The best method is to study the time series of urban expansion of the urban area using multi temporal airborne and spaceborne images, and you could later unify the scale and I would like to take a look on these links:

http://www.diva-portal.org/smash/get/diva2:621238/FULLTEXT01.pdf

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4234389

This article will help you. The authors include a brief review of urban mapping efforts.

A. Schneider, M. a. Friedl, and D. Potere, “Mapping global urban areas using MODIS 500-m data: New methods and datasets based on ‘urban ecoregions,’” Remote Sens. Environ., vol. 114, no. 8, pp. 1733–1746, Aug. 2010.

Another strategy is to use nightime image from DSMP or equivalent platform.

Hi. Two good tools are remote sensing and geographic information system (GIS). You can use satellite images or aerial photography from different dates to do a pixel classification and extract the urban footprint. Or you can use GIS and digitize polygons on an aerial photography to compare those areas along the time. Do a search on internet using "Land Use Classification".

Using remote sensing you can do a supervised classification. This consist on to train a program for separates the pixels on an image and group them in clases by its reflectance sign or range. Or you can do an unsupervised classification. On this one, the program do it by it selves without training areas. Later you need to do a field recognition (validation) and compare the classification with the field and see the % of error.

Hey,

you can find some simple ideas for urban sprawl detection (quantitative) in this paper:  https://www.researchgate.net/publication/251999091_Change_detection_of_urban_areas_-_the_Ljubljana_Slovenia_case_study

Article Change detection of urban areas - The Ljubljana, Slovenia case study

Now i am working with nighttime light data(DMSP and VIIRS data).  I advise you have a look at this data. The commonly used way is set a threshold for the DN value in nighttime image to extract the urban region. Chris Elvidge  and his workmates have done a lot of work in this domain. There is  a paper for nighttime light application in Urban area:  http://blogs.ei.columbia.edu/2013/11/11/night-time-lights-illuminate-trends-in-urbanization/

I am not sure if it is the most suitable method, but there are already papers using a urban sprawl index built upon secondary data from census. US have been ranking their cities according to that index. Have a look at: http://gis.cancer.gov/tools/urban-sprawl/

http://www.smartgrowthamerica.org/documents/measuring-sprawl-2014.pdf

Hope it helps

Ana

Urban sprawl is not spatial urban expansion. Extension of urban areas beyond municipality or corporation boundary especially along roads is considered urban sprawl. It can be analysed at any given moment of time by overlay method in GIS using map official boundary of an urban area and image interpreted or aerial potograph or recent map. However, for the purposes of simulation of sprawl in future and land cover/land use changes one needs a series of images, vertical aerial photographs or maps are required. 

Using satellite data  and remote sensing classification techniques one can easily identify the urban area by clustering or supervised classification and using temporal data, we can identify the changes occured. If using GIS for exact delineation, it is good to use cartosat imagery and identify the urban sprawl to digitize.

1) Residential density; 2) Neighborhood mix of homes, jobs, and services; 3)

Strength of centers, such as business districts; and 4) Accessibility via the street network. All of

these are well-established descriptors of urban sprawl in the relevant academic literature, but this

study represents the first effort to attempt to measure sprawl in all of these dimensions.

Kindly visit openstreet

http://www.openstreetmap.org/#map=5/51.500/-0.100

There are several research papers related to this plz go through. by applying supervised classification you can demarcate urban sprawl area.

dear try with NDBI (Normalize Difference Building Index)

try with temporal sat images

you can have good answer

You may find this new paper useful: "How suitable is entropy as a measure of urban sprawl? Landscape and Urban Planning184 (2019): 32-43."

From the abstract:

"Entropy has been one of the most often used metrics for the measurement of urban sprawl. However, its suitability in terms of requirements for measuring urban sprawl has not yet been examined systematically. Therefore, our study examines the behavior and suitability of entropy as a measure of urban sprawl by applying it to seven simple model landscapes and six real-world case studies. We also investigate the influence of the choice of the city center and associated translocation of zones and assess entropy with regard to 13 suitability criteria for measures of urban sprawl. Our results show that entropy is, in many cases, not sensitive to important differences between spatial patterns of built-up areas that represent different levels of urban sprawl, e.g., dispersed vs. compact spatial arrangement of built-up areas. In addition, the value of entropy is strongly affected by changes in the choice of zones within a landscape. Finally, entropy does not meet several important suitability criteria for measuring urban sprawl; it only meets 5 out of 13 suitability criteria. We conclude that entropy is not suitable as a measure of urban sprawl. More suitable metrics of urban sprawl are available that should be used instead."

I would like to recommend you to read Mr. Jochen Jaeger papers. He has good papers related to urban sprawl.

Note: the concept of urban sprawl is not similar to urban expansion.

Hope this helps.

using remote sensing data/images combined with sophisticated software that analyses urban expansion through analyzing change in pixel color.

You can use Remote Sensing techniques and then apply (Shannon) entropy theory, it's a good method.

https://www.researchgate.net/publication/230738894_Peri-Urban_to_Urban_Landscape_Patterns_Elucidation_through_Spatial_Metrics

https://www.researchgate.net/publication/229826816_Empirical_patterns_of_the_influence_of_Spatial_Resolution_of_Remote_Sensing_Data_on_Landscape_Metrics

Article Modelling the Relationship between Urban Growth Modes and th...

1. Using remote sensing data (NDBI).

2. Analyse the generator factors (spatially)

3. Define the topology

https://www.researchgate.net/publication/331159403_ANALISIS_TIPOLOGI_URBAN_SPRAWL_DI_KOTA_BANDUNG_MENGGUNAKAN_SISTEM_INFORMASI_GEOGRAFIS