# Learning Dual Multi-Scale Manifold Ranking for Semantic Segmentation of High-Resolution Images

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## Abstract

**:**

**DMSMR**) network, that combines the dilated, multi-scale strategies with the single stream MR optimization method in the deep learning architecture to further improve the performance. Experiments on high resolution images, including close-range and remote sensing datasets, demonstrate that the proposed approach can achieve competitive accuracy without additional aides in an end-to-end manner.

## 1. Introduction

**DMSMR**) network to estimate the predicted labels in an end-to-end fashion. In each scale, the dilated and non-dilated convolution layers are jointly optimized by MR. With the dual multi-scale contextual information, the combined results achieve competitive accuracy without any additional aides. An overview of our proposed approach is illustrated in Figure 1.

**Multi-label MR graphical model for semantic segmentation.**Unlike existing approaches that utilize the CRF as the post-processing or approximate inference in the discrete domain, we propose to model the MR method for semantic segmentation in a continuous domain. Our model is end-to-end optimization that can be linearly solved and guarantee a global optimal solution.

**Embedded feedforward single stream optimization method.**In contrast to Gaussian graphical models, we propose an embedded single stream technique that requires only the Laplacian matrix obtained from pairs of vertices, which makes the gathering of the low-level cues as the contextual information more efficient.

**Dual multi-scale manifold ranking network.**We adopt the multi-scale strategy to construct the dual-dilated and non-dilated networks and jointly optimize them with MR in a unified framework for semantic image segmentation. Our model is the first work to back propagate through manifold ranking and integrate it to deep learning architecture in the area of remote sensing.

## 2. Related Work

## 3. Manifold Ranking Formulation

#### 3.1. Binary Manifold Ranking

**f**:

#### 3.2. Multi-Label Manifold Ranking

## 4. Deep Multi-Scale Manifold Ranking Network

**DMSMR**network is constructed, in which the dilated [23] and non-dilated networks are jointly optimized through the multi-scale feedforward manifold ranking method .

#### 4.1. Embedded Feedforward Single Stream Manifold Ranking Optimization

#### 4.1.1. Manifold Ranking Inference

#### 4.1.2. Derivative to Smoothness Coefficients

#### 4.1.3. Derivative to Compatibility Matrix

#### 4.2. Dual Multi-Scale Manifold Ranking Network

**DMSMR**network can be represented as follows:

## 5. Experiments

**DMSMR**approach by comparing the methods that employ only one of the three strategies, namely, multi-scale convolution (

**MS**), broader receptive field (

**Dilated**) and MR optimization (

**MR-opti**) approaches. The detailed structures of the network with different strategies are explained in the Appendix (See Figure A1 and Table A1).

**DMSMR**model, the first five blocks are developed from the standard VGG-16 [54] structures, which comprise convolutional and non-dilated convolutional layers. The dilation kernel sizes are 6, 4, 2, 2, and 1 pixels. For each scale, the pooling layer is followed by the non-dilated layers, which comprise three convolutional layers. The parameters of our implementation are shown in detail in Table 1. The dilated and non-dilated layers are optimized with single stream manifold ranking algorithm and fused by Equation (17). The structure is illustrated in Figure 1. In the table and figure, the “ReLU” active function [74] is implicitly employed in each convolutional layer. In our model, all layers are randomly initialized without using the pre-trained VGG-16 model. The hyper-parameters, such as learning rate, momentum and weight decay, are confirmed via cross validation. The entire net is trained in an end-to-end manner using SGD algorithm. ${\sigma}_{1}$ and ${\sigma}_{2}$ in Equation (11) are both set to $3.0$ as in [32] in our experiments.

#### 5.1. Experiment on Close-Range Dataset

#### 5.1.1. Evaluation on PASCAL VOC

**DMSMR**performs significantly (averaged approximately eight points) better than the similar methods without additional aides (methods without qualifying comments in Table 2). This is because our method is composed of the dilated, multi-scale strategies and has characteristics that complement to a few basic networks, such as SegNet [27], dilated convolutional network [28] and DeepLab-Msc [24]. Compared to recent methods, such as CRF-RNN [25] and G-CRF [35], our method achieves a similar score by optimizing with a single stream MR algorithm in an end-to-end manner. However, our approach does not require multi-stage inference or training two streams (i.e., unary term and pairwise stream, with unary initialized by other networks). Furthermore, some approaches, such as DeepLab [24], have a worse result when they do not use all of the additional aides with a pre-trained model. However, our model yields superior results without these pre-trained weights.

#### 5.1.2. Evaluation on CamVid

**DMSMR**network. The experimental results are illustrated in Figure 4. The comparisons between the

**DMSMR**approach and the networks employing different strategies are reported in Table 3. We also analyze the accuracy change with respect to boundary in Figure 5. As shown in Figure 5a, we consider a narrow band, that is, trimap [81] boundary, on CamVid dataset. A trimap divides an image into three regions of foreground, background and unknown. Figure 5b shows boundary accuracy as the trimap width is varied. In this experiment, we set the same parameters as those in the

**DMSMR**model but with different strategies as previously stated. The three strategies, namely, multi-scale convolution (

**MS**), broader receptive field (

**Dilated**) and manifold ranking optimization (

**MR-Opti**) approaches, are utilized for comparison. Obviously, different strategies yield different performance for each of the classes. The

**MS**and

**Dilated**approaches help boost the performance in the situation where color and texture are uniformly distributed. In addition, the

**MR-Opti**achieves a score that is approximately 2.5% better than those of the

**MS**and

**Dilated**methods because more contextual information are considered. The results demonstrate that the combination of

**MS**,

**Dilated**and

**MR-Opti**approaches is possibly a better approach for semantic segmentation task on close-range images. Figure 5 shows that improving the recognition of pixels around the boundary helps delineate the object because the smoothness potentials of the correctly detected pixels increase. Additionally, as can be seen from Table 3, the

**DMSMR**method outperforms the approaches that employ only one strategy, indicating that the

**DMSMR**approach can improve the semantic segmentation result further by combing these strategies in close-range situations.

#### 5.2. Experiment on High Resolution Remote Sensing Dataset

#### 5.2.1. Evaluation on Vaihingen Dataset

**ADL**[59] and

**HUST**[83]) indeed helps improve the performance. Nevertheless, the upper left corner of the error map in the first row shows that even if the CRF post-processing method is employed, more incorrectly classified pixels will exist if the initial predictions are poorly provided. In Table 4, we compare our approach with the methods using additional aides, such as the VGG-16 pre-trained model [29,76,84], digital surface model (DSM) [49,85,86], and the CRF post-processing [59,83]. We also compare our approach with traditional feature based methods [87]. Recent advances in the area of computer vision have shown that very deep networks can improve the semantic segmentation accuracy [27,54]. Therefore, our

**DMSMR**approach reasonably outperforms the “

**SVL**” method by approximately $4\%$ in overall pixel-wise accuracy and $6\%$ on global F1 score. Although additional aides help improve accuracy, they are not the core to segmentation engine [53]. Our networks do not need these aides but achieve competitive scores compared with these approaches. For the fine-tuned networks from the pre-trained VGG-16 model (

**ONE**[84],

**DLR**[76],

**UOA**[29],

**RIT**[50]), their performances are not always steady compared to that of the proposed

**DMSMR**approach. Our overall accuracy varies approximately 0.1% (see

**Ano**(

**Ano**is available at http://ftp.ipi.uni-hannover.de/ISPRS_WGIII_website/ISPRSIII_4_Test_results/2D_labeling_vaih/2D_labeling_Vaih_details_Ano/index.html) and

**Ano2**in the ISPRS leader board.

**Ano**and

**Ano2**are initialized with the same hyper-parameters, but the weights and biases terms are randomly initialized.) when tested on this benchmark. This is mainly caused by uncertainty of weights when trying to transfer the VGG-16 classification networks into semantic segmentation task. The dense prediction problem, such as semantic segmentation, is structurally different from image classification [23]. Thus these performances are not as stable as expected. Our approach somehow utilizes the dual-dilated and non-dilated convolutional layers to prevent such instability.

#### 5.2.2. Evaluation on EvLab-SS Dataset

**Garden**class, which is reserved for validating the expressive power of CNNs in real scenes, is absent in our validation images.

**MS**,

**Dilated**or

**MR-Opti**) as the

**DMSMR**approach.

**DMSMR**method can better delineate the boundary of an object. The results demonstrate the superiority of the combination of multi-scale (

**MS**), broader receptive field (

**Dilated**), and manifold ranking optimization (

**MR-Opti**) strategies, which can more accurately classify each pixel with varying spatial resolutions. Figure 8 shows that although the mIoU score of the proposed DMSMR approach is relatively low with a small trimap width, it has become increasingly stable and competitive. By contrast, the mIoU scores of the MS, dilated, and MR-Opti approaches are unstable, even decreasing with a few small trimap widths. The main reason attribute to this phenomena is that the spatial resolution is different in the training patches, which may be ignored by only employing one strategy. In Table 5, the special class (

**Garden**) is detected as 0.0% in all approaches, indicating that these methods can preserve the intrinsic nature of CNNs well. For the real engineered remote sensing data, the

**Dilated**approach does not appear to boost performance and decreases in overall accuracy and mean IoU by approximately 2.96%, 2.32%, respectively. This can be attributed to the numerous inhomogeneous objects in the training patches. For example, the road and buildings may not be completely covered in a single patch, which renders training with dilation operations in some layer meaningless. Although the

**MR-Opti**approach improves the overall accuracy by approximately 4%, this approach may disregard a few classes, such as the Desert and Waters, due to insufficient contextual information with varying illumination and color. However, the

**MS**approach retains more contextual information in each scale space but still suffers from the optimization problem in each scale, resulting in 0.8% decrease in overall accuracy. Notably, the proposed

**DMSMR**approach can take the superior features of these strategies and overcome the drawbacks, achieving approximately 5% and 1% improvements in overall accuracy and mIoU score under the condition of limited training images and varying spatial resolutions.

## 6. Conclusions

**DMSMR**network for semantic image segmentation in a continuous domain. By extending the binary manifold ranking (MR) algorithm to a multi-label case, the assignment of a discrete label to each pixel can be linearly solved and a unique global optimum can be guaranteed. In addition, with the single stream MR method embedded into CNNs in a feedforward schema, the required parameters can be trained in an end-to-end manner. Furthermore, we propose to utilize dilated and non-dilated networks, which form dual layers to jointly optimize the results from the single stream manifold ranking network rather than on two separate streams, that is, unary and pairwise streams. Combined with multi-scale (

**MS**), broader receptive field (

**Dilated**) and manifold ranking optimization (

**MR-Opti**) strategies, the proposed

**DMSMR**network enables training without additional aides, such as multi-stage inference, region proposals, VGG-16 initialization, digital surface model (DSM) and CRF post-processing. Two groups of experiments on close-range and remote sensing high resolution datasets are designed to evaluate the performance. When discriminatively trained by submitting the results to the server on PASCAL VOC and ISPRS Vaihingen benchmarks, the proposed

**DMSMR**network can achieve competitive results without additional aides compared to recent methods. Our experiments on publicly available datasets, including CamVid and EvLab-SS datasets, demonstrate the superior capacity of the proposed

**DMSMR**approach over the methods that employ only one strategy. For the real world application in remote sensing, the combined strategy steadily boosts the performance even under limited training images and the varying spatial resolutions.

## Acknowledgments

## Author Contributions

**DMSMR**network and performed the experimental analysis. He also wrote the paper. Xiangyun Hu guided the algorithm design, initiated the EvLab-SS dataset production and revised the paper. Shiyan Pang help organize the paper. Like Zhao, Ye Lv and Min Luo contributed to the design of project homepage and edited the manuscript.

## Conflicts of Interest

## Appendix A

**MS**), dilated convolution (

**Dilated**), and manifold ranking optimization (

**MR-Opti**) approaches.

#### Appendix A.1. Learning Parameter α and β

#### Appendix A.2. Learning Compatibility Matrix $\tilde{\mathit{W}}$

#### Appendix A.3. Network with Different Strategies

**MS**), broader receptive field (

**Dilated**) and MR optimization (

**MR-opti**) approaches. Figure A1 shows the general structures of these approaches and Table A1 presents the corresponding implementation parameters in each convolutional layer. In the table and figure, the “ReLU” active function [74] is implicitly employed in each convolutional layer. The network depicted in Figure A1a serves as the baseline convolutional network for comparison. Figure A1c,d are the networks that use only the dilated convolutional kernel [23] and manifold ranking optimization methods, respectively. The only difference between network in Figure A1a,c is the dilation kernel. In our experiment, we set the kernel sizes in each block as 6, 4, 2, 2 and 1, as illustrated in Table A1a. For the MR optimization layer embedded in the baseline network shown in Figure A1d, initial parameters of $\alpha $ and $\beta $ are set to 3 and 5, respectively. Figure A1b presents the network with multi-scale strategy on the baseline network. After applying the pooling layer in each block, a convlutional block is adopted with three convolutional layers (named as poolx-conv-y in Table A1b. The scale is implicitly expressed in the pooling layer by factor 2.0.

**Figure A1.**The architectures of the networks with different strategies: (

**a**) Convolutional networks before employing the strategies (

**Before**); (

**b**) Networks using multi-scale strategy (

**MS**); (

**c**) Networks using dilated method (

**Dilated**); (

**d**) Networks using manifold ranking optimization (

**MR-Opti**).

(a) Networks before Employing the Strategies (Before) | ||||||

Block | Name | Kernel Size | Pad | Dilation | Stride | Number of Output |

0 | input | - | - | - | - | 3 |

1 | conv1-1 | 3 × 3 | 1 | 1 | 1 | 64 |

conv1-2 | 3 × 3 | 1 | 1 | 1 | 64 | |

pool1 | 3 × 3 | 1 | 0 | 1 | 64 | |

2 | conv2-1 | 3 × 3 | 1 | 1 | 1 | 128 |

conv2-2 | 3 × 3 | 1 | 1 | 1 | 128 | |

pool2 | 3 × 3 | 1 | 0 | 2 | 128 | |

3 | conv3-1 | 3 × 3 | 1 | 1 | 1 | 256 |

conv3-2 | 3 × 3 | 1 | 1 | 1 | 256 | |

pool3 | 3 × 3 | 1 | 0 | 2 | 256 | |

4 | conv4-1 | 3 × 3 | 1 | 1 | 1 | 512 |

conv4-2 | 3 × 3 | 1 | 1 | 1 | 512 | |

pool4 | 3 × 3 | 1 | 0 | 1 | 512 | |

5 | conv5-1 | 5 × 5 | 2 | 1 | 1 | 512 |

conv5-2 | 5 × 5 | 2 | 1 | 1 | 512 | |

pool5 | 3 × 3 | 1 | 0 | 1 | 512 | |

- | fc6 | 3 × 3 | 1 | 1 | 1 | 1024 |

fc7 | 1 × 1 | 0 | 1 | 1 | 1024 | |

* | fc8 | 1 × 1 | 0 | 1 | 1 | 12 |

- | output | 1 × 1 | 0 | 1 | 1 | 12 |

(b) Networks Using Multi-Scale Strategy (MS) | ||||||

Scale (Block) | Name | Kernel Size | Pad | Dilation | Stride | Number of Output |

0 | input | - | - | - | - | 3 |

1 | conv1-1 | 3 × 3 | 1 | 1 | 1 | 64 |

conv1-2 | 3 × 3 | 1 | 1 | 1 | 64 | |

pool1 | 3 × 3 | 1 | 0 | 2 | 64 | |

2 | conv2-1 | 3 × 3 | 1 | 1 | 1 | 128 |

conv2-2 | 3 × 3 | 1 | 1 | 1 | 128 | |

pool2 | 3 × 3 | 1 | 0 | 2 | 128 | |

3 | conv3-1 | 3 × 3 | 1 | 1 | 1 | 256 |

conv3-2 | 3 × 3 | 1 | 1 | 1 | 256 | |

pool3 | 3 × 3 | 1 | 0 | 2 | 256 | |

4 | conv4-1 | 3 × 3 | 1 | 1 | 1 | 512 |

conv4-2 | 3 × 3 | 1 | 1 | 1 | 512 | |

pool4 | 3 × 3 | 1 | 0 | 1 | 512 | |

5 | conv5-1 | 5 × 5 | 2 | 1 | 1 | 512 |

conv5-2 | 5 × 5 | 2 | 1 | 1 | 512 | |

pool5 | 3 × 3 | 1 | 0 | 1 | 512 | |

- | fc6 | 3 × 3 | 1 | 1 | 1 | 1024 |

fc7 | 1 × 1 | 0 | 1 | 1 | 1024 | |

* | fc8 | 1 × 1 | 0 | 1 | 1 | 12 |

1 | pool1-conv-1 | 3 × 3 | 1 | 1 | 4 | 128 |

pool1-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool1-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

2 | pool2-conv-1 | 3 × 3 | 1 | 1 | 2 | 128 |

pool2-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool2-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

3 | pool3-conv-1 | 3 × 3 | 1 | 1 | 1 | 128 |

pool3-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool3-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

4 | pool4-conv-1 | 3 × 3 | 1 | 1 | 1 | 128 |

pool4-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool4-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

- | output | 1 × 1 | 0 | 1 | 1 | 12 |

(c) Networks Using Dilated Method (Dilated) | ||||||

Block | Name | Kernel Size | Pad | Dilation | Stride | Number of Output |

0 | input | - | - | - | - | 3 |

1 | conv1-1 | 3 × 3 | 6 | 6 | 1 | 64 |

conv1-2 | 3 × 3 | 6 | 6 | 1 | 64 | |

pool1 | 3 × 3 | 1 | 0 | 2 | 64 | |

2 | conv2-1 | 3 × 3 | 4 | 4 | 1 | 128 |

conv2-2 | 3 × 3 | 4 | 4 | 1 | 128 | |

pool2 | 3 × 3 | 1 | 0 | 2 | 128 | |

3 | conv3-1 | 3 × 3 | 2 | 2 | 1 | 256 |

conv3-2 | 3 × 3 | 2 | 2 | 1 | 256 | |

pool3 | 3 × 3 | 1 | 0 | 2 | 256 | |

4 | conv4-1 | 3 × 3 | 2 | 2 | 1 | 512 |

conv4-2 | 3 × 3 | 2 | 2 | 1 | 512 | |

pool4 | 3 × 3 | 1 | 0 | 1 | 512 | |

5 | conv5-1 | 3 × 3 | 2 | 2 | 1 | 512 |

conv5-2 | 3 × 3 | 2 | 2 | 1 | 512 | |

pool5 | 3 × 3 | 1 | 0 | 1 | 512 | |

- | fc6 | 3 × 3 | 1 | 1 | 1 | 1024 |

fc7 | 1 × 1 | 0 | 1 | 1 | 1024 | |

* | fc8 | 1 × 1 | 0 | 1 | 1 | 12 |

- | output | 1 × 1 | 0 | 1 | 1 | 12 |

(d) Networks Using Manifold Ranking Optimization (MR-Opti) | ||||||

Block | Name | Kernel Size | Pad | Dilation | Stride | Number of Output |

0 | input | - | - | - | - | 3 |

1 | conv1-1 | 3 × 3 | 1 | 1 | 1 | 64 |

conv1-2 | 3 × 3 | 1 | 1 | 1 | 64 | |

pool1 | 3 × 3 | 1 | 0 | 1 | 64 | |

2 | conv2-1 | 3 × 3 | 1 | 1 | 1 | 128 |

conv2-2 | 3 × 3 | 1 | 1 | 1 | 128 | |

pool2 | 3 × 3 | 1 | 0 | 2 | 128 | |

3 | conv3-1 | 3 × 3 | 1 | 1 | 1 | 256 |

conv3-2 | 3 × 3 | 1 | 1 | 1 | 256 | |

pool3 | 3 × 3 | 1 | 0 | 2 | 256 | |

4 | conv4-1 | 3 × 3 | 1 | 1 | 1 | 512 |

conv4-2 | 3 × 3 | 1 | 1 | 1 | 512 | |

pool4 | 3 × 3 | 1 | 0 | 1 | 512 | |

5 | conv5-1 | 5 × 5 | 2 | 1 | 1 | 512 |

conv5-2 | 5 × 5 | 2 | 1 | 1 | 512 | |

pool5 | 3 × 3 | 1 | 0 | 1 | 512 | |

- | fc6 | 3 × 3 | 1 | 1 | 1 | 1024 |

fc7 | 1 × 1 | 0 | 1 | 1 | 1024 | |

* | fc8 | 1 × 1 | 0 | 1 | 1 | 12 |

- | Manifold Ranking Optimization | 12 | ||||

- | output | 1 × 1 | 0 | 1 | 1 | 12 |

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**Figure 1.**Dual multi-scale manifold ranking (

**DMSMR**) network overview. For each dilated convolutional layer, a non-dilated convolution layer is applied following the pooling layer in each scale. The dilated and non-dilated convolution layers form a dual layer, in which the corresponding layers are optimized with the embedded feedforward single stream manifold ranking network. The scale factor is implicitly represented by the pooling layer in each block. Figure 2 illustrates how to embed the manifold ranking optimization method into the single stream network (marked with orange color in this figure). The optimized outputs of each scale, that is, ${\widehat{\mathbf{F}}}_{l}$ generated in each scale, are combined by Equation (17).

**Figure 2.**The embedded feedforward single stream manifold ranking optimization network. The output of the convolutional features that upsample to full image resolution for each class, such as road, sky and building, within the CamVid dataset [68,69] depicted in the figure, serves as the initial manifold ranking score ${\tilde{\mathbf{F}}}^{*}$ to be optimized. By applying the feedforward MR inference with the contextual information extracted from the input image, the optimal MR score $\widehat{\mathbf{F}}$ of each class can be obtained by Equation (10). The only requirement for the proposed network is the multi-label neighborhood relationship, which is designed for constructing the Laplacian matrix $\tilde{\mathbf{L}}$ in a single stream rather than the unary and pairwise streams presented in [26,29].

**Figure 3.**Several semantic segmentation results on PASCAL VOC 2012 validation images.

**DMSMR**: Semantic segmentation result predicted by dual multi-scale manifold ranking network.

**GT**: Ground Truth.

**Figure 4.**Semantic segmentation results on CamVid images.

**DMSMR**: Semantic segmentation result predicted by dual multi-scale manifold ranking network (

**DMSMR**).

**GT**: Ground Truth.

**Figure 5.**Accuracy analysis with respect to boundary on CamVid dataset. (

**a**) Trimap visualization on CamVid dataset. Top-left: source image. Top-right: ground truth. Bottom-left: trimap with one pixel band width. Bottom-right: trimap with three pixels band width. (

**b**) Pixel mIoU with respect to band width around object boundaries. We measure the relationship of our model before and after employing the multi-scale (

**MS**), dilated convolution (

**Dilated**), single stream Manifold Ranking (

**MR-Opti**) and joint strategies (

**DMSMR**).

**Figure 6.**Visualization of the comparative results on a few Vaihingen testing imagery (tile numbers 2, 4, 6 and 8). For each image, we generate the dense prediction results and corresponding error maps (red/green image) with different approaches.

**Figure 7.**Semantic segmentation results with different strategies on the EvLab-SS validation patches. Four kinds of image patches with different spatial resolutions and illuminations are depicted in the figure. The first and second rows are the GeoEye and World-View 2 satellite images with resample GSD of 0.5 m and 0.2 m. The third and the last rows are the aerial images with resample GSD of 0.25 m and 0.1 m, respectively.

**MS**: Predictions with multi-scale approach.

**MR-Opti**: Semantic segmentation results using manifold ranking optimization method.

**DMSMR**: Segmentation result predicted by dual multi-scale manifold ranking network.

**GT**: Ground Truth.

**Figure 8.**Accuracy analysis with respect to boundary on EvLab-SS dataset. (

**a**) Visualization of trimap for EvLab-SS dataset. Top-left: source patch. Top-right: ground truth. Bottom-left: trimap with one pixel band width. Bottom-right: trimap with three pixels band width. (

**b**) Pixel mIoU with respect to band width around object boundaries. We measure the relationship for our model before and after employing the multi-scale (

**MS**), dilated convolution (

**Dilated**), single stream Manifold Ranking (

**MR-Opti**) and joint strategies (

**DMSMR**) on the EvLab-SS dataset.

(a) Dilated Convolutional Layers | ||||||
---|---|---|---|---|---|---|

Scale (Block) | Name | Kernel Size | Pad | Dilation | Stride | Number of Output |

0 | input | - | - | - | - | 3 |

1 | conv1-1 | 3 × 3 | 6 | 6 | 1 | 64 |

conv1-2 | 3 × 3 | 6 | 6 | 1 | 64 | |

pool1 | 3 × 3 | 1 | 0 | 2 | 64 | |

2 | conv2-1 | 3 × 3 | 4 | 4 | 1 | 128 |

conv2-2 | 3 × 3 | 4 | 4 | 1 | 128 | |

pool2 | 3 × 3 | 1 | 0 | 2 | 128 | |

3 | conv3-1 | 3 × 3 | 2 | 2 | 1 | 256 |

conv3-2 | 3 × 3 | 2 | 2 | 1 | 256 | |

pool3 | 3 × 3 | 1 | 0 | 2 | 256 | |

4 | conv4-1 | 3 × 3 | 2 | 2 | 1 | 512 |

conv4-2 | 3 × 3 | 2 | 2 | 1 | 512 | |

pool4 | 3 × 3 | 1 | 0 | 1 | 512 | |

5 | conv5-1 | 3 × 3 | 2 | 2 | 1 | 512 |

conv5-2 | 3 × 3 | 2 | 2 | 1 | 512 | |

pool5 | 3 × 3 | 1 | 0 | 1 | 512 | |

- | fc6 | 3 × 3 | 1 | 1 | 1 | 1024 |

fc7 | 1 × 1 | 0 | 1 | 1 | 1024 | |

* | fc8 | 1 × 1 | 0 | 1 | 1 | 12 |

- | Manifold Ranking Optimization | 12 | ||||

(b) Non-Dilated Convolutional Layers | ||||||

Scale (Block) | Name | Kernel Size | Pad | Dilation | Stride | Output Size |

1 | pool1-conv-1 | 3 × 3 | 1 | 1 | 4 | 128 |

pool1-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool1-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

- | Manifold Ranking Optimization | 12 | ||||

2 | pool2-conv-1 | 3 × 3 | 1 | 1 | 2 | 128 |

pool2-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool2-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

- | Manifold Ranking Optimization | 12 | ||||

3 | pool3-conv-1 | 3 × 3 | 1 | 1 | 1 | 128 |

pool3-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool3-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

- | Manifold Ranking Optimization | 12 | ||||

4 | pool4-conv-1 | 3 × 3 | 1 | 1 | 1 | 128 |

pool4-conv-2 | 1 × 1 | 0 | 1 | 1 | 128 | |

pool4-conv-3 | 1 × 1 | 0 | 1 | 1 | 12 | |

- | Manifold Ranking Optimization | 12 |

**Table 2.**PASCAL VOC12 dataset [72] results. We compare our proposed network with recent methods that support inference techniques. Additional aides, such as region proposal, multi-stage inference, and extra unary initialized model, are unnecessary in our approach. Some of the methods use the CRF as a post optimization procedure. In contrast, our proposed approach achieves competitive accuracy without post-processing in an end-to-end manner.

Aeroplane | Bicycle | Bird | Boat | Bottle | Bus | Car | Cat | Chair | Cow | Diningtable | Dog | Horse | Motorbike | Person | Pottedplant | Sheep | Sofa | Train | Tvmonitor | Mean IoU | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

SegNet [27] | 73.6 | 37.6 | 62.0 | 46.8 | 58.6 | 79.1 | 70.1 | 65.4 | 23.6 | 60.4 | 45.6 | 61.8 | 63.5 | 75.3 | 74.9 | 42.6 | 63.7 | 42.5 | 67.8 | 52.7 | 59.9 |

FCN-8s [22] (Multi-stage training) | 76.8 | 34.2 | 68.9 | 49.4 | 60.3 | 75.3 | 74.7 | 77.6 | 21.4 | 62.5 | 46.8 | 71.8 | 63.9 | 76.5 | 73.9 | 45.2 | 72.4 | 37.4 | 70.9 | 55.1 | 62.2 |

DeepLab-Msc [24] (VGG-16 initialization) | 74.9 | 34.1 | 72.6 | 52.9 | 61.0 | 77.9 | 73.0 | 73.7 | 26.4 | 62.2 | 49.3 | 68.4 | 64.1 | 74.0 | 75.0 | 51.7 | 72.7 | 42.5 | 67.2 | 55.7 | 62.9 |

DilatedConv Front end [28] (VGG-16 initialization) | 82.2 | 37.4 | 72.7 | 57.1 | 62.7 | 82.8 | 77.8 | 78.9 | 28 | 70 | 51.6 | 73.1 | 72.8 | 81.5 | 79.1 | 56.6 | 77.1 | 49.9 | 75.3 | 60.9 | 67.6 |

DeconvNet + CRF [28] (Region Proposals) | 87.8 | 41.9 | 80.6 | 63.9 | 67.3 | 88.1 | 78.4 | 81.3 | 25.9 | 73.7 | 61.2 | 72.0 | 77.0 | 79.9 | 78.7 | 59.5 | 78.3 | 55.0 | 75.2 | 61.5 | 70.5 |

CRF-RNN [25] (Multi-stage training) | 87.5 | 39.0 | 79.7 | 64.2 | 68.3 | 87.6 | 80.8 | 84.4 | 30.4 | 78.2 | 60.4 | 80.5 | 77.8 | 83.1 | 80.6 | 59.5 | 82.8 | 47.8 | 78.3 | 67.1 | 72.0 |

DMSMR | 87.6 | 40.3 | 80.6 | 62.9 | 71.3 | 88.1 | 84.4 | 84.7 | 29.6 | 77.8 | 58.5 | 79.9 | 80.9 | 85.4 | 82.1 | 54.9 | 83.8 | 48.2 | 80.2 | 65.3 | 72.4 |

G-CRF [35] (Unary Initialized with DeepLab CNN) | 85.2 | 43.9 | 83.3 | 65.2 | 68.3 | 89.0 | 82.7 | 85.3 | 31.1 | 79.5 | 63.3 | 80.5 | 79.3 | 85.5 | 81.0 | 60.5 | 85.5 | 52.0 | 77.3 | 65.1 | 73.2 |

Building | Tree | Sky | Car | Sign | Road | Pedestrian | Fence | Pole | Sidewalk | Bicyclist | Mean IoU | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Before | 45.5 | 73.5 | 78.0 | 23.7 | 14.5 | 87.2 | 11.3 | 36.9 | 2.5 | 74.3 | 13.1 | 41.9 |

MS | 81.4 | 88.1 | 80.3 | 40.1 | 16.3 | 95.6 | 26.2 | 40.0 | 3.7 | 82.0 | 37.4 | 53.7 |

Dilated | 59.8 | 82.8 | 79.5 | 29.0 | 19.4 | 91.0 | 17.5 | 48.0 | 6.7 | 81.2 | 44.7 | 50.9 |

MR-Opti | 90.6 | 95.1 | 74.6 | 94.6 | 21.9 | 98.2 | 53.1 | 64.3 | 9.8 | 92.6 | 42.1 | 54.8 |

DMSMR | 93.1 | 94.5 | 82.9 | 92.7 | 45.5 | 97.4 | 72.5 | 77.2 | 7.2 | 94.5 | 68.9 | 63.6 |

**Table 4.**Vaihingen dataset [88] results. We compare our proposed approach with a few recent state-of-the-art methods listed on the ISPRS Vaihingen 2D contest leader board. Traditional approaches and methods that employ additional aides (methods with qualifying comments) are referenced for comparison.

Imp.surf. | Building | Low veg. | Tree | Car | Overall F1 | Overall Acc. | |
---|---|---|---|---|---|---|---|

SVL [87] (Feature based) | 86.1 | 90.9 | 77.6 | 84.9 | 59.9 | 79.88 | 84.7 |

ADL [59] (CRF post-processing) | 89.0 | 93.0 | 81.0 | 87.8 | 59.5 | 82.06 | 87.3 |

UT_Mev [85] (DSM supported) | 84.3 | 88.7 | 74.5 | 82.0 | 9.9 | 67.88 | 81.8 |

HUST [83] (CRF post-processing) | 86.9 | 92.0 | 78.3 | 86.9 | 29.0 | 74.62 | 85.9 |

ONE [84] (VGG-16 pre-trained model) | 87.8 | 92.0 | 77.8 | 86.2 | 50.7 | 78.90 | 85.9 |

DLR [76] (VGG-16 pre-trained model) | 90.3 | 92.3 | 82.5 | 89.5 | 76.3 | 86.18 | 88.5 |

UOA [29] (VGG-16 pre-trained model) | 89.8 | 92.1 | 80.4 | 88.2 | 82.0 | 86.50 | 87.6 |

RIT [50] (DSM supported, VGG-16 pre-trained model) | 88.1 | 93.0 | 80.5 | 87.2 | 41.9 | 78.14 | 86.3 |

ETH_C [86] (DSM supported) | 87.2 | 92.0 | 77.5 | 87.1 | 54.5 | 79.66 | 85.9 |

DST [49] (DSM supported) | 90.3 | 93.5 | 82.5 | 88.8 | 73.9 | 85.80 | 88.7 |

DMSMR | 90.4 | 93.0 | 81.4 | 88.6 | 74.5 | 85.58 | 88.4 |

**Table 5.**Quantitative evaluation of the semantic segmentation results on the EvLab-SS dataset. The proposed

**DMSMR**approach outperforms the methods that employ only one strategy.

Background | Farmland | Garden | Woodland | Grassland | Building | Road | Structures | Digging Pile | Desert | Waters | Overall Accuracy | Mean IoU | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Before | 75.16 | 35.73 | 0.0 | 51.65 | 8.99 | 66.59 | 35.12 | 46.19 | 19.05 | 3.56 | 3.13 | 49.76 | 21.35 |

MS | 75.73 | 39.36 | 0.0 | 49.33 | 11.89 | 65.85 | 32.80 | 46.94 | 12.91 | 16.69 | 5.87 | 48.93 | 21.42 |

Dilated | 40.59 | 29.18 | 0.0 | 46.48 | 11.36 | 61.74 | 40.46 | 42.54 | 18.10 | 11.57 | 19.84 | 46.8 | 19.03 |

MR-Opti | 79.44 | 20.52 | 0.0 | 57.84 | 2.95 | 74.29 | 28.96 | 49.60 | 17.55 | 0.10 | 0.99 | 53.51 | 21.85 |

DMSMR | 40.59 | 22.14 | 0.0 | 62.47 | 8.11 | 68.84 | 39.80 | 51.06 | 14.56 | 16.52 | 19.45 | 54.15 | 22.17 |

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**MDPI and ACS Style**

Zhang, M.; Hu, X.; Zhao, L.; Lv, Y.; Luo, M.; Pang, S. Learning Dual Multi-Scale Manifold Ranking for Semantic Segmentation of High-Resolution Images. *Remote Sens.* **2017**, *9*, 500.
https://doi.org/10.3390/rs9050500

**AMA Style**

Zhang M, Hu X, Zhao L, Lv Y, Luo M, Pang S. Learning Dual Multi-Scale Manifold Ranking for Semantic Segmentation of High-Resolution Images. *Remote Sensing*. 2017; 9(5):500.
https://doi.org/10.3390/rs9050500

**Chicago/Turabian Style**

Zhang, Mi, Xiangyun Hu, Like Zhao, Ye Lv, Min Luo, and Shiyan Pang. 2017. "Learning Dual Multi-Scale Manifold Ranking for Semantic Segmentation of High-Resolution Images" *Remote Sensing* 9, no. 5: 500.
https://doi.org/10.3390/rs9050500