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Unsupervised Change Detection in Multi-temporal VHR Images Based on Deep Kernel PCA Convolutional Mapping Network

Chen Wu, Hongruixuan Chen, Bo Do, Liangpei Zhang

arXiv:1912.08628v1eess.IVcs.CV

TL;DR

Deep-learning change detection for VHR images often requires annotated samples. This paper proposes unsupervised KPCA convolution and a siamese KPCA-MNet for binary and multi-class detection, with experiments showing effectiveness across both settings. The approach extracts nonlinear spatial-spectral features and maps feature differences into a polar domain for thresholding or clustering.

  • Problem

    Existing deep-learning change-detection models for VHR images commonly require annotated training samples, while unsupervised multi-class methods remain limited.

  • Method

    KPCA-MNet uses unsupervised KPCA convolution in a weight-shared deep siamese network, then maps feature differences into a 2-D polar domain for thresholding and clustering.

  • Results

    Experiments on two binary and one multi-class data set show that KPCA-MNet outperforms conventional, deep-learning, and several unsupervised change-detection methods.

  • Takeaways & Limitations

    The proposed KPCA convolution and KPCA-MNet provide a versatile unsupervised approach for binary and multi-class VHR change detection.

  • Takeaways & Limitations

    Future work is needed to apply KPCA convolution and KPCA-MNet to heterogeneous image change detection and hyperspectral image classification.

Abstract

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With the development of Earth observation technology, very-high-resolution (VHR) image has become an important data source of change detection. Nowadays, deep learning methods have achieved conspicuous performance in the change detection of VHR images. Nonetheless, most of the existing change detection models based on deep learning require annotated training samples. In this paper, a novel unsupervised model called kernel principal component analysis (KPCA) convolution is proposed for extracting representative features from multi-temporal VHR images. Based on the KPCA convolution, an unsupervised deep siamese KPCA convolutional mapping network (KPCA-MNet) is designed for binary and multi-class change detection. In the KPCA-MNet, the high-level spatial-spectral feature maps are extracted by a deep siamese network consisting of weight-shared PCA convolution layers. Then, the change information in the feature difference map is mapped into a 2-D polar domain. Finally, the change detection results are generated by threshold segmentation and clustering algorithms. All procedures of KPCA-MNet does not require labeled data. The theoretical analysis and experimental results demonstrate the validity, robustness, and potential of the proposed method in two binary change detection data sets and one multi-class change detection data set.

I. INTRODUCTION

Change detection in multi-temporal VHR imagery is important because such images provide detailed spatial and spectral information, but existing approaches face limitations in exploiting spatial context and avoiding annotated training data. The paper addresses these issues with an unsupervised KPCA-based feature-extraction and change-detection framework.

  • VHR images support detection of subtle surface changes through abundant spatial details and distribution information.
  • Pixel-based methods transform spectral information but do not fully exploit spatial context in VHR imagery.
  • Object-based and spatial-feature methods incorporate context through segmented objects or local texture and spatial descriptors.
  • Deep learning extracts representative high-level VHR features, but many existing models require labeled samples or rely on pre-detection algorithms.
  • The proposed KPCA-MNet extracts spatial-spectral features unsupervised, subtracts multi-temporal features, maps differences into a 2-D polar domain, and uses thresholding or clustering.

B. CNN

CNNs extract hierarchical features from grid-like image data through alternating convolution, activation, and pooling operations. Their conventional training, however, uses annotated data and backpropagation.

  • CNNs process grid-like data such as images using convolutional layers, activation functions, and pooling layers.
  • Convolutional layers generate feature maps from trainable kernels, while activation functions introduce nonlinearity.
  • Pooling subsamples feature maps, removes redundant information, and provides approximate spatial-translation invariance.
  • CNN training is supervised, using annotated data and stochastic-gradient descent with backpropagation to optimize parameters.

III. METHODOLOGY

The methodology adapts PCA-style convolution to VHR imagery so spatial-spectral features can be extracted from local image patches. PCA eigenvectors serve as convolution kernels, while the resulting feature maps retain spatial structure.

  • The proposed convolution operation uses KPCA to extract representative spatial-spectral features from VHR images without supervision.
  • Local s1 × s2 × c patches are vectorized, and n randomly selected patches form the training samples for feature extraction.
  • The first k PCA components transform image patches into k-dimensional spatial-spectral features.
  • PCA feature extraction is equivalent to convolution, with reshaped eigenvectors acting as convolution kernels.

2) Kernel PCA Convolution:

KPCA convolution maps image patches into a nonlinear feature space and extracts nonlinear spatial-spectral maps through kernel-based principal components. It preserves the convolutional structure while learning parameters without annotated data.

  • 2) Kernel PCA Convolution:: KPCA convolution introduces nonlinear feature extraction to improve the representativeness and discriminability of spatial-spectral features.
  • 2) Kernel PCA Convolution:: Vectorized image patches are mapped into a high-dimensional nonlinear feature space before KPCA components are computed.
  • 2) Kernel PCA Convolution:: Kernel functions compute dot products of mapped data without explicitly constructing the nonlinear mapping.
  • 2) Kernel PCA Convolution:: The nonlinear procedure is equivalent to convolution with implicit kernels and an implicit nonlinear function.
  • 2) Kernel PCA Convolution:: When the mapping is the identity, KPCA convolution reduces to PCA convolution, making the linear operation a special case.
  • 2) Kernel PCA Convolution:: KPCA convolution extracts spatial-spectral features in two dimensions while learning parameters unsupervised and requiring no annotated data.

B. Deep Siamese KPCA Convolutional Mapping Network

KPCA-MNet uses preprocessed multi-temporal VHR images to extract representative spatial-spectral features with weight-shared KPCA convolutional layers, then maps their differences into a 2-D polar domain for change detection.

  • KPCA-MNet first preprocesses multi-temporal VHR images before extracting representative spatial-spectral feature maps.
  • Several weight-shared KPCA convolutional layers extract features from the multi-temporal images.
  • Pixel-wise subtraction produces a feature difference map containing change information.
  • The high-level difference features are mapped into a 2-D polar domain, after which binary and multi-class change results are generated.

1) Data Pre-processing:

KPCA-MNet preprocesses aligned multi-temporal images, trains KPCA convolutional layers without labels, and uses a deep siamese architecture to extract comparable spatial-spectral features.

  • Data Pre-processing: Image registration aligns multi-temporal images so corresponding pixels represent the same geographic locations before change detection.Registration includes matched point-pair collection, transformation-model establishment, and image transformation.
  • Deep KPCA Convolution: KPCA convolution extracts nonlinear spatial-spectral features from randomly sampled image patches through kernel construction, KPCA, coefficient normalization, and channel stacking.The resulting channels are stacked into a nonlinear spatial-spectral feature map.
  • Data Pre-processing: Radiometric correction suppresses differences caused by imaging conditions through relative normalization based on z-score standardization.The method standardizes images with zero mean and unit variance.
  • Deep KPCA Convolution: Multiple KPCA convolutional layers are stacked to capture multi-scale and higher-level VHR features beyond a single layer’s limited receptive field.
  • Deep KPCA Convolution: Two siamese subnetworks use identical convolutional settings to extract features from the two multi-temporal images in the same way.The subnetworks share convolution kernel size, kernel parameters, and network depth.
  • Deep KPCA Convolution: Each KPCA convolutional layer is trained unsupervised, layer by layer, using randomly selected pairs of patches covering the same area.

3) Feature Mapping and Change Detection:

KPCA-MNet compares high-level feature maps, represents change through magnitude and direction in a 2-D polar domain, and derives binary or multi-class maps using segmentation and clustering.

  • Feature Mapping and Change Detection: Pixel-wise subtraction of the two high-level feature maps produces a feature difference map containing change information.
  • Feature Mapping and Change Detection: Feature magnitude ρ indicates change likelihood: larger ρ_i corresponds to a higher probability that pixel i has changed.Threshold segmentation methods such as OTSU and EM can generate the binary change map.
  • Feature Mapping and Change Detection: The feature difference map can support unsupervised multi-class detection because different objects become more discriminative in the learned feature space.
  • Feature Mapping and Change Detection: Direct clustering in the original difference space may be ineffective because redundant information and unequal channel informativeness obscure change classes.
  • Feature Mapping and Change Detection: Eigenvalue-weighted feature directions use more informative channels more heavily when mapping differences into θ.The eigenvalue corresponds to a convolution kernel in the last KPCA convolutional layer.
  • Feature Mapping and Change Detection: Binary detection thresholds ρ, whereas multi-class detection first separates changed from unchanged pixels and then clusters changed pixels using θ.

A. Data Description

The study evaluates KPCA-MNet for binary change detection on WH and QU VHR image pairs against conventional, object-based, and deep-learning methods. KPCA-MNet produces accurate maps and outperforms comparison methods on key quantitative criteria while avoiding annotated training data.

  • Datasets: WH uses 4-band GF-2 image pairs from Wuhan with 1000 × 1000 pixels and 4 m spatial resolution, while QU uses 4-band QuickBird pairs with 358 × 280 pixels and 2.4 m resolution.WH was acquired in 2016; QU was acquired in 2002 and 2005.
  • Experimental settings: The evaluation compares KPCA-MNet with CVA, MAD, IRMAD, USFA, ISFA, PCA-Kmeans, OBCD, SVM, DSCN, RNN-CD, and SAE using threshold segmentation methods including K-means, OTSU, and FCM.SVM, DSCN, and RNN-CD use annotated samples selected through unsupervised automatic pre-detection for fairness.
  • WH results: KPCA-MNet obtains the best WH binary change map, with less noise, more complete changed regions, and improved robustness to over-exposed areas through spatial-spectral feature extraction.The method uses a deep siamese KPCA convolutional architecture and feature magnitude to merge change information.
  • WH results: On WH, KPCA-MNet outperforms the compared methods with the best OE, OA, and KC, while OBCD has the lowest FP and SAE has the best FN.MAD and USFA have low KC values of 0.2662 and 0.2335, respectively.
  • QU results: On QU, KPCA-MNet achieves accurate binary change maps and outperforms the compared methods with FN of 1795, OE of 3468, OA of 0.9019, and KC of 0.7778.RNN-CD performs well on WH but worse than MAD and SFA on QU because automatic pre-detection can include false-alarm samples.

D. Discussion

The discussion examines how KPCA-MNet performance changes with network depth, kernel size, training-sample count, and kernel function. It identifies practical settings that balance accuracy, spatial context, representativeness, and computational cost.

  • Network depth: Deeper networks improve performance, but depths beyond 4 increase computation without substantially improving accuracy; L values from 2 to 4 are recommended.The network is trained layer by layer, which makes excessive depth computationally burdensome.
  • Kernel size: Larger convolution kernels expand the receptive field, but excessive size introduces unrelated information and can reduce performance.For WH, performance peaks as w increases from 3 to 5; for QU, improvement becomes negligible above 9, with a suitable real kernel size of 20m to 30m.
  • Training samples: The number of training samples controls feature representativeness and computational cost: more samples improve spatial-spectral features, but excessive n enlarges the kernel matrix and complicates KPCA.The discussion identifies n = 200 as a good choice.
  • Kernel function: RBF is the best of five tested kernel functions, while sigmoid also performs well and both improve change detection over linear PCA convolution.The comparison is conducted on both binary change-detection data sets.
  • Number of kernels: Using more KPCA convolution kernels extracts more features, but p = 8 is selected as a trade-off between accuracy and computational expense.The parameter p is directly tied to the number of features extracted from multi-temporal images.

V. EXPERIMENT OF MULTI-CLASS CHANGE DETECTION

The HY experiment evaluates unsupervised multi-class change detection using KPCA-MNet against seven representative methods and a LinearPCA-MNet variant. KPCA-MNet detects changed and unchanged regions accurately while distinguishing city, water, and soil changes.

  • Experiment setting: The HY data set contains two 1000 × 1000 GF-2 images acquired over Hanyang in April and September 2016 at 4 m resolution.
  • Comparison methods: Seven representative methods are compared with KPCA-MNet, including PCC, 2D-CVA, C2VA, PCA, IRMAD, SAE, and RandNet.
  • Qualitative results: KPCA-MNet accurately detects most changed and unchanged regions and efficiently distinguishes city, water, and soil changes.
  • Quantitative results: SAE achieves OA of 0.9576 and KP of 0.7712, while KPCA-MNet shows superiority across all evaluation criteria.
  • Quantitative results: LinearPCA-MNet reaches KP of 0.7745 but remains inferior to KPCA-MNet, especially in accuracy for individual change classes.

D. Discussion

The discussion examines how polar-domain representations and feature mapping affect unsupervised multi-class change detection. KPCA-MNet produces compact, discriminative representations, while WFD weighting improves use of channel-specific change information.

  • Polar-domain representation: KPCA-MNet makes unchanged pixels compact and different change types discriminative in the 2-D polar domain.
  • Polar-domain representation: C2VA, SAE, and RandNet show limitations from spectral-only inputs, weak highlighting of city changes, or non-discriminative random filters.
  • Feature mapping: The WFD weights feature-difference channels according to their change information, rather than treating all channels equally.
  • Feature mapping: KP of M-1 is 0.4015, whereas M-3 reaches OA of 0.9630 and KP of 0.8028, showing that mapping choices materially affect performance.
  • Overall findings: Experiments on binary and multi-class data sets show KPCA-MNet outperforming conventional and deep learning-based comparison methods.
  • Future work: Future work includes applying KPCA convolution and KPCA-MNet to heterogeneous image change detection and hyperspectral image classification.
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