GNR607 Principles of Satellite Image Processing Instructor: Prof. B. Krishna Mohan CSRE, IIT Bombay bkmohan@csre.iitb.ac.in Slot 2 Lecture 32-34 Principal Component Transform and Band Arithmetic October 14, 2014 10.35 AM – 11.30 AM October 16, 2014 11.35 AM – 12.30 PM, 3.30 – 5.00 PM
IIT Bombay Slide 47 Decorrelation Stretch GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 47a Decorrelation Stretch • Variance of lower order principal components is low • Apply enhancement to these lower order PCs • Apply Inverse PCT (discussed next) • Form color composites (FCC, True color composites) • See improvement in visual quality GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 47b ASTER Satellite Image Enhancement Source: http://www.gisdevelopment.net/technology/rs/techrs0023a.htm GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 47c Enhancement of Rock Art Paintings Burham Canyon (KER-273) Source: http://www.dstretch.com/AlgorithmDescription.html GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 48 Inverse PCT • Inverse PCT is used to generate the bands in the original domain • If ALL PCTs are retained, inverse will give back the original bands • If any PCTs are dropped, inverse will give new bands in the original domain that may be close to the original bands depending on how many PCTs are discarded GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 49 Inverse PCT From the principle of PCT, we have y = D t x D t contains eigenvectors of S x , covariance matrix from the original image. D has eigenvectors as columns, thus D t has the eigenvectors as rows Since D t is an orthonormal matrix, D t . D = I (each row is orthogonal to other rows) (D t ) t = (D t ) -1 From each pixel vector in PC domain, x = (D t ) t y GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 50 Inverse PCT For k band image, matrix D is square, of size k x k If m principal components are dropped, we are left with a matrix (D 1 ) of size k x (k-m) The vector y is reduced to y 1 of size k-m x 1 Therefore the modified vector x 1 is given by x 1 = D 1 y 1 The difference between x and x 1 is a measure of the loss of information due to removal of some of the PCs GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 51 Comments on PCT • One of the other important applications of PCT is data fusion • Images from two sensors can be fused to produce a new image that has the strong points of both the input images • PCT based fusion is a well known approach GNR607 Lecture 32-34 B. Krishna Mohan
Data Fusion
IIT Bombay Slide 52 Data Fusion • Combine datasets to prepare a superior dataset • Stack up all the datasets to create a large higher dimensional dataset – e.g., multitemporal data from same sensor • Fuse the datasets to create a higher resolution dataset • Fuse the datasets to create a new dataset that has attributes of individual ones GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 53 Data Fusion • Most commonly employed by endusers of remotely sensed data • Supported by most software packages GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 54 Introduction • Merging multi-sensor data can help exploit strengths of various data sets – Radiometric resolution advantage – Spatial resolution advantage – Spectral resolution advantage – Temporal resolution advantage GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 55 Spatial Resolution Enhancement • This is the most common application of data fusion – Low resolution images have fewer pixels per unit area due to larger pixel size – Improve spatial resolution – High resolution images provide more pixels per unit area by smaller sampling interval (pixel size) GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 56 Zooming is NOT resolution enhancement • How is spatial resolution enhanced? • Low resolution absence of high spatial frequency content • High frequency information is to be transferred from another data source (of higher resolution) GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 57 Resolution Sharpening • Most often, data from the lower spatial resolution multispectral sensors and the higher spatial resolution panchromatic sensors are merged • Results in multispectral data at higher spatial resolution GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 58 Multi-sensor Data Merging Most common operation • PAN images to sharpen multispectral data e.g., IRS pan + IRS ms • Sharpening low resolution multispectral images with high resolution multispectral images For instance, SPOT ms + TM ms (20 metres) (30 metres) GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 59 Input Image Preparation • Contrast Adjustment – Zoom low resolution image to the same physical size of the high resolution image – Match histogram of the MS image with that of PAN image using histogram based techniques • Image Registration – Register the zoomed low resolution image to the high resolution image. This should be accurate to a fraction of a pixel GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 60 Image Sharpening • MS hr = f(MS lr , PAN hr ) , where • MS = multispectral Image • PAN = Panchromatic Image • lr = low resolution • hr = high resolution GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 61 Sharpening Techniques • Principal Component Analysis method • Intensity-Hue-Saturation method • Ratio-based (Brovey Transform) • Arithmetic algorithm • Multiplicative • Wavelet Transform method GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 62 PCA Merge •The 1 st PC is most influential •It should be used while merging so that the effect is felt on all bands GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 63 PCA Merge • The 1 st principal component is replaced by the high resolution image • Inverse PCT is applied GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 64 Results • This technique is useful to transform all bands at a time • Often works well in producing good fusion results GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 65 PCA Merge • Very effective when the correlation between PAN image and the multispectral image is good • Does not work very well when fusion is done with images from different types of sensors such as SAR and optical GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 66 Input High Resolution Image GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 30 Sample Eigenvectors and Eigenvalues 34 . 89 55 . 62 52 . 87 22 . 71 Covariance Matrix 55 . 62 105 . 95 99 . 58 43 . 33 52 . 87 99 . 58 104 . 02 45 . 80 22 . 71 43 . 33 45 . 80 21 . 35 Eigenvalues 253 . 44 7 . 91 3 . 96 0 . 89 0 . 34 −0 . 61 0 . 71 −0 . 06 Eigenvectors 0 . 64 −0 . 40 −0 . 65 −0 . 06 0 . 63 0 . 57 0 . 22 0 . 48 0 . 28 0 . 38 0 . 11 −0 . 88 GNR607 Lecture 32-34 B. Krishna Mohan
IIT Bombay Slide 31 Sample Eigenvectors and Eigenvalues GNR607 Lecture 32-34 B. Krishna Mohan
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