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Clasificaciones y Análisis de Clasificaciones y Análisis de Mezclas Espectrales Mezclas Espectrales Clasificaciones y Análisis de Mezclas Espectrales Clasificaciones y Análisis de Mezclas Espectrales

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Page 1: Document

Clasificaciones y Análisis de Clasificaciones y Análisis de Mezclas EspectralesMezclas Espectrales

Clasificaciones y Análisis de Mezclas EspectralesClasificaciones y Análisis de Mezclas Espectrales

Page 2: Document

Ejercicios para hoyEjercicios para hoy

1.1. Correcciones atmosféricasCorrecciones atmosféricas

2.2. Análisis de Componentes Principales (PCA) y la Análisis de Componentes Principales (PCA) y la Transformación de la Fracción de Ruido Mínimo Transformación de la Fracción de Ruido Mínimo (MNF Transform)(MNF Transform)

3.3. Clasificación no supervisadaClasificación no supervisada3.3. Clasificación no supervisadaClasificación no supervisada

4.4. Conversión de raster a vectorConversión de raster a vector

5.5. Colección de muestrasColección de muestras

6.6. Clasificación supervisadaClasificación supervisada

7.7. Despliegue en N dimensionesDespliegue en N dimensiones

8.8. Análisis de mezclas espectrales (SMA)Análisis de mezclas espectrales (SMA)

9.9. Filtración de los resultadosFiltración de los resultados

Page 3: Document

Cobertura de la tierra Cobertura de la tierra -- 2008*2008*

¿Porque necesitamos hacer ¿Porque necesitamos hacer

clasificaciones?clasificaciones?

*Para validar

clasificaciones?clasificaciones?

Page 4: Document

El El problemaproblema

DespuésDespués de casi 40 de casi 40

años de percepción años de percepción

remota ambiental desde el remota ambiental desde el

lanzamiento de Landsatlanzamiento de Landsat--1 1

en el 23 de julio de 1972, en el 23 de julio de 1972, en el 23 de julio de 1972, en el 23 de julio de 1972,

todavía existe el problema todavía existe el problema

de identificar cobertura de de identificar cobertura de

la tierra (delineación e la tierra (delineación e

cuantificación) fácilmente cuantificación) fácilmente

y con exactitudy con exactitud

Page 5: Document

Belize City

False color LandSat TM mosaic courtesy of NASA / USGS

Page 6: Document

Source: TBDSource: TBD

Page 7: Document

Simulated true color LandSat TM image courtesy of NASA / USGS; image captured 28 March 2000

Page 8: Document

Simulated false color LandSat TM image courtesy of NASA / USGS; image captured 28 March 2000

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Aerial photo of interface between savanna and forest near Belize City, April 5, 2009Aerial photo of interface between savanna and forest near Belize City, April 5, 2009

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No.Date -

Ground Condition

Date - Publication

Original Source

Published as Imagery Used Resolution Geographic coverage, original

Number of Classes

1

c. 1990, c.

2000

2005 Earth

Satellite

Corporation

GeoCover LC

1990

Landsat TM,

Landsat ETM+30m global 11

2 1992-93 USGS GLCC AVHRR 1km global 96

3

1992-93 1998

PROARCA

/ CAPAS

"Central

American

Vegetation/L

and Cover

Classification

and

Conservation

Status"

AVHRR 1km regional 25

1991-99 2002 "Central

America

4 World Bank

America

Ecosystems

Mapping

Project"

Landsat TM 30m regional 196

52000 2002

JRC GLC 2000SPOT

Vegetation1km global 23

6

2000, 2001,

2002, 2003,

2004, 2005

2008UMD /

NASAMOD44B MODIS 500m global N / A

72000, 2003,

2004, 2005

2006 U. Ark. /

SERVIR

SERVIR

MesoClassMODIS 500m regional 6

8 2005 2005 USGS MODIS 500m regional 9

9

2004-06 2008 ESA /

MEDIAS

France

GlobCover

projectMERIS 300m global 24*

102000, 2005,

2007, 2008

2008 ESA /

GeoVille

DIVERSITY

projectMERIS* 300m regional 12

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Mosaico temporal de imágenes de

2009, con menos que 2% de

nubosidad

Page 14: Document
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Source: p. 2Source: p. 2--25, GOFC25, GOFC--GOLD REDD Sourcebook, Nov. 2009 editionGOLD REDD Sourcebook, Nov. 2009 edition

Page 19: Document

Source: Goodenough et al (2002): “Report on the Evaluation and Validation of EOSource: Goodenough et al (2002): “Report on the Evaluation and Validation of EO--11

for Sustainable Development (EVEOSD) Project”for Sustainable Development (EVEOSD) Project”

Page 20: Document

Radiometric calibrationRadiometric calibration

Mosaic, as necessaryMosaic, as necessary

Image Processing: CorrectionsImage Processing: Corrections

Preferably in ENVIPreferably in ENVI

Atmospheric correctionAtmospheric correction Dark object subtractionDark object subtraction

IntraIntra--scene calibrationscene calibration Histogram matchingHistogram matching

In ERDASIn ERDAS

In ERDASIn ERDAS

In ERDASIn ERDAS

Page 21: Document

El sistema ideal de percepción remota

(1) Fuente

uniforme de

energía

(4) Súper

sensor

(2) Atmosfera

sin interferencia

(3) Interacciones

únicas con el

superficie de la tierra

Fuente: M. Vasquez (2006)

Page 22: Document

Interacciones de Energía con la Atmosfera

Scattering

Refracción

Absorción

Fuente: B. Howell (2006)

Page 23: Document

Energía en el Objeto

Radiacion Incidente puede ser…• Reflejada• Transmitida• Absuelto (y reEmitida)

I = R + T + A

Fuente: B. Howell (2006)

Page 24: Document

Usos de Percepción Remota

• Actualizar o reemplazar mapas existentes

• Determinar áreas de categorías conocidas

• Hacer inventarios de tipos de cobertura

• Documentar cambios entre periodos

• Medir condiciones en una área• Medir condiciones en una área

• Medidas cuantitativa de propiedades

Fuente: B. Howell (2006)

Page 25: Document

Centroamérica:Centroamérica:50 imágenes cubren50 imágenes cubren

50 millón de ha,50 millón de ha,

=25 GB de datos para procesar=25 GB de datos para procesar

Entonces, desde L4 en 1984 Entonces, desde L4 en 1984

hasta al presente, hay ~769 hasta al presente, hay ~769

escenas disponible para escenas disponible para

cualquier área (23 imágenes cualquier área (23 imágenes

por año por L5 y L7)por año por L5 y L7)

Page 26: Document

Senderos de LandSat para CentroaméricaSenderos de LandSat para Centroamérica

Los senderosLos senderos

fijos en elfijos en el

sistemas de sistemas de

referencia de referencia de

LandsatLandsat

Page 27: Document

Resultados de una búsqueda en Glovis Resultados de una búsqueda en Glovis para El Salvador para El Salvador –– 262 imágenes con 262 imágenes con menos de 30% de nubosidad, entre enero menos de 30% de nubosidad, entre enero de 2007 y febrero de 2009de 2007 y febrero de 2009

Page 28: Document
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Landsat TMLandsat TMFalse color mosaicFalse color mosaic2828--0303--20002000

Land cover mapLand cover map20042004

Landsat TMLandsat TMFalse color mosaicFalse color mosaic2828--0303--20002000

Land cover mapLand cover map20042004(Source: BTFS)(Source: BTFS)

Page 30: Document

Landsat TMLandsat TMFalse color mosaicFalse color mosaic2828--0303--20002000

Land cover mapLand cover map20042004(Source: BTFS)(Source: BTFS)

1.1. Green Green isis forestforest

2.2. To be able to extract To be able to extract

the green is to be the green is to be

Identifying Forest Cover w/ Satellite ImageryIdentifying Forest Cover w/ Satellite Imagery

able to extract the able to extract the

forest coverforest cover

Page 31: Document

Landsat TMLandsat TMFalse color mosaicFalse color mosaic2828--0303--20002000

Forest cover mapForest cover map20042004(Source: BTFS)(Source: BTFS)

Page 32: Document

••El Sistema de El Sistema de

Sistemas de la Sistemas de la

Observación de Observación de

la Tierra la Tierra

(GEOSS)(GEOSS)

El Sistema de Visualización y Monitoreo(SERVIR)

TerraTerra

Aqua

LandSat MODISSRTM AMSR-EIKONOS ASTER

Mesoamerica’s Earth Observation& Forecasting Platform

Fires

Red Tides

Land Cover / Use Change

Data ingest fromEOS and Central

EDOSEDOS

Central American

Users

••La Carta La Carta

Internacional Internacional

sobre el Espacio sobre el Espacio

y Grandes y Grandes

CatástrofesCatástrofes

••El Sistema de El Sistema de

Información Información

Ambiental Ambiental

Mesoamericano Mesoamericano

(SIAM)(SIAM)

Test-bed atNASA MSFC

EnvironmentalMonitoring & Decision

Support Products

Web Interfacewww.servir.net

Operational Nodeat CATHALAC Panama

AgricultureBiodiversityClimateEcosystemsEnergyDisastersHealthWaterWeather

ThematicAreas

Central AmericanGovernment agenciesNGOs, researchersEducators, etc.

Impacts

Emergency ResponsePolicy ChangesCorridor PreservationSpecies PreservationSustained DevelopmentImproved livelihoods

SERVIR tiene herramientas muy relevantes al tema de monitoreo de REDDSERVIR tiene herramientas muy relevantes al tema de monitoreo de REDD

Page 33: Document

SERVIR Disaster Response (2004SERVIR Disaster Response (2004--))1. Red tide event - El Salvador (June 2004)

2. Flooding – Panama City, Panama (Sept. 2004)

3. Flooding - Rio Sixaola, Costa Rica / Panama (Jan 2005)

4. Hurricane Stan – Guatemala, Mexico, El Salvador (Oct .2005)

5. Flooding – Colon Province, Panama (Nov. 2006)

6. Fire - Mountain Pine Ridge Forest Reserve, Belize (May 2007)

7. Hurricane Dean – Mexico / Belize (Aug. 2007)

8. Hurricane Felix – Nicaragua / Honduras (Sept. 2007)

9. Tropical Storm Noel – Dominican Republic (Oct. 2007)

10. Tropical Storm Olga – Dominican Republic (Dec. 2007)

11. Turrialba Volcano – Costa Rica (April 2008)11. Turrialba Volcano – Costa Rica (April 2008)

12. Tropical Storm Arthur – Belize (June 2008)

13. Hurricane Gustav – Haiti / Dominican Rep. (August 2008)

14. Hurricane Hanna – Haiti (Sept. 2008)

15. Hurricane Ike – Haiti (Sept. 2008)

16. Landslide – Huahua Michoacán, Mexico (Oct. 2008)

17. Tropical Depression 16 – Belize / Guatemala / Honduras (Oct. 2008)

18. Flooding – Costa Rica / Panama (Nov. 2008)

19. Landslide – Alta Verapaz, Guatemala (Jan. 2009)

20. Earthquake – San Jose metropolitan area, Costa Rica (Jan. 2009)

21. Fire – Volcan Santo Tomas, Quetzaltenango, Guatemala (Feb. 2009)

22. Flooding – Lago Enriquillo, Dominican Republic (Feb. 2009)

Page 34: Document
Page 35: Document
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Extracción de Objetos

• Clasificación

• Índices / ratios

• Umbrales de bandas (“band thresholding”)

• Supervisada

• No supervisada

• NDVI

• NBR / NDBR

(“band thresholding”)

• Análisis de mezclas espectrales

• Varios – Sombra, Suelo, Vegetación; Sombra, Suelo, Vegetación verde, vegetación no fotosintética

Page 37: Document

Pasos básicos en clasificación de imágenes:

1) Estudio y organización de los datos

2) Aplicación de un algoritmo de clasificación

3) Validación3) Validación

Page 38: Document

Estudio y organización de los datos

Estudio

¿Que esta en la escena / imagen?

¿ Cuales bandas están disponible?

¿ Cuales preguntas necesitan respuestas?

¿ Se puede responder a las preguntas con la imagen?

¿ Hay suficiente información para distinguir que esta en la escena?¿ Hay suficiente información para distinguir que esta en la escena?

Organización de los datos

¿ Cuantas clusters se puede re-organizar en espacio n?

¿ Como son los limites de los clusters?

¿ Los clusters corresponde a los clases deseados?

Page 39: Document

Clasificación

Clasificación es el proceso de asignar los pixeles a

clases homogéneos basado en análisis de las

estadísticas de valores de reflectancia en uno o mas

bandas.

Clasificación es el proceso de derivar information clases

informativos / utiles de clases espectrales.

Se nombran los procesos de clasificación como Se nombran los procesos de clasificación como

supervisada o no supervisada basado en la metodología

para “entrenar” el classifier (clasificador?).

Con datos de ‘entrenamiento,’ los dos sistemas utilicen

la misma forma de operación (división basada en las

estadísticas).

Fuente: B. Howell (2006)

Page 40: Document

Clasificación

Pros:

• Puede apoyar en la descripción de usos y cobertura de

la tierra

• Puede simplificar el proceso de detección de cambios

• Con procesamiento posterior, puede generar polígonos

con atributos para uso en un SIG

The Attainment of the Sanc GraelDante Gabriel Rosetti

Contra:

• Clasificación con ella misma, no va extraer información

útil de la data

• No hay clasificadores universales

• NO es perfecto

• Necesita procesamiento posterior para llegar a una foto

bonita

Fuente: B. Howell (2006)

Page 41: Document

Histogramas deHistogramas decada bandacada banda

Fuente: B. Howell (2006)

Page 42: Document

Respuestas espectrales

Fuente: B. Howell (2006)

Histogramas deHistogramas decada bandacada banda

Page 43: Document

ASTER: ASTER: AAdvanced dvanced SSpaceborne paceborne TThermal hermal EEmission & mission & RReflection Radiometereflection Radiometer

Terra

�� Uno de los 5 sensores en el satélite Terra (lanzando en Uno de los 5 sensores en el satélite Terra (lanzando en Dic. de 1999); debe estar encendidoDic. de 1999); debe estar encendido

�� Similar que el sensor ‘Thematic Mapper’ de LandSatSimilar que el sensor ‘Thematic Mapper’ de LandSat

�� Tamaño de una escena es 1/9 de una escena de LandSatTamaño de una escena es 1/9 de una escena de LandSat

�� 14 bandas (3 de 15m / 6 de 30m / 5 de 90m) midiendo 14 bandas (3 de 15m / 6 de 30m / 5 de 90m) midiendo luz en longitudes de onda visible a infrarrojo termalluz en longitudes de onda visible a infrarrojo termal

�� One of 5 sensors on the satellite Terra One of 5 sensors on the satellite Terra (launched in Dec. 1999); ‘on(launched in Dec. 1999); ‘on--call’call’

�� Similar to the Thematic Mapper sensor Similar to the Thematic Mapper sensor on the LandSat satelliteson the LandSat satellites

�� Swath about 1/9 the size of LandSat Swath about 1/9 the size of LandSat swathswath

�� 14 bands (3 15m / 6 30m / 5 90m) 14 bands (3 15m / 6 30m / 5 90m) measuring light from the visible to measuring light from the visible to infrared thermal wavelengthsinfrared thermal wavelengths

Page 44: Document

Respuestas espectrales

Fuente: B. Howell (2006)

Histogramas deHistogramas decada bandacada banda

Page 45: Document

Firmas espectrales de materiales comunes

Absorción de

clorofilaDispersión en

las celdas

Absorción

de agua

Page 46: Document

Firmas espectrales

Fuente: B. Howell (2006)

Page 47: Document

Clasificación No Clasificación No SupervisadaSupervisadaSupervisadaSupervisada

Page 48: Document

Belize City

False color LandSat TM mosaic courtesy of NASA / USGS

Page 49: Document

¯14-Nov-1980

Belize City pop’n ~39,771

Ladyville area

Belize’s

International

Airport

0 3 61.5 km

False color LandSat MSS image courtesy of NASA / USGSPopulation data from Belize CSO

Page 50: Document

¯27-Dec-1989

Savanna clearing for

shrimp farm development

Diminishing mangrove forests

Coastal development

(Buttonwood Bay &

Bella Vista)

0 3 61.5 km

False color LandSat TM image courtesy of NASA / USGSPopulation data from Belize CSO

Page 51: Document

¯28-Mar-2000

Expansive shrimp ponds

Settlement on former mangrove

forest (Vista del Mar)

New beachfront properties

Cleared mangrove

Expansion of

north-side Belize

City (Belama)

0 3 61.5 km

Coastal development

Expansion of

south-side

Belize City

City (Belama)

False color LandSat TM image courtesy of NASA / USGSPopulation data from Belize CSO

Page 52: Document

¯12-Feb-2004

Nova Shrimp Farm

at size of Belize City

Clearing of 100s of acres of

mangrove for Port developmentLand reclamation at

the Marine Parade

0 3 61.5 km

False color LandSat ETM image courtesy of NASA / USGSPopulation data from Belize CSO

Page 53: Document

¯31-March-2007Nova Shrimp Farm

ceases operations

Further wetland clearing at

Belama Phase IV

0 3 61.5 km

False color ASTER image courtesy of NASA / JAXAPopulation data produced by extrapolating Belize CSO data

Page 54: Document

19801980 19891989 19981998

La Ciudad de Belice: 1980 hasta 2006La Ciudad de Belice: 1980 hasta 2006

20002000 20022002 20062006

La Ciudad de Belice: 1980 hasta 2006La Ciudad de Belice: 1980 hasta 2006

Page 55: Document
Page 56: Document
Page 57: Document

27-Dec-1989

False color LandSat TM image courtesy of NASA / USGSPopulation data interpolated from Belize CSO data

Belize City pop’n

~42,518

Page 58: Document

27-Dec-1989

False color LandSat TM image courtesy of NASA / USGSPopulation data interpolated from Belize CSO data

Belize City pop’n

~42,518

Approx. area:

2,089 acres (845 ha.)

Page 59: Document

2-Feb-2006

False color ASTER image courtesy of NASA / JAXAPopulation data extrapolated from Belize CSO data

Belize City pop’n

~64,700

Page 60: Document

2-Feb-2006

False color ASTER image courtesy of NASA / JAXAPopulation data extrapolated from Belize CSO data

Belize City pop’n

~64,700

Approx. area:

3,382 acres (1,369 ha.)

Page 61: Document

Antes: Belize City en 1980

• ~39,771 habitantes

• 1,706 acres (6.9 km2)

• Densidad de 5,756 personas / km2

• Densidad nacional de 6 personas / km2

Reciente: Belize City en 2007

• ~66,422 habitantes

• 3,449 acres (14 km2)

• Densidad de 4,758 personas / km2

• Densidad nacional de 13 personas / km2• Densidad nacional de 13 personas / km2

• El área ha doblado entre 1980 y 2007

• El crecimiento anual era ~106 acres / 43 ha.

• La mayoría de la expansión de 705 ha fue

deforestación de manglares y destrucción de

humedales

False color ASTER image courtesy of NASA / JAXA

Page 62: Document

2,500

3,000

3,500

4,000

Are

a (a

cres

)

40,000

50,000

60,000

70,000

Pop

ulat

ion

Tendencias del crecimiento de la población y Tendencias del crecimiento de la población y expansión urbana en la Ciudad de Beliceexpansión urbana en la Ciudad de Belice

0

500

1,000

1,500

2,000

31-Mar-072-Feb-0619-Sep-0228-Mar-0015-Sep-9827-Dec-8914-Nov-80

Date

Are

a (a

cres

)

0

10,000

20,000

30,000Pop

ulat

ion

Area Population

Page 63: Document

80

100

120

140

160

180

Tendencias de expansión urbana (cambios anuales)Tendencias de expansión urbana (cambios anuales)

143 acres cortadas

448 acres cortadas

Annual

expansi

on r

ate

(acr

es /

yr)

0

20

40

60

1981 1990 1999 2000 2003 2006

383 acres cortadas

654 acres cortadas

48 acres cortadas / reclamadas

67 acres cortadas / reclamadas

Annual

expansi

on r

ate

(acr

es /

yr)

Expansión de 705 ha entre nov Expansión de 705 ha entre nov

de 1980 y marzo de 2007de 1980 y marzo de 2007

Page 64: Document

Rates of Urban Expansion & Population Density

Date Area Pop’n Pop’nDensity(people/ km

2)

ChangeFrom

previousperiod(acres)

Avg. changeper year from

Previousperiod(acres)

Periodof

Change

Major Drivers ofLand Cover Conversionin PeriodAcres Ha. Km

2

Mar-07 3,449 1,396 13.96 66,422 4,758 67 57.3

2006-

2007

Belama Phase

IV

Feb-06 3,382 1,369 13.69 64,128 4,684 48 13.7

2002-

2006

Land

reclamation

Sep-02 3,334 1,349 13.49 56,700 4,203 448 179.2

2000-

2002

Development of

Port

Mar-00 2,886 1,168 11.68 49,050 4,199 143 95.3

1998-

2000

General

expansion

Sep-98 2,743 1,110 11.10 47,947 4,320 654 72.7

1989-

1998

Belama Phases

I-III

Dec-89 2,089 845 8.45 42,518 5,032 383 42.6

1980-

1989

Buttonwood Bay,

general expansion

Nov-80 1,706 691 6.91 39,771 5,756 N / A N / A N / A N / A

Aerial photo by Emil A. Cherrington

Page 65: Document

Unsupervised Classification

Basic Iterative Clustering Algorithm (K-Means)

• Place K points into the feature space containing the samples to be clustered. These points represent initial group centroids.

• Assign each sample to the group that has the closest centroid.

• When all samples have been assigned, recalculate the positions of the K centroids.

• Repeat Steps 2 and 3 until the centroids no longer move.

Fuente: B. Howell (2006)

Page 66: Document

Unsupervised Classification

Basic Iterative Clustering Algorithm (K-Means)

• Place K points into the feature space containing the samples to be clustered. These points represent initial group centroids.

• Assign each sample to the group that has the closest centroid.

• When all samples have been assigned, recalculate the positions of the K centroids.

• Repeat Steps 2 and 3 until the centroids no longer move.

Fuente: B. Howell (2006)

Page 67: Document

Unsupervised Classification

Basic Iterative Clustering Algorithm (K-Means)

• Place K points into the feature space containing the samples to be clustered. These points represent initial group centroids.

• Assign each sample to the group that has the closest centroid.

• When all samples have been assigned, recalculate the positions of the K centroids.

• Repeat Steps 2 and 3 until the centroids no longer move.

Fuente: B. Howell (2006)

Page 68: Document

Unsupervised Classification

Basic Iterative Clustering Algorithm (K-Means)

• Place K points into the feature space containing the samples to be clustered. These points represent initial group centroids.

• Assign each sample to the group that has the closest centroid.

• When all samples have been assigned, recalculate the positions of the K centroids.

• Repeat Steps 2 and 3 until the centroids no longer move.

Fuente: B. Howell (2006)

Page 69: Document

Unsupervised Classification

Improving clustering

• “Real world” sample distributions are much more likely to be irregularly shaped with cluster axes rotated to each other.

• These distributions are better characterized by parametric characterized by parametric statistics.

• Simple n-dimensional space segregation is more likely to assign pixels to incorrect clusters.

Fuente: B. Howell (2006)

Page 70: Document

Unsupervised Classification

Improving clustering

• “Real world” sample distributions are much more likely to be irregularly shaped with cluster axes rotated to each other.

• These distributions are better characterized by parametric characterized by parametric statistics.

• Simple n-dimensional space segregation is more likely to assign pixels to incorrect clusters.

Fuente: B. Howell (2006)

Page 71: Document

Unsupervised Classification

Improving clustering

• “Real world” sample distributions are much more likely to be irregularly shaped with cluster axes rotated to each other.

• These distributions are better characterized by parametric characterized by parametric statistics.

• Simple n-dimensional space segregation is more likely to assign pixels to incorrect clusters.

Fuente: B. Howell (2006)

Page 72: Document

Unsupervised Classification

ISODATA (Iterative Self-Organizing Data Analysis Technique)

• Operates in the same iterative fashion as K-Means with three significant differences…

• Uses parametric statistics to describe clusters and determine nearest centroids

• New clusters can formed by splitting “elongated” clusters into multiples

• Clusters with centroids that are “too close” can be lumped together

• Because of these differences, K becomes a “desired” number of final classes, not an absolute

Fuente: B. Howell (2006)

Page 73: Document

Unsupervised Classification

ISODATA (Iterative Self-Organizing Data Analysis Technique)

• Operates in the same iterative fashion as K-Means with three significant differences…

• Uses parametric statistics to describe clusters and determine nearest centroids

• New clusters can formed by splitting “elongated” clusters into multiples

• Clusters with centroids that are “too close” can be lumped together

• Because of these differences, K becomes a “desired” number of final classes, not an absolute

Fuente: B. Howell (2006)

Page 74: Document

Unsupervised Classification

ISODATA (Iterative Self-Organizing Data Analysis Technique)

• Operates in the same iterative fashion as K-Means with three significant differences…

• Uses parametric statistics to describe clusters and determine nearest centroids

• New clusters can be formed by splitting “elongated” clusters into multiples

• Clusters with centroids that are “too close” can be lumped together

• Because of these differences, K becomes a “desired” number of final classes, not an absolute

Fuente: B. Howell (2006)

Page 75: Document

Unsupervised Classification

ISODATA (Iterative Self-Organizing Data Analysis Technique)

• Operates in the same iterative fashion as K-Means with three significant differences…

• Uses parametric statistics to describe clusters and determine nearest centroids

• New clusters can formed by splitting “elongated” clusters into multiples

• Clusters with centroids that are “too close” can be lumped together

• Because of these differences, K becomes a “desired” number of final classes, not an absolute

Fuente: B. Howell (2006)

Page 76: Document

Unsupervised Classification

ISODATA (Iterative Self-Organizing Data Analysis Technique)

• Operates in the same iterative fashion as K-Means with three significant differences…

• Uses parametric statistics to describe clusters and determine nearest centroids

• New clusters can formed by splitting “elongated” clusters into multiples

• Clusters with centroids that are “too close” can be lumped together

• Because of these differences, K becomes a “desired” number of final classes, not an absolute

Fuente: B. Howell (2006)

Page 77: Document

a)a) ISODATAISODATA initial distribution of five initial distribution of five

hypothetical mean vectors using hypothetical mean vectors using ±±11σσ

standard deviations in both bands as standard deviations in both bands as

beginning and ending points. b) In the first beginning and ending points. b) In the first

iteration, each candidate pixel is compared iteration, each candidate pixel is compared

to each cluster mean and assigned to the to each cluster mean and assigned to the

cluster whose mean is closest in Euclidean cluster whose mean is closest in Euclidean

distance. c) During the second iteration, a distance. c) During the second iteration, a

new mean is calculated for each cluster new mean is calculated for each cluster

based on the actual spectral locations of the based on the actual spectral locations of the

pixels assigned to each cluster, instead of pixels assigned to each cluster, instead of

the initial arbitrary calculation. This the initial arbitrary calculation. This

involves analysis of several parameters to involves analysis of several parameters to involves analysis of several parameters to involves analysis of several parameters to

merge or split clusters. After the new cluster merge or split clusters. After the new cluster

mean vectors are selected, every pixel in the mean vectors are selected, every pixel in the

scene is assigned to one of the new clusters. scene is assigned to one of the new clusters.

d) This splitd) This split––mergemerge––assign process assign process

continues until there is little change in class continues until there is little change in class

assignment between iterations (the assignment between iterations (the TT

threshold is reached) or the maximum threshold is reached) or the maximum

number of iterations is reached (number of iterations is reached (MM). ).

Jensen, 2005

Page 78: Document

a) Distribution of 20 a) Distribution of 20 ISODATA ISODATA

mean vectors after just one mean vectors after just one

iteration using Landsat TM iteration using Landsat TM

band 3 and 4 data of band 3 and 4 data of

Charleston, SC. Notice that the Charleston, SC. Notice that the

initial mean vectors are initial mean vectors are

distributed along a diagonal in distributed along a diagonal in

twotwo--dimensional feature space dimensional feature space

according to the according to the ±±22σσ standard standard

deviation logic discussed. b) deviation logic discussed. b)

Distribution of 20 ISODATA Distribution of 20 ISODATA

mean vectors after 20 mean vectors after 20 mean vectors after 20 mean vectors after 20

iterations. The bulk of the iterations. The bulk of the

important feature space (the important feature space (the

gray background) is partitioned gray background) is partitioned

rather well after just 20 rather well after just 20

iterations. iterations.

Jensen, 2005

Page 79: Document

Jensen, 2005

Page 80: Document

Plot of the Charleston, SC,

Landsat TM training statistics

for five classes measured in

bands 4 and 5 displayed as

cospectral parallelepipeds.

The upper and lower limit of

each parallelepiped is ±1σ.

The parallelepipeds are

superimposed on a feature

space plot of bands 4 and 5.

Jensen, 2005Jensen, 2005

Page 81: Document

ISODATA ISODATA

ClusteringClustering

LogicLogic

Jensen, 2005

Page 82: Document

Classification Classification

Based on Based on

ISODATA ISODATA

ClusteringClustering

Jensen, 2005

Page 83: Document

Clasificación SupervisadaClasificación Supervisada

Page 84: Document

Clasificación supervisadaClasificación supervisada

1) estimación de similitud espectral

2) asociación de tipos espectrales con clases útiles

SUPOSICION BASICO

Objetos de interés tienen “firmas espectrales” clarosObjetos de interés tienen “firmas espectrales” claros

*Esto no siempre es el caso

A veces hay que modificar la data para que sea real

- combinaciones de bandas

- imágenes multi-temporales

Page 85: Document

Clases, áreas de muestras, y mímicosClases, áreas de muestras, y mímicos

Clase: Unido deseado, en la forma de un cluster espectral

2 atributos: identidad y firma espectral

Área de muestra: una región de una imagen que es un buen

ejemplo de un clase; se utilice para definirejemplo de un clase; se utilice para definir

clústeres espectrales de una clase especifica; se

define la identidad con foto-interpretación o

información del campo

Mímicos: otros unidos de mapeo con clústeres similares

Page 86: Document

Clasificación supervisada

Supervised classification involves imposing a priori

information classes on a landscape.

Implicit in the supervised classification process is the

notion that the spectral data of members of a class will

have similar statistical characteristics and that those

characteristics can be visually discerned and manually

segregated by a human.

The process of creating a class structure and The process of creating a class structure and

determining the statistical characteristics of each class

is called training.

Training is the method by which a classifier “learns” the

appearance of individual classes.

For the classifier to be successful in properly assigning

pixels to a class, the training samples must be “pure”

(consisting of class members only).

Fuente: B. Howell (2006)

Page 87: Document

Clasificación supervisada

• Filosofía y estrategia de entrenamiento manual

• Seleccionar las bandas insumos con mayor

información

• Mostrar combinaciones de bandas con mayor

contraste entre clases

• No seleccionar muestras que no son miembros

del clase de interés

• Examinar histogramas para determinar si las

muestras son buenas (separables)

• Seleccionar un rango de muestras de un clase, y

combinarlos antes de la clasificación

Fuente: B. Howell (2006)

Page 88: Document

ParallelepipedParallelepiped

HybridHybrid

Minimum DistanceMinimum Distance

Maximum LikelihoodMaximum Likelihood HybridHybridMaximum LikelihoodMaximum Likelihood

Page 89: Document

Classifiers

Parallelepiped

• Determines class membership using parallelepipeds

(n-dimensional “boxes” in feature space)

• Advantages:

• Very fast

• Can classify 100% of candidates

• Makes good-looking output• Makes good-looking output

• Disadvantages:

• Candidates that fall outside any parallelepiped

remain unclassified

• Candidates that fall in overlaps are assigned to

the “first” parallelepiped

• Poorly matched to normal data distributions

Fuente: B. Howell (2006)

Page 90: Document

Classifiers

Minimum Distance

• Determines class membership by measuring distance

from class centroid

• Advantages:

• Fast

• More accurate* classification than Parallelepiped

• Better than Parallelepiped for handling “real • Better than Parallelepiped for handling “real

world” data distributions

• Disadvantages:

• Candidates that fall outside distance limits remain

unclassified

• Candidates that fall in overlaps are assigned by

an operator defined rule

• Imperfectly matched to normal data distributions

*assuming you know how to make it so

Fuente: B. Howell (2006)

Page 91: Document

Classifiers

Maximum Likelihood

• Determines class membership using parametric

statistics

• Advantages:

• Very well matched to normal data distributions

• More accurate classification* than Parallelepiped

or Minimum Distanceor Minimum Distance

• Candidates that fall into overlaps are assigned

based on likelihood of membership

• Disadvantages:

• Candidates that fall outside any parallelepiped

remain unclassified

• Accuracy heavily dependent on normal data

distributions

*assuming you know how to make it so

Fuente: B. Howell (2006)

Page 92: Document

Classifiers

Hybrid

• Determines class membership using parametric and

nonparametric techniques

• Advantages:

• Fast and very accurate*

• Perform first-order classifications using

ParallelepipedsParallelepipeds

• Perform second-order classification on outliers

and overlaps using distance or likelihood rule

• Disadvantages:

• Virtually every mistake that can be made using

Parallelepiped, Minimum Distance, and Maximum

Likelihood classifiers can be achieved in a single

operation

*assuming you know how to make it so

Fuente: B. Howell (2006)

Page 93: Document
Page 94: Document
Page 95: Document
Page 96: Document
Page 97: Document

Análisis de Mezclas EspectralesAnálisis de Mezclas Espectrales

•Imágenes multiespectrales miden

spectra integrada en cada píxel

•Cada píxel contiene materiales

diferentes, cada con su firma diferentes, cada con su firma

espectral diferente

•Varios tipos de spectra usualmente

están mezclados. Esos son mezclas.

•Otros tipos no mezcla mucho.

Fuente: A. Gillespie, la Universidad de WashingtonFuente: A. Gillespie, la Universidad de Washington

Page 98: Document

Usualmente, el numero de clases (‘endmembers’)

útiles para datos de Landsat es 4-5

Puede ser 8-10 para datos híper-espectrales

Hay muchos componentes espectrales en varias Hay muchos componentes espectrales en varias

escenas, pero usualmente no mezclan, entonces no son

útiles.

Page 99: Document

Análisis de mezclas espectrales es útil

porque –

1) Genera imágenes de fracciones que

se puede entender fácilmente

2) Reducción en la dimensionalidad de

los datos sin botar mucha los datos sin botar mucha

información útil

3) Identificación de efectos topográficos

para mas estable información para

análisis en SIG

Page 100: Document

Soil Soil

100

90

80

70

60

50

10

20

30

40

50

60

Sombra

Soil Soil40

30

20

10

100908070605040302010

100

60

70

80

90

% sueloSueloVegetación

verde

Fuente: UW ESS 421 (2004)Fuente: UW ESS 421 (2004)

Page 101: Document

Fuente: Lu et al (2002)Fuente: Lu et al (2002)

Page 102: Document

Imagen de Landsat5

de un parte de la

Reserva Forestal

Nacional Gifford

Pinchot de los

EE.UU.

Fuente: UW ESS 421 (2004)Fuente: UW ESS 421 (2004)

Page 103: Document

BurnedMature

regrowth

Old growth

Immature

regrowth

BroadleafBroadleaf

Deciduous

Clearcut

Grasses

Fuente: UW ESS 421 (2004)Fuente: UW ESS 421 (2004)

Page 104: Document

Vegetacion

verdeVegetacion no

fotosintetica

(NPV)

Claro = abundancia del objeto

Sombra

Rojo = NPV

Verde = veg. verde

Azul = sombra

Fuente: UW ESS 421 (2004)Fuente: UW ESS 421 (2004)

Page 105: Document
Page 106: Document

SMA can easily SMA can easily extract areas of extract areas of

bare soilbare soil

Page 107: Document

Interpreting spectral Interpreting spectral unmixing resultsunmixing results

Color Code

Color in RG comp % Soil

% Photosynthetic Vegetation Description

1 Yellow

Very high

(90-100%)

Very high

(90-100%) Cropland

2

Light

green

Low-Very Low

(0-30%)

High

(80-100%) Open forest

3

Light

green

Medium

(60-70%)

Medium

(40-50%) Shrubland

CATHALAC (unpublished, Nov CATHALAC (unpublished, Nov

2009)2009)

3 green (60-70%) (40-50%) Shrubland

4

Dark

green

Very low

(0-10%)

Medium

(40-80%) Closed forest

5 Red

Very high

(90-100%)

Low

(10-20%) Bare land / urban

6

Coffee

brown

Low

(10-30%)

Low-Medium

(30-50%) Mangrove scrub

7 Black

Very low

(0-10%)

Low-Very Low

(0-20%) Water

Black

Very low

(0-10%)

Low-Medium

(20-40%) Wetland

Page 108: Document

Interpreting spectral unmixing resultsInterpreting spectral unmixing results

Color Code

Color in RG comp % Soil

% Photosynthetic Vegetation Description

1 Yellow

Very high

(90-100%)

Very high

(90-100%) Cropland

2

Light

green

Low-Very Low

(0-30%)

High

(80-100%) Open forest

3

Light

green

Medium

(60-70%)

Medium

(40-50%) Shrubland

CATHALAC (unpublished, Nov CATHALAC (unpublished, Nov

2009)2009)

3 green (60-70%) (40-50%) Shrubland

4

Dark

green

Very low

(0-10%)

Medium

(40-80%) Closed forest

5 Red

Very high

(90-100%)

Low

(10-20%) Bare land / urban

6

Coffee

brown

Low

(10-30%)

Low-Medium

(30-50%) Mangrove scrub

7 Black

Very low

(0-10%)

Low-Very Low

(0-20%) Water

Black

Very low

(0-10%)

Low-Medium

(20-40%) Wetland

Page 109: Document
Page 110: Document

4. Closed tree canopy4. Closed tree canopy

(e.g. ‘mature’ forest):(e.g. ‘mature’ forest):

Should be defined Should be defined

principally by low soil principally by low soil

exposure and moderate to exposure and moderate to

high chlorophyll contenthigh chlorophyll content

3. Open tree canopy3. Open tree canopy

(e.g. ‘open’ forest):(e.g. ‘open’ forest):

Should be defined Should be defined

principally by some soil principally by some soil

exposure and high exposure and high

1.1. 2.2. 3.3. 4.4.

Source: ITTO / JOFCA

2. Low vegetation 2. Low vegetation

(e.g. cropland, (e.g. cropland,

shrubland):shrubland):

Should be defined Should be defined

by high chlorophyll by high chlorophyll

content and some content and some

soil exposure b/c of soil exposure b/c of

usual low plant usual low plant

density (i.e. no density (i.e. no

canopy)canopy)

1. Bare land1. Bare land

(e.g. urban areas):(e.g. urban areas):

Should be defined by Should be defined by

high soil exposure high soil exposure

and no chlorophyll and no chlorophyll

contentcontent

exposure and high exposure and high

chlorophyll contentchlorophyll content

Page 111: Document

Spectral Mixture Analysis works with spectra that mix together

to estimate mixing fractions for each pixel in a scene.

Spectral Mixtures, green leaves and soil

100

0

20

40

60

80

0 1 2 3

Wavelength, micrometers

Ref

lect

ivity

, %

0% leaves

25% leaves

50% leaves

75% leaves

100% leaves

The extreme

spectra that mix and

that correspond to

scene components

are called spectral

endmembers.

Please note – wavelength scale is messed upSource: TBDSource: TBD

Page 112: Document

Forest Spectral Endmembers

0

20

40

60

80

100

0 1 2 3

Ref

lect

ivit

y, %

dry grass

leaves

soil

Endmembers from one

type of scene – forest,

lake, desert – form a

In a forest, important endmembers may be leaves, wood,

shade, and soil.

In a desert, leaves may be less important, but there may

several rock types.

0 1 2 3

Wavelength, micrometers lake, desert – form a

cohort.

Source: TBDSource: TBD

Page 113: Document

Soil Soil

100

90

80

70

60

50

10

20

30

40

50

60

We can use a

ternary diagram

used to show

mixtures of forest

endmembers.

We will see a

Shade

Soil Soil 40

30

20

10

100908070605040302010

100

60

70

80

90

percent soil

We will see a

detailed example

of this in a later

lecture

SoilGV

Source: TBDSource: TBD

Page 114: Document

BurnedMature

regrowth

Old growth

Immature

regrowth

BroadleafBroadleaf

Deciduous

Clearcut

Grasses

Source: TBDSource: TBD

Page 115: Document
Page 116: Document
Page 117: Document

Round 1: 1Round 1: 1stst set of samples, selected from PPI of all MNF componentsset of samples, selected from PPI of all MNF components

1: Unconstrained

All MNF components

2: Constrained – Weight 1

All MNF components

3: Constrained – Weight

All MNF components

Page 118: Document

Round 1: 1Round 1: 1stst set of samples, selected from PPI of all MNF componentsset of samples, selected from PPI of all MNF components

4: Constrained – Weight 50

All MNF components

5: Unconstrained

ALI bands 3,4,5,6,8,9

6: Constrained – Weight

ALI bands 3,4,5,6,8,9

Page 119: Document

Round 2: 2Round 2: 2ndnd set of samples, selected from PPI of first 3 componentsset of samples, selected from PPI of first 3 components

7: Constrained – Weight 1

ALI bands 4,5,6,8

8: Constrained – Weight 1,000

ALI bands 4,5,6,8

9: Constrained – Weight 1

MNF components 1,2,3

Page 120: Document

Round 2: 2Round 2: 2ndnd set of samples, selected from PPI of first 3 componentsset of samples, selected from PPI of first 3 components

10: Constrained – Weight 1

MNF components 1,3

11: Constrained – Weight 100

MNF components 1,3

12: Constrained – Weight

MNF components 1,3

Page 121: Document

Round 2: 2Round 2: 2ndnd set of samples, selected from PPI of first 3 componentsset of samples, selected from PPI of first 3 components

13: Unconstrained

MNF components 1,3

14: Constrained – Weight 1

All MNF components

15: Constrained – Weight

Page 122: Document

Color 2000 2005 2010Black Low Low Low

Red High Low Low

Green Low High Low

Blue Low Low High

Yellow High High Low

Magenta High Low High

Cyan Low High High

White High High High

RGB NDVI composite: 2000RGB NDVI composite: 2000--20052005--20102010

Page 123: Document

Cambio de cobertura: 2000Cambio de cobertura: 2000--20102010

Page 124: Document

Cambio de Cambio de cobertura:cobertura:20002000--20102010

Color KeyBlack No change: forest

Red Regenerated 2000-05; no change 2005-10

Green Cut 2000-05, regenerated 2005-10

Blue No change 2000-05; cut 2005-10

Yellow No change 2000-05; regeneration 2005-10

Magenta Regenerated 2000-05, re-cut 2005-10

Cyan Cut 2000-05; no change 2005-10

White No change: non-forest

Color 2000 2005 2010Black High High High No change: forest

Red Low High High Regenerated 2000-05; no change 2005-10

Green High Low High Cut 2000-05, regenerated 2005-10

Blue High High Low No change 2000-05; deforested 2005-10

Yellow Low Low High No change 2000-05; regeneration 2005-10

Magenta Low High Low Regenerated 2000-05, re-cut 2005-10

Cyan High Low Low Cut 2000-05; no change 2005-10

White Low Low Low No change: non-forest

White No change: non-forest

Page 125: Document

ÍndicesÍndices

Page 126: Document

A

NDx

ND

y

A

B

° x

NDx

ND

y

Sombra

° x

A con sol

B con sol

Page 127: Document

A

Línea de ratio constante

y

x

x/y

y/z

A

B

NDx

ND

y

A

B

° x

NDx

ND

y

Sombra

° x

A con sol

B con sol

Page 128: Document

°Después: LandSat7 Después: LandSat7 -- 11 de mayo de 200711 de mayo de 2007

Plumas de humoPlumas de humo

0 1 2 3 40.5Miles

CicatricesCicatrices

Page 129: Document

°Antes: LandSat7 Antes: LandSat7 -- 21 de marzo de 200621 de marzo de 2006

0 1 2 3 40.5Miles

Page 130: Document

°20062006

°20072007

Procesamiento Procesamiento DigitalDigital

Principio: Principio: Se puede aplicar Se puede aplicar

metodologías para extraer info útil de metodologías para extraer info útil de

imágenes satelitalesimágenes satelitales

0 1 2 3 40.5Miles °

0 1 2 3 40.5Miles

20072007

Normalized Difference Vegetation Normalized Difference Vegetation Index (NDVI): Index (NDVI): ratio entre la luz ratio entre la luz

infrarrojo cercano (NIR) y rojo (R), infrarrojo cercano (NIR) y rojo (R),

indicando vegetación en estrésindicando vegetación en estrés

Normalized Burn Ratio (NBR): Normalized Burn Ratio (NBR): ratio ratio

entre infrarrojo medio (SWIR) y entre infrarrojo medio (SWIR) y

infrarrojo cercano (NIR), para delinear infrarrojo cercano (NIR), para delinear

cicatrices (muy similar a NDVI)cicatrices (muy similar a NDVI)

Page 131: Document

°LandSat: 21 March 2006LandSat: 21 March 2006

NDVI: March 2006High : 0.964912

Low : -0.957447

0 0.9 1.8 2.7 3.60.45Miles

Page 132: Document

°LandSat: 11 May 2007LandSat: 11 May 2007

Contamination por Contamination por

el humoel humo

NDVI: May 2007High : 0.964912

Low : -0.957447

0 0.9 1.8 2.7 3.60.45Miles

Page 133: Document

°Differencing 2007 NDVI against 2006 NDVIDifferencing 2007 NDVI against 2006 NDVI

NDVI differenceHigh : 0.919945

Low : -1.04501

0 0.9 1.8 2.7 3.60.45Miles

Page 134: Document

°LandSat: 21 March 2006LandSat: 21 March 2006

0 0.9 1.8 2.7 3.60.45Miles

Normalized Burn RatioHigh : 0.978947

Low : -0.931034

Page 135: Document

°LandSat: 11 May 2007LandSat: 11 May 2007

0 0.9 1.8 2.7 3.60.45Miles

Normalized Burn RatioHigh : 0.978947

Low : -0.931034

Page 136: Document

°Differencing 2007 NBR against 2006 NBRDifferencing 2007 NBR against 2006 NBR

0 0.9 1.8 2.7 3.60.45Miles

Normalized Difference

Burn Ratio

-1.22 - -0.42

-0.42 - -0.31

-0.31 - -0.18

-0.18 - 0

0 - 1

Page 137: Document

°

0 0.9 1.8 2.7 3.60.45Miles

Normalized Difference

Burn Ratio

-1.22 - -0.42

-0.42 - -0.31

-0.31 - -0.18

-0.18 - 0

0 - 1

NDVI differenceHigh : 0.919945

Low : -1.04501

°

0 0.9 1.8 2.7 3.60.45Miles

°°

NDBRNDBR NDVI Diff.NDVI Diff.

°

0 1 2 3 40.5Miles

°

0 1 2 3 40.5Miles

20062006 20072007

Page 138: Document

°LandSat7: 11 de mayo de 2007LandSat7: 11 de mayo de 2007

Estimación: ~24,000 acres quemadasEstimación: ~24,000 acres quemadas

0 0.9 1.8 2.7 3.60.45Miles

Page 139: Document

ValidaciónValidación

Page 140: Document

c. 2000c. 2000

Page 141: Document

c. 2009c. 2009

Page 142: Document

Matrices de confusion / Matrices de error

Datos de validación

A B C D E F

A

B

clas

ific

ació

n Sumas de filas

480 0 5 0 0 0 485

0 52 0 20 0 0 72B

C

D

E

FDat

os

de

la c

clas

ific

ació

n

Sumas de columnas

0

0

0

0

0

0

0

0

480

52

16

68

0 20 0 0 72

Page 143: Document

Classmangroves

no mangroves water Total

User accuracy

Producer accuracy

Total class accuracy

Number %

mangroves 1 59 10 70 21% 1% 50% 26%

no mangroves 1 75 5 81 24% 93% 55% 74%

water 0 2 186 188 55% 99% 93% 96%

Total 2 136 201 339 100%

Producer

Accuracy 50% 55% 93% 77.3%

Classmangroves

no mangroves water Total

User accuracy

Producer accuracy

Total class accuracy

Number %

mangroves 2 77 6 85 26% 2% 100% 51%

no mangroves 0 54 5 59 18% 92% 39% 65%

water 0 7 182 189 57% 96% 94% 95%

Total 2 138 193 333100

%

Producer

Accuracy 100% 39% 94% 71.5%

Page 144: Document

Fuentes de Mayor InformaciónFuentes de Mayor InformaciónLibros (vea www.amazon.com) -

• Teledetección Ambiental (2002) – Emilio Chuvieco

• Remote Sensing and Image Interpretation (2007) – Thomas Lillesand, Ralph Kiefer, Jonathan Chipman

• Remote Sensing of the Environment (2006) – John R. JensenJensen

• Remote Sensing for GIS Managers (2005) – Stan Aronoff

En línea -

• TELEDET: http://www.teledet.com.uy/tutorial-imagenes-satelitales/imagenes-satelitales-tutorial.htm

• NASA: http://rst.gsfc.nasa.gov/

• CATHALAC: [email protected]

• GOOGLE / Wikipedia

Page 145: Document

Referencias / ReconocimientosReferencias / Reconocimientos

Mucha de la información en este presentación

fue adoptada de los siguientes fuentes:

• Burgess Howell, NASA GSFC (2006)• Burgess Howell, NASA GSFC (2006)

• Jason Tullis, University of Arkansas (2005)

• Lecturas / materiales del curso ESS 421 y ESS

422 de la U. de Washington (2004)

Page 146: Document

¿¿Preguntas?Preguntas?