Multiscale and supervised image analysis in earth observation and remote sensing
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1 Multiscale and supervised image analysis in earth observation and remote sensing Sébastien Lefèvre Univ. Bretagne-Sud & CNRS IRISA, OBELIX team Blåtand Program November, 2014 Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 1/53
2 Outline My Research Environment: University, Institute, and Team Remote sensing image analysis for earth observation Dealing with few labels in manifold learning Multiscale features from morphological scale-spaces Hierarchical representations Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 2/53
3 Université de Bretagne-Sud A recent and small university Officially created in 1995 in Vannes and Lorient (but faculties established in 70s) students, 250+ faculty members (+150 lecturers) 4th French university for professional insertion Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 3/53
4 IRISA: Research Institute in Computer Science and Random Systems The main research institute in computer science in Brittany Officially created in 1975 in Rennes (established in 1970) Joint research institute between: CNRS INRIA Universities (Bretagne Sud, Rennes) Graduate Schools (INSA, ENS, Telecom, Supelec) members (including 250+ permanent researchers) staff in Vannes: 50+ members including 25 faculty members Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 4/53
5 Research at IRISA 7 research departments Large-scale Systems; Networks, Telecommunications and Services; Architecture; Language and Software Engineering; Digital Signals and Images, Robotics; Media and Interactions; Data and Knowledge Management teams 4 (co)located in Vannes ARCHWARE software architectures; CASA mobile computing; EXPRESSION gesture/speech/text understanding and OBELIX. Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 5/53
6 OBELIX EO Learning with Few labels Morphological scale-spaces Hierarchical representations Conclusion The OBELIX team I supported by UBS, UR2, CNRS I closely related to OSUR & LETG Rennes I located in Vannes & Rennes I permanent staff (8): 1 Full Prof., 1 Research Director, 6 Ass.Prof. I temporary staff (12): 6 PhD students (+ 3 defended 2014), 1 engineer + 2 postdocs I incoming open positions (Postdoc, PhD) S ebastien Lef` evre Broceliande Forest, Oct. 13 Multiscale and supervised image analysis in earth observation and remote sensing 6/53
7 Research at OBELIX Environment Observation through Complex Imagery image analysis and processing machine learning and data mining coupling physical models with observation data visual analytics in the context of remote sensing of environment Challenges address complex data (multi*) exploit prior knowledge ensure scalability Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 7/53
8 Recent methodological achievements knowledge-driven features and models for description of multivariate data (MSc 14, WHISPERS 14, ICIP 14, ALCIP 13) efficient algorithms for hierarchical image representation and analysis (MSc 14, PRRS 14, ISMM 13, ICIAP 13) classification of time series (SAR, multispectral) (MSc 14, JARS 14) domain adaptation for classification of hyperspectral data (ECML 14, ICPR 14) manifold learning with few labeled samples (JSTARS 14) non-negative matrix factorization (ML 14), anomaly detection (ECML 14), manifold subsampling (GSI 13) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 8/53
9 Active Projects & Grants ASTERIX* French National Research Agency ANR 275 ke VEGIDAR* French National Spatial Agency CNES 150 ke RESIDUAL* International Space Science Institute ISSI 38 ke SENSE Labex CominLabs 105 ke Littoralg Univ. Bretagne-Sud 48 ke + industrial contracts (MGDIS, WIPSEA, ACT-TER), ca. 60 ke OBELIX acts as PI for starred projects Publications (since 2012) 19 journal papers, 27 conference papers and 2 book chapters. Available at and HAL repository Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 9/53
10 Collaborations Researchers: Prof. Pasi Franti (UEF) Dr. Adam Herout (BUT) Dr. Erchan Aptoula (U Okan) Dr. Devis Tuia (EPFL / U Zurich) Dr. Cris Luengo (U Uppsala) Dr. Norman Kerle (ITC / U Twente) Prof. Baogang Hu (LIAMA Beijing) Prof. Tang Ping (CAS China) Prof. Daniel Racoceanu (IPAL / NUS Singapore) Dr. Suhaib Fahmy (NTU Singapore) Visits & Stays: Uppsala, Joensuu, EPFL, LIAMA Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 10/53
11 Outline My Research Environment: University, Institute, and Team Remote sensing image analysis for earth observation Dealing with few labels in manifold learning Multiscale features from morphological scale-spaces Hierarchical representations Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 11/53
12 Earth Observation from The team is addressing remote sensing of the environment. Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 12/53
13 Earth Observation Current sensing facilities from Airbus Defence and Space formerly Astrium/EADS (image from Various (semantic) analysis scales from Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 13/53
14 Complex EO imagery Massive data Gpixels images, TB of data, worldwide EO data reaching the ZB scale (10 21 ) High-dimensional data Hyperspectral images are made of hundreds of spectral bands (1 pixel = 100+ values) Heterogenous data A scene can be observed from various sensors with different properties such as spatial/spectral resolution, date, image type (raster: optical data, radar; 3D: LIDAR; vector: GIS) Temporal data Spatio-temporal data, with continuous growth in image repetivity Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 14/53
15 Remote sensing image analysis workflow Input Image (data) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
16 Remote sensing image analysis workflow Input Image (data) Feature Extraction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
17 Remote sensing image analysis workflow Input Image (data) Feature Extraction Features Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
18 Remote sensing image analysis workflow Input Image (data) Feature Extraction Features Clustering Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
19 Remote sensing image analysis workflow Input Image (data) Feature Extraction Features Clustering Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
20 Remote sensing image analysis workflow Input Image (data) Labels (knowledge) Feature Extraction Features Clustering Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
21 Remote sensing image analysis workflow Input Image (data) Labels (knowledge) Feature Extraction Features Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
22 Remote sensing image analysis workflow Input Image (data) Labels (knowledge) Feature Extraction Features Classification Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
23 Remote sensing image analysis workflow Input Image (data) Labels (knowledge) Feature Extraction Features Classification Semantic Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 15/53
24 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
25 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Segmentation Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
26 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Segmentation Objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
27 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Segmentation Objects Feature extraction Features Classification Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
28 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Segmentation Objects Feature extraction Features Classification Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
29 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Segmentation Objects Feature extraction Multiscale Features Classification Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
30 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Segmentation Hierarchies Feature extraction Multiscale Features Classification Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
31 VHR Remote sensing image analysis workflow Input image (data) Labels (knowledge) Segmentation Hierarchies Feature extraction Multiscale Features Classification Multiscale Map Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 16/53
32 Outline My Research Environment: University, Institute, and Team Remote sensing image analysis for earth observation Dealing with few labels in manifold learning Multiscale features from morphological scale-spaces Hierarchical representations Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 17/53
33 Challenges in hyperspectral classification 1. Processing a huge amount of high dimensional data leads to significant time and memory requirements 2. Most classifiers suffer the dimensionality curse: the classification accuracy decreases with the dimension of the data when the number of available pixels is fixed. SVM: state of the art classification technique in this context alleviate the dimensionality curse generally outperform traditional classification techniques but they learn a boundary between classes they have to be retrained when a new class is added their performances are not optimal when the number of training examples is low Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 18/53
34 Challenges in hyperspectral classification 1. Processing a huge amount of high dimensional data leads to significant time and memory requirements 2. Most classifiers suffer the dimensionality curse: the classification accuracy decreases with the dimension of the data when the number of available pixels is fixed. SVM: state of the art classification technique in this context alleviate the dimensionality curse generally outperform traditional classification techniques but they learn a boundary between classes they have to be retrained when a new class is added their performances are not optimal when the number of training examples is low Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 18/53
35 PerTurbo algorithm (Courty & Burger, ECML 2011) Idea from computer graphics: sampling point clouds, keeping the most informative points Need for metric to quantify the modification of the definition of the object surface induced by a new sample The manifold M can be modeled using a Gaussian kernel ( x K ij (M) = K(x i, x j i x j 2 ) ) = exp 2σ 2 The perturbation of the spectrum of K(M) is used to evaluate the interest of a sample 1 K T x K(M) 1 K x with K x = K(M, x) whose ith term is K(x i, x) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 19/53
36 The perturbation of K(S l ) quantifies the interest of a sample. The perturbation of the manifold M l induced by a point x is an interesting clue of the membership of this point to the class l! Application to remote sensing: L. Chapel et al. PerTurbo manifold learning algorithm for weakly labelled hyperspectral image classification. In: IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 7.4 (2014), pp doi: /JSTARS Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 20/53
37 Classical classification problem Training set S = { (x 1, y 1 ),..., (x N, y N ) } R d {u 1,..., u L } S l is the set of all the training examples with label u l belonging to S Aim: build a predictive function that associates to each pixel x n its corresponding class y n Classwise manifold learning For each class l, a dedicated manifold M l is considered Each manifold is learned independently and represented by a particular matrix K l Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 21/53
38 Perturbo algorithm Training step class l, K(S l ) 1 is computed. Testing step For each test sample x 1. Compute the perturbation of M l induced by x: τ( x, M l ) = 1 K T x K(S l) 1 K x with K x = K(S l, x) whose ith term is K(x i, x) 2. Predict the class with the least induced perturbation, which reads as: arg min l τ( x, M l ) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 22/53
39 Perturbo algorithm Training step class l, K(S l ) 1 is computed. Testing step For each test sample x 1. Compute the perturbation of M l induced by x: τ( x, M l ) = 1 K T x K(S l) 1 K x with K x = K(S l, x) whose ith term is K(x i, x) 2. Predict the class with the least induced perturbation, which reads as: arg min l τ( x, M l ) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 22/53
40 Perturbo algorithm Training step class l, K(S l ) 1 is computed. Testing step For each test sample x 1. Compute the perturbation of M l induced by x: τ( x, M l ) = 1 K T x K(S l) 1 K x with K x = K(S l, x) whose ith term is K(x i, x) 2. Predict the class with the least induced perturbation, which reads as: arg min l τ( x, M l ) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 22/53
41 Perturbo algorithm In the seminal paper, it shows similar performances in comparison with SVM on several toy examples Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 22/53
42 PerTurbo s main characteristics provides a class-wise classification non-parametric method: no need for explicit formulation of the decision function like in SVM very simple, easy to implement and involves few parameters to tune Regularization helps to take into account outliers or mislabeled pixels works as long as K(S l ) is invertible Tikhonov regularization: K(S l ) = K(S l ) + α l I Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 23/53
43 PerTurbo s main characteristics provides a class-wise classification non-parametric method: no need for explicit formulation of the decision function like in SVM very simple, easy to implement and involves few parameters to tune Regularization helps to take into account outliers or mislabeled pixels works as long as K(S l ) is invertible Tikhonov regularization: K(S l ) = K(S l ) + α l I Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 23/53
44 Datasets 3 hyperspectral scenes Pavia University: 102 spectral bands, 7456 pixels for training, for testing, 9 classes of interest Pavia Centre: 103 spectral bands, 3921 pixels for training, for testing, 9 classes of interest Indian Pines: 224 spectral bands, 695 pixels for training, 9554 for testing, 16 classes of interest DC Mall: 191 spectral bands, Parameter settings SVM: grid search for (σ, C), one-vs-all strategy PerTurbo: grid search for σ and (σ, α) each experiment is repeated 20 times for pines dataset Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 24/53
45 INDIAN PINES ( pixels, 224 bands, 9 classes) Training set size SVM PerTurbo (truncated) PerTurbo (Tikhonov) z OA (% / #) OA[%] κ[%] OA[%] κ[%] OA[%] κ[%] 0.5 / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± PAVIA UNIVERSITY ( pixels, 102 bands, 9 classes) Training set size SVM PerTurbo (truncated) PerTurbo (Tikhonov) z OA (% / #) OA[%] κ[%] OA[%] κ[%] OA[%] κ[%] 0.1 / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± PAVIA CENTER ( pixels, 103 bands, 9 classes) Training set size SVM PerTurbo (truncated) PerTurbo (Tikhonov) z OA (% / #) OA[%] κ[%] OA[%] κ[%] OA[%] κ[%] / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± WASHINGTON DC MALL ( pixels, 191 bands, 7 classes) Training set size SVM PerTurbo (truncated) PerTurbo (Tikhonov) z OA (% / #) OA[%] κ[%] OA[%] κ[%] OA[%] κ[%] 0.5 / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ± / ± ± ± ± ± ±
46 Indian Pines dataset The colour code is the following: Corn-notill, Corn-mintill, Grass-pasture, Grass-trees, Hay-windrowed, Soybean-notill, Soybean-mintill, Soybean-clean, Woods. false colour available PerTurbo map PerTurbo map composition reference data (5 points by class (56 points by class for training) for training) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 26/53
47 Outline My Research Environment: University, Institute, and Team Remote sensing image analysis for earth observation Dealing with few labels in manifold learning Multiscale features from morphological scale-spaces Hierarchical representations Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 27/53
48 Mathematical Morphology: Binary case Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
49 Mathematical Morphology: Binary case within a structuring element b Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
50 Mathematical Morphology: Binary case erosion ε shrinks objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
51 Mathematical Morphology: Binary case erosion ε shrinks objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
52 Mathematical Morphology: Binary case erosion ε shrinks objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
53 Mathematical Morphology: Binary case erosion ε shrinks objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
54 Mathematical Morphology: Binary case dilation δ enlarges objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
55 Mathematical Morphology: Binary case dilation δ enlarges objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
56 Mathematical Morphology: Binary case dilation δ enlarges objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
57 Mathematical Morphology: Binary case dilation δ enlarges objects Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 28/53
58 Mathematical Morphology: Grayscale case Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
59 Mathematical Morphology: Grayscale case within a flat or functional structuring element b Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
60 Mathematical Morphology: Grayscale case erosion ε shrinks maxima and enlarges minima Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
61 Mathematical Morphology: Grayscale case erosion ε shrinks maxima and enlarges minima Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
62 Mathematical Morphology: Grayscale case erosion ε shrinks maxima and enlarges minima Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
63 Mathematical Morphology: Grayscale case dilation δ enlarges maxima and shrinks minima Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
64 Mathematical Morphology: Grayscale case dilation δ enlarges maxima and shrinks minima Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
65 Mathematical Morphology: Grayscale case dilation δ enlarges maxima and shrinks minima Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 29/53
66 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
67 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
68 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
69 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
70 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
71 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
72 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
73 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
74 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
75 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
76 Morphological scale-spaces Multiscale representations built from successive applications of morphological filters used to produce morphological descriptions of images or pixels Gaussian smoothings Openings by reconstruction Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 30/53
77 Differential Morphological Profile Each pixel p in image f is associated with a series of responses from morphological filters ψ with increasing scale λ: Π ψ (f )(p) = (Π ψ λ (f )(p)) 0 λ n. The DMP is the series of first-order derivatives considering filters by reconstruction: DMP(f )(p) = ρ (f )(p) DMP Pixel A Pixel B Pixel C Pixel D SE size Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 31/53
78 Mathematical Morphology: Multivariate case Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 32/53
79 Mathematical Morphology: Multivariate case Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 32/53
80 Mathematical Morphology: Multivariate case color / multivariate ordering is required Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 32/53
81 Mathematical Morphology: Multivariate case but there is no such natural ordering! Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 32/53
82 Multivariate morphology marginal processing: each spectral band is a grayscale image vectorial processing: pixel values are vectors Vectorial strategies partial ordering e.g. marginal strategy (but lack of correlation) pre-ordering e.g. reduced ordering (but no unique extrema) total ordering e.g. lexicographical ordering (but unbalanced) Proposal Vectorial ordering could rely on domain knowledge E. Aptoula and S. Lefèvre. A comparative study on multivariate mathematical morphology. In: Pattern Recognition (Nov. 2007), pp Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 33/53
83 Multivariate morphology marginal processing: each spectral band is a grayscale image vectorial processing: pixel values are vectors Vectorial strategies partial ordering e.g. marginal strategy (but lack of correlation) pre-ordering e.g. reduced ordering (but no unique extrema) total ordering e.g. lexicographical ordering (but unbalanced) Proposal Vectorial ordering could rely on domain knowledge E. Aptoula and S. Lefèvre. A comparative study on multivariate mathematical morphology. In: Pattern Recognition (Nov. 2007), pp Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 33/53
84 Multivariate morphology marginal processing: each spectral band is a grayscale image vectorial processing: pixel values are vectors Vectorial strategies partial ordering e.g. marginal strategy (but lack of correlation) pre-ordering e.g. reduced ordering (but no unique extrema) total ordering e.g. lexicographical ordering (but unbalanced) Proposal Vectorial ordering could rely on domain knowledge E. Aptoula and S. Lefèvre. A comparative study on multivariate mathematical morphology. In: Pattern Recognition (Nov. 2007), pp Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 33/53
85 End-members Each pixel in an hyperspectral image is assigned a vector of reflectances sampled over different wavelengths Spatial resolution and scattering effect lead to mixed pixels, with values that are actually combination of spectra, each of them describing the reflectance of a pure material These pure material are called end-members, and can be identified by several algorithms e.g., N-FINDR While the end-members are usually employed for spectral unmixing, they can also be used for devising a supervised ordering with physical foundations E. Aptoula, N. Courty, and S. Lefèvre. An end-member based ordering relation for the morphological description of hyperspectral images. In: IEEE International Conference on Image Processing (ICIP). Paris, France, Oct Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 34/53
86 Proposed ordering 1. Extraction of end-members m i, used as reference spectra 2. Distance between each pixel p and end-member m i is computed 3. Ordering of the pixels based on their distance to the closest end-member (inspired from ordering hues) min {d(f (p), m i )} < min {d(f (q), m j )} f(q) < M f (p) i j 4. a lexicographical cascade is added to avoid ties (not in practice) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 35/53
87 Proposed ordering End-member C Spectra under comparison Maximum (dilation) Band i Minimum (erosion) End-member A End-member B Band j Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 35/53
88 OBELIX EO Learning with Few labels Morphological scale-spaces Hierarchical representations Conclusion Illustration on Pavia University image (9 classes) Original image (80,90,70) S ebastien Lef` evre Dilation 3 3 square SE Erosion 3 3 square SE Multiscale and supervised image analysis in earth observation and remote sensing 36/53
89 Dataset: Indian Pines image: pixels, 200 spectral bands learning set: 16 classes, 10, 249 labeled pixels Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 36/53
90 Setup N-FINDR with 16 end-members (i.e. number of classes) Euclidean distance between pixels and end-members Morphological operators are used to compute DMP of size 3, 5, 7 and 9, leading to a profile of length 9 for each band We limit the number of spectral bands to 16 (regular sampling) to limit the feature vector to 9 16 = 144 We perform classification using random forest (100 trees), 10 pixel/class for training (the rest for testing), results averaged over 30 runs Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 37/53
91 Classification results Class Set Size MARG (s.dev) NORM (s.dev) SAD (s.dev) ENDM (s.dev) Alfalfa (1.74) 91 (1.71) (1.74) (1.91) Corn-notill 1, (1.85) (1.49) (1.87) 59.5 (1.69) Corn-mintill (1.63) (1.23) (1.63) (1.54) Corn (1.96) (1.53) (1.42) (1.62) Grass-pasture (1.85) (1.86) (1.41) (1.87) Grass-trees (1.84) (1.67) (1.31) (1.65) Grass-pasture-mowed (1.45) 100 (0.14) 100 (0.11) 100 (0.4) Hay-windrowed (1.85) (1.12) (1.63) (1.9) Oats (0.2) 96.4 (0.34) 94.8 (1.62) 100 (0.44) Soybean-notill (1.01) (1.45) 53.8 (1.41) (1.83) Soybean-mintill 2, (1.84) (1.57) (1.73) (1.95) Soybean-clean (1.9) (1.15) (1.92) (1.84) Wheat (1.85) (1.46) (1.28) 98.4 (1.8) Woods 1, (1.96) (1.27) (1.73) (1.5) Build.-Grass-Trees-Drives (1.84) (1.83) 80.5 (1.84) (1.41) Stone-Steel-Towers (0.98) (0.84) (1.85) (1.62) Average Accuracy 87.3 (1.65) (1.29) (1.53) (1.56) Overall Accuracy (1.95) (1.55) (1.74) (1.81) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 38/53
92 Supervised feature extraction A perturbo-based ordering: x a > l x b τ l (x a ) > τ l (x b ) where τ l ( ) = τ(, M l ) (+ lexicographical comparison of x a and x b to ensure totality). Learning set Manual labelling Total Ordering class 1 Total Ordering class 2 Total Ordering class 3 Total Ordering class n Alternating Sequential filters Pertubation measures computation Maximum likelihood Final label map Hyperspectral Image with n classes n perturbation maps related to n classes N. Courty, E. Aptoula, and S. Lefèvre. A Classwise Supervised Ordering Approach for Morphology Based Hyperspectral Image Classification. In: IAPR International Conference on Pattern Recognition (ICPR). Tsukuba, Japan, Nov Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 39/53
93 Supervised feature extraction We replace here the DMP by a simple alternate sequential filter that aims to smooth the image. Example is given for the Asphalt class. Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 40/53
94 Supervised feature extraction input ground truth Perturbo EMP Proposed Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 41/53
95 Outline My Research Environment: University, Institute, and Team Remote sensing image analysis for earth observation Dealing with few labels in manifold learning Multiscale features from morphological scale-spaces Hierarchical representations Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 42/53
96 Multiscale description.. spatial-spectral features Hyperspectral image... Hierarchical representation Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 43/53
97 Multiscale description driven by domain knowledge.. enhanced spatial-spectral features Hyperspectral image +labels... Hierarchical representation with side information pixelwise classification Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 43/53
98 The α-tree model image α-cc α-tree Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 44/53
99 The α-tree model image α-cc α-tree d(p, q) 0 p and q neighbors Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 44/53
100 The α-tree model image α-cc α-tree d(p, q) 1 p and q neighbors Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 44/53
101 The α-tree model image α-cc α-tree d(p, q) 2 p and q neighbors Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 44/53
102 The α-tree model image α-cc α-tree d(p, q) 3 p and q neighbors Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 44/53
103 Knowledge-driven distance Mahalanobis distance d(a, b) = (a b) t M(a b) with M = cov(a, b) 1 gives classical Mahalanobis distance Additional knowledge must-link S = {(a, b) a, b belong to the same class} cannot-link D = {(a, b) a, b are in different classes} The optimal matrix M can be learnt from those pairs a,b S d(a, b) is minimum d(a, b) is maximum a,b D Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 45/53
104 The chaining effect image α-cc α-tree d(p, q) 1 p and q neighbors pixels with very distinct values are gathered in a unique α-cc assumed to be of low complexity Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 46/53
105 The chaining effect image α-cc α-tree d(p, q) 1 p and q neighbors pixels with very distinct values are gathered in a unique α-cc assumed to be of low complexity Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 46/53
106 (α, ω) connected components Threshold ω on the global range of the α-cc d(p, q) α, p, q neighbors d(u, v) ω, u, v α-cc Storing the minimum and maximum values of each α-cc in grayscale image Extension to hyperspectral images? Complexity O(n 3 ) 1. can not be computed from the maximum and minimum 2. no universal ordering for vectorial data Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 47/53
107 Efficient overestimation for hyperspectral images Solution 1: α and ω criteria shall be fulfilled in all spectral bands Solution 2: total ordering on pixel values Here, overestimation of the global range 1. compute the diagonal of the set (bounding box) but dimensionality curse! 2. diameter of a bounding sphere: only need to store the gravity centers and the (α, ω)-cc size (not optimal!) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 48/53
108 Efficient overestimation for hyperspectral images Solution 1: α and ω criteria shall be fulfilled in all spectral bands Solution 2: total ordering on pixel values Here, overestimation of the global range 1. compute the diagonal of the set (bounding box) but dimensionality curse! 2. diameter of a bounding sphere: only need to store the gravity centers and the (α, ω)-cc size (not optimal!) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 48/53
109 Efficient overestimation for hyperspectral images Solution 1: α and ω criteria shall be fulfilled in all spectral bands Solution 2: total ordering on pixel values Here, overestimation of the global range 1. compute the diagonal of the set (bounding box) but dimensionality curse! 2. diameter of a bounding sphere: only need to store the gravity centers and the (α, ω)-cc size (not optimal!) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 48/53
110 Efficient overestimation for hyperspectral images Solution 1: α and ω criteria shall be fulfilled in all spectral bands Solution 2: total ordering on pixel values Here, overestimation of the global range 1. compute the diagonal of the set (bounding box) but dimensionality curse! 2. diameter of a bounding sphere: only need to store the gravity centers and the (α, ω)-cc size (not optimal!) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 48/53
111 Efficient overestimation for hyperspectral images Solution 1: α and ω criteria shall be fulfilled in all spectral bands Solution 2: total ordering on pixel values Here, overestimation of the global range 1. compute the diagonal of the set (bounding box) but dimensionality curse! 2. diameter of a bounding sphere: only need to store the gravity centers and the (α, ω)-cc size (not optimal!) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 48/53
112 Efficient overestimation for hyperspectral images Solution 1: α and ω criteria shall be fulfilled in all spectral bands Solution 2: total ordering on pixel values Here, overestimation of the global range 1. compute the diagonal of the set (bounding box) but dimensionality curse! 2. diameter of a bounding sphere: only need to store the gravity centers and the (α, ω)-cc size (not optimal!) Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 48/53
113 Experimental setup: Pavia Center (sample) Features = spectral bands Tree-based features extract (α, ω)-ccs using a regular sample of ω values stack the size, within cluster variance, averaged spectral signature for all the bands of all the CCs 1% of the points for learning, SVMs Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 49/53
114 Extracted (α, ω) zones Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 50/53
115 Results raw features spatial-spectral features Pavia University Pavia Center Method OA (%) OA (%) Spectral bands features ± ± 0.90 Tree-derived features ± ± 0.62 Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 51/53
116 Results raw features spatial-spectral features Pavia University Pavia Center Method OA (%) OA (%) Spectral bands features ± ± 0.90 Tree-derived features ± ± 0.62 Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 51/53
117 Image analysis is a key step in Earth Observation. Data volumes faced in EO raise a major challenge. Scalability can be achieved through multiscale approaches. Such strategies also fit well with EO. User involvement has to be kept reasonable. Meanwhile, automatic techniques are not expected (neither desired!). New ways to put the human in the loop are needed. Combining new developments in image analysis, computer vision, and machine learning is expected to have a high impact in remote sensing. Any questions? Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 52/53
118 Sébastien Lefèvre Multiscale and supervised image analysis in earth observation and remote sensing 53/53
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