | Bag of Visual Words |

HOG | Histogram of Oriented Gradient |

LBP | Local Binary Pattern |

SA | Soft Assignment |

FV | Fisher Vectors |

VLAD | Vector of Locally Aggregated Descriptors |

LU | 21-Class Land Use |

GMM | Gaussian Mixture Model |

DNN | Deep Neural Network |

SIFT | Scale Invariant Feature Transformation |

SPCK | Spatial Pyramid Co-occurrence Kernel |

CLBP | Completed Local Binary Pattern |

HA | Hard Assignment |

LCC | Local Coordinate Coding |

LLC | Locality-constrained Linear Coding |

SVC | Super Vector Coding |

UCMCVL | University of California at Merced Computer Vision Lab |

SVM | Support Vector Machine |

ELM | Extreme Learning Machine |

RBF | Radial Basis Function |

DBN | Deep Belief Networks |

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**Figure 1.**The architecture of the proposed Hierarchical Coding Vector (HCV). The representation of HCV is deeper with richer semantic information by constructing a hierarchical coding structure. SVMs, Support Vector Machines; FV, Fisher Vectors; BOVW, Bag of Visual Words; SIFT, Scale Invariant Feature Transformation.

**Figure 4.**Sample images from each of the 21 categories in the Land Use (LU) database: (

**a**) agricultural; (

**b**) airplane; (

**c**) baseball diamond; (

**d**) beach; (

**e**) buildings; (

**f**) chaparral; (

**g**) dense residential; (

**h**) forest; (

**i**) freeway; (

**j**) golf course; (

**k**) harbor; (

**l**) intersection; (

**m**) medium density residential; (

**n**) mobile home park; (

**o**) overpass; (

**p**) parking lot; (

**q**) river; (

**r**) runway; (

**s**) sparse residential; (

**t**) storage tanks; (

**u**) tennis courts.

**Figure 5.**Sample images from the RSSCN7 database: (

**a**) grassland; (

**b**) farmland; (

**c**) industrial and commercial regions; (

**d**) river and lake; (

**e**) forest field; (

**f**) residential region; (

**g**) parking lot. There are four scales, from top to bottom (in rows): 1:700, 1:1300, 1:2600, and 1:5200.

**Figure 6.**Comparison of the pre-class accuracies of Hierarchical Coding Vector (HCV) with the Fisher Vector (FV) and the combination of the two on the LU database.

**Figure 7.**Some images are predicted correctly by the HCV, but not by the FV on the LU database: (

**a**) storage tanks images; (

**b**) river images; (

**c**) tennis courts images.

**Figure 8.**Visual coding result of the Hierarchical Coding Vector (HCV) of different parameters on the LU database. Each vertical column represents the coding result of a different $\beta $ for the same image. Each horizontal row represents the coding result of same $\beta $ for different images.

**Figure 9.**Evaluation of the effect on the classification accuracy of HCV of the parameter $\beta $ on the LU database.

Parameter | Dim. | Definition |
---|---|---|

X | E × K | Low-level descriptors |

B_{1} | E × M | K-means codebook |

D | M × K | Coding result of BOVW coding layer |

F | M × T | Semi-local features |

B_{2} | M × N | Gaussian mixture model (GMM) codebook |

G | M × 2N | Hierarchical coding Vector |

x_{k} | E | The k-th low-level descriptor |

d_{k} | M | The k-th coding result in D |

b_{m} | E | The m-th codeword in B_{1} |

b_{n} | M | The n-th codeword in B_{2} |

f_{t} | M | The t-th semi-local feature |

${g}_{n}^{(1)}$ | M | Gaussian mean difference |

${g}_{n}^{(2)}$ | M | Gaussian variance difference |

E | 1 | Dimension of low-level descriptors |

T | 1 | Number of semi-local features |

M | 1 | Size of K-means codebook |

N | 1 | Size of GMM codebook |

K | 1 | Number of low-level descriptors |

P | - | Local pooling region |

$\widehat{e}({x}_{k},{b}_{m})$ | 1 | Euclidean distance between x_{k} and b_{m} |

$\beta $ | 1 | Smoothing factor in SA coding |

$\alpha $ | 1 | Smoothing factor in Power-normalization |

${\alpha}_{t}(n)$ | 1 | Soft assignment weight of f_{t} to b_{n} |

${w}_{n}$ | 1 | Mixture weights of b_{n} |

${\mu}_{n}$ | 1 | Means of b_{n} |

${\sigma}_{n}$ | 1 | Diagonal covariance of b_{n} |

**Table 2.**Classification accuracy (%) of HCV with varying K-means/GMM codebook size on the LU database.

K-means/GMM | 2 | 4 | 8 | 16 | 32 |
---|---|---|---|---|---|

50 | 71.55 | 76.98 | 81.62 | 84.33 | 87.62 |

100 | 77.05 | 82.02 | 85.79 | 85.98 | 87.93 |

200 | 83.00 | 84.74 | 87.31 | 88.10 | 88.21 |

600 | 86.86 | 88.69 | 89.50 | 89.45 | 88.81 |

1000 | 88.36 | 89.29 | 90.00 | 88.57 | 88.40 |

1400 | 88.26 | 89.76 | 89.17 | 88.49 | 88.36 |

**Table 3.**Comparison of our approach (FV + HCV) with the state-of-the-art performance reported in the literature on the LU database under the same experimental setup: 80% of images from each class are used for training and the remaining images are used for testing. The average classification accuracy (mean ± SD) is set as the evaluation index.

Method | Accuracy (%) |
---|---|

BOVW [1] | 76.8 |

SPM [1] | 75.3 |

BOVW + spatial co-occurrence kernel [1] | 77.7 |

Color Gabor [1] | 80.5 |

Color histogram [1] | 81.2 |

SPCK [4] | 73.1 |

SPCK + BOW [4] | 76.1 |

SPCK + SPM [4] | 77.4 |

Structural texture similarity [33] | 86.0 |

Wavelet BOVW [29] | 87.4 ± 1.3 |

Unsupervised feature learning [34] | 81.1 ± 1.2 |

Saliency-guided feature learning [35] | 82.7 ± 1.2 |

Concentric circle-structured BOVW [2] | 86.6 ± 0.8 |

Multifeature concatenation [36] | 89.5 ± 0.8 |

Pyramid-of-spatial-relations [3] | 89.1 |

CLBP [27] | 85.5 ± 1.9 |

MS-CLBP [27] | 90.6 ± 1.4 |

HCV | 90.5 ± 1.1 |

Our method | 91.8 ± 1.3 |

**Table 4.**Comparison of our approach (FV + HCV) with the state-of-the-art performance reported in the literature on the RSSCN7 database under the same experimental setup: half of images from each class are used for training and the rest are used for testing. The average classification accuracy (mean ± SD) is set as the evaluation index. DBN: Deep Belief Networks.

Method | Accuracy (%) |
---|---|

GIST * | 69.5 ± 0.9 |

Color histogram * | 70.9 ± 0.8 |

BOVW * | 73.1 ± 1.1 |

LBP * | 75.3 ± 1.0 |

DBN based feature selection [26] | 77.0 |

HCV | 84.7 ± 0.7 |

Our method | 86.4 ± 0.7 |

*****Our own implementation.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wu, H.; Liu, B.; Su, W.; Zhang, W.; Sun, J.
Hierarchical Coding Vectors for Scene Level Land-Use Classification. *Remote Sens.* **2016**, *8*, 436.
https://doi.org/10.3390/rs8050436

**AMA Style**

Wu H, Liu B, Su W, Zhang W, Sun J.
Hierarchical Coding Vectors for Scene Level Land-Use Classification. *Remote Sensing*. 2016; 8(5):436.
https://doi.org/10.3390/rs8050436

**Chicago/Turabian Style**

Wu, Hang, Baozhen Liu, Weihua Su, Wenchang Zhang, and Jinggong Sun.
2016. "Hierarchical Coding Vectors for Scene Level Land-Use Classification" *Remote Sensing* 8, no. 5: 436.
https://doi.org/10.3390/rs8050436