Lecture_w10_PrincipalComponents.ppt

Principal Component Analysis Splits up image data into components that can be used for image enhancement, image compression, etc. Based on notion that there is redundancy in multispectral image data. Some bands are highly correlated… Principal Component Analysis Dimensionality: number of bands in the dataset that must be analyzed to produce usable results. Determining the dimensionality of a dataset is the goal of PCA. Compression, and image enhancement are the benefits. Principal Component Analysis Idea is to re-express multispectral datasets by calculating a new set of spectral coordinates. Consider a positively-correlated, two-band dataset plotted in a 2-D Cartesian space with one band on each axis. The coordinate frame can be rotated (transformed) to express the same pixels in terms of new, orthogonal variables. Principal Component Analysis This can be extended to n-dimensional datasets, with additional coordinate directions defined as required by the number of bands. Goal is to express the data in terms of a new set of mutually-orthogonal coordinates (a basis). Each of these directions is a principal component (eigenvector). Principal Component Analysis How? Define the first new coordinate such that it is parallel to the trend of maximum density of data. Determine new DNs for each pixel relative to the new coordinates. Use the new DNs to generate an image of the first principal component. Define the next coordinate based on the new DNs, again in the direction of maximum data density, and perpendicular to the previously-defined coordinates. Continue… Principal Component Analysis Apply a transformation to a correlated set of multispectral data that results in a uncorrelated set of data with ordered variance properties. Consider a 2-band dataset, x1 and x2, with means m1 and m2. If data is clustered in a tight zone in x1-x2 space, there is substantial redundancy in the data as presented. Covariance and correlation coefficient will indicate high, positive c