Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

baltsavias, emmanuel p.

Bibliographic data

Monograph

Persistent identifier:: 856473650

Author:: Baltsavias, Emmanuel P.

Title:: Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

Sub title:: Joint ISPRS/EARSeL Workshop ; 3 - 4 June 1999, Valladolid, Spain

Scope:: III, 209 Seiten

Year of publication:: 1999

Place of publication:: Coventry

Publisher of the original:: RICS Books

Identifier (digital):: 856473650

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: TECHNICAL SESSION 3 OBJECT AND IMAGE CLASSIFICATION

Document type:: Monograph

Structure type:: Chapter

Chapter

Title:: SCALE CHARACTERISTICS OF LOCAL AUTOCOVARIANCES FOR TEXTURE SEGMENTATION. Annett Faber, Wolfgang Förstner

Document type:: Monograph

Structure type:: Chapter

International Archives of Photogrammetry and Remote Sensing,Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 fixing the second moments of the distribution. The covari ance function can be assumed to be a decaying function characterized by its value at zero Cj, (0,0) = a) being the variance of f and the curvature C'^(0,0) = H fi at zero being the Hessian of the covariance function. The real image function g(r,c) — f(r,c) -f n(r,c) is com posed of the true image signal /(r, c) and the noise n(r, c), which is assumed to be white, n ~ JV(0, <r 2 n ). The separation of the segments is based not only on their expected value m, as in classical segmentation procedures, but also on their covariance structure. For the characterization of the covariance function we use the negative Hessian of the autocovariance function of g. Due to the moment theorem (Papoulis, 1984), it is identical to the covariance matrix Tg of the gradient V s g of the image function g over a window G’ t . The filter kernels h(x) of the gradient V s g and the window G t have width s and t (Fuchs, 1998). For the estimation of the negative Hessian of the available image function g we thus obtain: r 3t = G t * {'Vsg V S 0 T ) = - H g (1) / 9r gr£ c \ \ Mh 9c ) We need to specify two scale parameters: 1. Differentiation scale «: The image resolution in terms of the sharpness of the edges defines the scale for the differentiation kernel. E. g. the 3 x 3-Sobel kernels correspond to the 3 x 3-Binomial kernel having scale 5 = 1/72. 2. Integration kernel t: The width of the expected edges motivates the window size of the integration kernel. Observe, that the edge extraction does not distinguish between step and bar edges, thus also the expected width of bar edges can be used for specifying the inte gration kernel t. 4.2 Texture parameters The core of the representation is the characterization of the local autocorrelation function, represented by the squared gradient Tg of the autocovariance function. By analyzing the eigenvalues A* of the matrix Tg, we obtain three local features. These are (Forstner, 1991): • the strength a (amplitude) of the texture. It represents the local variation of the intensity function and is mea sured using the variance of gradients, being the trace of the squared gradient: Fg: a =\r Tg = gt + gl = \i + \ 2 • the direction <p or the orientation of the texture. The squared gradient is large in the direction of large in tensity variations, but small in directions with small in tensity variations, which in case of directed textures is identical to the subjective perception of the orientation of the texture. Instead of determining Gabor filters with different orientations, thus sampling the radial variation of the gradient, we directly determine the direction of smallest variation, being the direction «¿> of the eigen vector of Tg corresponding to the smallest eigenvalue: 1 , 2 Q v Q c (x = - arctan —- __ r 0 9 9 z 9r - gz The orientation lies in the range 0 < y < n, thus at pure edges the information on the direction of the gra dient is lost. • the anisotropy q (quality of direction) of the texture. It indicates the angular variation of texture and edge characteristics. The anisotropy can be measured by the ratio v of eigenvalues Ai and A 2 or, equivalently by the form factor: 4detT^f ^ /Ai -A 2 \ 2 \r 2 Tg \ Ai 4- \ 2 ) Isotropic, i. e. non-oriented, texture is characterized by q = 1, whereas anisotropic, i. e. oriented, texture is characterized by q< I- These three characteristic texture features are quite infor mative as can be seen in Fig. 4 and Fig. 5 1 . In the figures the strength is coded from low values (white) to large val ues (black), the direction is coded from <f> = -n/2 (white) to 4> = 7r/2 (black) and the anisotropy is coded from q = 0 (white) to q = 1 (black). As the squared gradient of the given image function g in stead of the true image function / is used, we can expect the properties of the texture to be recoverable only in im ages with low noise. An information preserving filtering cf. (Forstner, 1991, Weidner, 1994) is useful as preprocessing step to reduce noise without smoothing the edges. 4.3 Laplacian pyramid The texture parameters discussed above describe texture properties of a small image region, defined by the scale parameters s and t of the Gaussian windows in eq. (1). However, textures contain interesting characteristics: they are hierarchically structured. The texture parameters vary within the local neighborhood. This gives rise to a scale space analysis, which determines the variation of the tex ture features depending on the size of the local neighbor hood. To use the complete information, contained in the image signal, we perform a spectral decomposition of our texture parameters. To obtain a spatial scale decomposition, we use a Laplacian image pyramid (Burt and Adelson, 1983) applied to all three texture features. It separates the different spectral bands of the texture image features. The basis of the generation of an image k(r, c) of the Laplacian pyramid is the difference formation between two subsequent levels i and * — 1 of the Gaussian pyramid g,(r, c) U(r,c) = gi(r,c) - fifi-i(r,c) ^he used image ’’Avenches” belongs to the data set in www.geod.ethz.ch/p02/proj ect s/AMOBE/index.html

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