Proceedings of the Symposium on Global and Environmental Monitoring: Proceedings of the Symposium on Global and Environmental Monitoring

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Persistent identifier:: 856665355

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts ; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856665355

Language:: English

Document type:: Multivolume work

Volume

Persistent identifier:: 856669164

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Scope:: XIV, 912 Seiten

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856669164

Illustration:: Illustrationen, Diagramme, Karten

Signature of the source:: ZS 312(28,7,1)

Language:: English

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

Editor:: International Society for Photogrammetry and Remote Sensing, Commission of Photographic and Remote Sensing Data

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:: Volume

Collection:: Earth sciences

Chapter

Title:: [WP-1 ADVANCED COMPUTING FOR INTERPRETATION]

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: A Method for Proportion Estimation of Mixed Pixel (MIXEL) by Means of Inversion Problem Solving. Kohei Arai and Yasunori Terayama

Document type:: Multivolume work

Structure type:: Chapter

344 3. Context classification featuring proportion estimation 3.1 Procedure The proposed contextual classification method is an element of the proposed ICAI system. First, homogeneous areas are extracted and classified by using homogeneity measure proposed in ECHO classification method(Ref. 4). After that spatial features such as line-likeness, area-likeness, etc. and properties such as directionality, length, width, etc. of heterogeneous areas are calculated followed by referencing of contextual information together with relational information. Instead of it, it is also possible to extract the pixels which have macroscopic spatial properties by using the aforementioned spatial features. If the confidence interval at the designated confidence level in terms of classification accuracy is not enough, then a mixing ratio of the pixel of interest for the classes of the surrounding pixels is to be a classification result as one of classification for Fuzzy pixels. Namely proportion would be enough for classified result of MIXELs. 3.2 Proportion estimation based on Inversion Problem Solving * 1 Based on Inversion Problem Solving by Towmey(Ref.5). a proportion estimation method is derived. Let observed vector be I with the dimensionality of M, mixing ratio vector be B with the number of classes of N and the matrix representing the spectral response of each class be A. 1 = A B + E (1) where E denotes error vector. Since 1 is a given vector, if A is assumed then B is determined under the constrains that minimizing 2 of square error:E , and variance 2 of the solution:(B - ) , M 2 t SUM Ei = E E — —> min. (2) i=l N 2 SUM (Bj - ) — —> min. (3) j=l N where = SUM Bk / N. (4) k=l (Bj - ) can be expressed by the following equation. (Bj - ) = (-1/N, — 1/N 1-1/N. -1/N, —1/N) B (5) Let us consider the following Q, t Q = (B1 - , B2 - ,...) = C B (6) where C=I 1-1/N -1/N -1/N ....-1/N I (7) I -1/N 1-1/N -1/N .... -1/N I I -1/N -1/N -1/N ... 1-1/N I Cij = { 1-1/N (i.oq. j) (8) -1/N (¡.no. j). Then minimizing the following equation. N 2 t t t SUM (Bj - ) = (C B) (C B) = B C C B j=l > min. (9) Solution B is obtained based on eq. (1) under the constrains of eq. (2) and (9). It is not always that solution is existing so that the following r is introduced. t t t R = EE + rBCCB > min. (10) Let us consider the following differentiation of R about B t t t 0R/0B = @ {(1 —AB) (I-AB) + rB C C B( / 0B (11) where t t t t t CCB + BCC = CCB+(CB)C t t t = C C B + (C C B) (12) t t - A (I - A B) - (1 - A B) A t t t = - A (I - A B) - (A (I - A B)} (13) then the following equation is reduced, t t 0R/0B = rC CB - A (I-AB) t t t + (rC CB - A (I-AB)} = 0 (14) From above equation, t t rC CB - A (I-AB) = 0 (15) results in t t -1 t B = (A A + rC C) A I. (16) Proportion vector B is estimated with given observation vector I, previously designated spectral response matrix A and determined r for convergence. 4. Experiment 4.1 Data used Landsat-5 TM data of Ushizu-machi, Saga, Japan observed in May 1986 was used. Topographic map and image of TM band-4 are shown in Fig. 2. The study area includes mostly paddy field with tiny pond, partially residential area and creek, road and railway networks. 4.2 Procedure 4.2.1 Designation of classes and their anchor points In order to show just an example, three classes, paddy field, road and water body. Their anchor points were determined as the corners of the triangle corresponding to the three classes, as all the sampled data for the designated classes are to be included, in 3-D feature space with TM band-1, 3 and 4 as is illustrated in Fig. 3.

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