Impact of the Scale on Several Metrics Used in Geographical Object-Based Image Analysis: Does GEOBIA Mitigate the Modifiable Areal Unit Problem (MAUP)?

Didier Josselin,Romain Louvet

doi:10.3390/ijgi8030156

Abstract

Using two GEOBIA (Geographical Object Based Image Analysis) algorithms on a set of segmented images compared to grid partitioning at different scales, we show that statistical metrics related to both objects and sets of pixels are (more or less) subject to the Modifiable Areal Unit Problem. Subsequently, even in a same spatial partition, there may be a bias in statistics describing the objects due to some size effect of the pixel samples. For instance, pixels homogeneity based on Grey Level Cooccurrence Matrices (GLCM), Landscape Shape Index, entropy, object compacity, perimeter/area ratio are studied according to scale. The approach consists in studying the behavior of a given statistical metrics through scales and to compare the results on several image segmentations, according to different partitioning processes, from GEOBIA (Baatz & Schäpe algorithm and Self Organizing Maps) or using reference grids. We finally discuss about the relationship between GEOBIA metrics and scale. By analysing object shape and pixels composition from different metrics points of views, we show that GEOBIA does not always mitigate the Modifiable Areal Unit Problem.

Highlights

IntroductionThe first aspect is in a vertical dimension (scaling), while the second one is in a horizontal dimension (zoning)
The Modifiable Areal Unit (MAUP) has two related aspects depending on the way we consider surface units [1]: scale or spatial partitioning, which are tightly related to multilevel modeling [2,3,4]
We propose to focus on the first approach using a series of metrics that objectively describe the objects through scales, especially their homogeneity

Summary

Introduction

The first aspect is in a vertical dimension (scaling), while the second one is in a horizontal dimension (zoning) Both lead to the same problem: the way spatial entities are aggregated or delineated [5] provides a spatial partition whose polygons organization and shapes have a non negligible impact on any (geo)statistics measuring the parts and the whole, according to different boundary definitions (cf [6]). This issue is shared by many disciplines and domains (see Figure 1) with different highlights, it mainly results in a statistical bias. It is intimately related to the ecological inference problem or fallacy formulated by Robinson in 1950 [7] to denounce the use of aggregated statistics to infer knowledge on individual behavior [8]

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Methods

Results