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SUBMITTED VERSION. PUBLISHED VERSION AVAILABLE AT: https://ieeexplore.ieee.org/document/8727430
Abstract— The characterization of fine temporal-resolution
land surface dynamics from broadband optical satellite sensors is
constrained by sparse acquisitions of high-quality imagery; inter-
scene variation in radiometric, phenological, atmospheric, and
illumination conditions; and subpixel variability in heterogeneous
environments. In this letter, we address these concerns by
developing and testing the automatic adaptive signature
generalization and regression (AASGr) algorithm. Provided a
robust reference map corresponding to the date of one image,
AASGr automates the prediction of continuous fields maps from
imagery time series that is adaptive to the spectral and radiometric
characteristics of each target image, and thereby requires neither
atmospheric correction nor data normalization. We tested AASGr
on a 22-year Landsat time series to quantify subannual impervious
fractional cover dynamics in Houston, TX – an area characterized
by a high degree of spatial heterogeneity in surface cover and high
frequency in landcover change. The map time series achieved high
accuracy in a three-part validation procedure, and reveals spatio-
temporal dynamics of urban intensification and extensification at
a level of detail previously elusive in discrete classifications or
coarse temporal-resolution map products. The automation of
continuous fields time series is enabling a new generation of land
surface products capable of characterizing precise morphologies
along a continuum of spatio-temporal change. While AASGr was
applied here to predict subpixel impervious fractional cover from
Landsat imagery, the method is generalizable to a range of
imagery and applications requiring dense continuous fields time
series with uncertainty estimates of geo-physical and biochemical
characteristics such as leaf area index, biomass, and albedo.
Index Terms—continuous fields, impervious cover, land cover
change, Landsat, machine learning, random forests, signature
generalization, time series, urbanization.
I. INTRODUCTION
he steady deployment of satellite remote sensing platforms
in recent decades has provided scientists with prodigious
data streams of medium spatial resolution, broad-band imagery
for observing change on the Earth surface [1]. Bi-temporal
change detection using image pairs has been used effectively to
quantify state change (e.g. land cover class) or relative change
in surface characteristics between two dates, but is unable to
capture higher-order temporal dynamics, including gradual
change, periodicity, and change rates [2]. Reflecting the
demand for more temporally-frequent land surface data
products for disparate applications from land cover change to
biophysical land surface models [3], [4], the use of multi-
temporal image time series has increased rapidly [5].
Among all medium spatial resolution satellite sensors, the
Landsat program stands out for providing consistent, multi-
Manuscript submitted December 3, 2018. (Corresponding author
Christopher R. Hakkenberg).
C.R. Hakkenberg is with the Department of Statistics and the Kinder Institute
for Urban Research, Rice University, Houston, TX 77251 USA (email:
ch55@rice.edu, chrishakkenberg@gmail.com)
M.P. Dannenberg is with the Department of Geographical and Sustainability
Sciences, University of Iowa, Iowa City, IA 52242 USA (email: matthew-
decadal, high quality land surface imagery [6]. However, even
with Landsat sensor calibration and product quality assurance
[7], the consistent characterization of multi-temporal land
surface dynamics is impeded by inter-scene and inter-image
variation in radiometric, phenological, atmospheric, and
illumination/BRDF conditions [8]. The general scarcity of
high-quality, cloud-free image pairs at or near inter-annual
anniversary dates only exacerbates the challenge of ensuring
inter-date consistency [9]. A number of approaches have been
used to circumvent issues associated with sparsely acquired
imagery, including input data enhancements like best-available-
pixels composites, data blending, and multi-sensor data fusion
techniques [10], [11] as well as compromises in model output
such as the utilization of multi-year imagery for the
characterization of a single, nominal year [12]. Despite this,
inter-image discrepancies may still require onerous, and
potentially confounding, data correction and normalization
procedures that run the risk of exacerbating confusion between
radiometric differences among image dates (noise) and land
cover change (signal) [8].
Alongside the added value of fine temporal resolution time
series products, land surface models at medium spatial
resolution can benefit from more precise information on land
surface characteristics than simple discrete class designations.
This is especially so in spatially-heterogeneous environments,
where critical information may be lost by classifying complex,
intergrading land surfaces as discrete classes which can be
converted but not undergo subtle changes in intensity [13], [14].
Continuous fields pixel values offer several advantages over
discrete classifications by retaining maximum information
content and more precisely characterizing subpixel
heterogeneity [15].
Due to the demand for automated workflows for producing
temporally-dense, continuous fields land surface time series, we
developed the automatic adaptive signature generalization and
regression (AASGr) algorithm. AASGr builds upon AASG
classification - a training data selection algorithm that adapts to
image noise and inter-scene variation [16], [17] - to automate
the prediction of continuous fields land surface characteristics
based on a single reference map and time series imagery.
AASGr thus circumvents the resource-intensive and error-
prone process of manual training data selection, while ensuring
that all models in the series are individually tuned to unique
image characteristics and optimized for predictive accuracy.
This letter consists of four components: a description of the
AASGr algorithm (II.A), experimental implementation to
dannenberg@uiowa.edu).
C. Song is with the Department of Geography, University of North Carolina
at Chapel Hill, Chapel Hill, NC, 27599 USA (email: csong@email.unc.edu)
G. Vinci is with the Department of Statistics, Rice University, Houston, TX
77251 USA (email: gv9@rice.edu)
Christopher R. Hakkenberg, Matthew P. Dannenberg, Conghe Song, and Giuseppe Vinci
Automated continuous fields prediction from Landsat
time series: application to fractional impervious cover
T
SUBMITTED VERSION. PUBLISHED VERSION AVAILABLE AT: https://ieeexplore.ieee.org/document/8727430
quantify subannual impervious fractional cover dynamics over
a 22-year time series in Houston, TX (II.B), a three-part
validation of the map time series (II.C – III), and a short
discussion of applications and implications for the novel class
of products enabled by AASGr (IV).
II. METHODS
A. AASGr training data selection and predictive modeling
Provided a reference image (IR) paired with a reference map
(MR) from the same date, AASG automates training data
selection for prediction in a spatially-coincident stack of target
imagery (IT) by first delineating ‘stable sites’ - locations
ostensibly not experiencing land cover change between the
dates of the IR and IT [17] – which are used as the basis for
signature extension from the reference date to the target date(s).
To do this, a series of image differences (∆Ii) are created, where:
∆Ii = IR[x,y,zi] - IT[x,y,zi]; i=1…k
(1)
in the xy coordinate plane for the ith among k spectral bands (z).
Under the assumption that the majority of a sufficiently large
landscape did not undergo landcover change between the dates
of the IR and IT, pixels with stable land cover will tend to have
∆I values located at or near the mode of the image difference
histogram. By extension, unstable sites - pixels having
experienced significant landcover change – possess ∆I values
significantly dislocated from the histogram mode. Because
modal values are relative to the two images in question, stable
sites reflect relative stability between dates rather than absolute
spectral differences between images [17]. Thereafter, band-
specific difference images are combined into a multi-band
difference image (∆I), defined as:
(2)
where a pixel value of 0 in the ∆I would be expected for a
maximally stable pixel that exhibits the minimum possible
(relative) spectral difference between dates among all k bands.
Concurrently, a spatio-temporally coincident reference map
(MR) consisting of continuous or consecutive integer values of
the response variable in question is stratified into m bins
spanning the range of pixel values in the MR. Then,
for each we select pixels
according to:
(3)
(4)
(5)
where = σ × c, is the standard deviation of the values
in , c is a user-defined threshold parameter regulating the
maximum allowed total sample size N, T is the total number of
pixels in MR, w denotes w rounded to the nearest integer, and
(h,l) denotes a pixel location. That is, pixels are randomly
sampled without replacement from each of the m sets ,
whose corresponding value in the ∆I is less than a threshold
defining the set of stable sites. To ensure a maximally
representative training dataset optimized for prediction on
independent data, the number of stable site pixels sampled
from each set is proportional to the number of pixels in the
full MR whose values fall in . For example, for a Landsat
image, the distribution of subsampled pixels (n=1x106) will
closely resemble (R2=0.99) that of the full dataset (n=6x1010),
though at a fraction of the size and consisting of only the most
stable site pixels for model training (Fig. 1). Provided that m is
large enough to capture the full distribution of values in the MR,
the number of bins for stratification is user-defined.
Fig. 1. Reference map subsampling. (a) Density histogram for reference pixel
values from NLCD 2001 impervious and subsampled pixels, (b) QQ plot for all
reference pixel values versus those in the subsample.
While a priori training data stratification and proportional
allotment provides an efficient method for sampling stable site
pixels among bins, sampled pixels in the MR retain
their original continuous integer values. Once the location of all
stable site pixels in the MR is determined, a full training dataset
is compiled from the stable site values in the MR and spatially-
corresponding pixels in the IT to predict a continuous fields
target map (MT) and associated uncertainties from the full IT.
To summarize, the algorithmically-generated training data set
exhibits three desirable properties:
(1) multi-band stable sites: sampled pixels exhibit the minimum
relative spectral difference across multiple spectral bands
between dates in reference and target imagery;
(2) proportional allotment: the distribution of sample values is
proportional to that of the full reference map, thereby
ensuring representation across the range of parameter
space for optimized prediction on an independent dataset;
(3) random stratified sampling: within stratified bins of
candidate stable sites, sample selection is randomized.
AASGr is not beholden to any one sensor or regression
model, and in this experiment predictive regression was
performed on Landsat imagery using random forests (RF), an
ensemble of regression trees based on votes across bootstrap
replicates [18]. As an ensemble algorithm with predictors
randomly permuted at tree nodes, RF is able to efficiently
handle data noise, and is noted for its record of high predictive
accuracy and generalizability [19]. These properties make it
attractive for Landsat image time series, as RF has been shown
to effectively handle collinearity among spectral bands, noise
due to atmospheric and radiometric contamination, or
georegistration issues arising from image misalignment [19].
B. Experimental implementation
AASGr was tested on a 22-year Landsat image stack covering
a 2720 km2 portion of central Houston, TX (see Fig 2a).
Houston’s spatially heterogenous cover and its rapid growth
from 1997-2018 makes it a compelling test case for assessing
0%
1%
2%
3%
4%
0.00 0.25 0.50 0.75 1.00
Reference pixel values
Density
all pixels
subsample
(a)
R2=0.9998
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
All pixels
Subsample
1000
2000
3000
Frequency
(b)
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the performance of AASGr to detect fractional impervious
cover as a continuous field. Imagery consisted of all available
radiometrically-calibrated and orthorectified Landsat
Collection 1 Level-1 imagery (WRS2 path/row 25/39)
possessing <10% cloud cover. In total, 66 images fulfilled these
criteria. Imagery spanned a range of phenological states
(DOYs) and atmospheric conditions, over a range of three
satellites/sensors: Landsat-5 TM between 1997-2011, Landsat
7 ETM+ for 1999-2012, and Landsat 8 OLI for 2013-2018.
Reference maps (MR) consist of wall-to-wall subpixel
impervious fraction maps possessing continuous values
between 0.00-1.00 from the U.S. Geological Service (USGS)
National Land Cover Database (NLCD) Percent Developed
Imperviousness product from 2001, 2006 and 2011 [12]. The
three reference maps were paired with Landsat reference
imagery for each respective year, and applied to the most
temporally-proximate target imagery (i.e. IR-2001 and MR-2001 was
paired with IT-1997 - IT-2003, IR-2006 and MR-2006 with IT-2004 - IT-2008,
and IR-2011 and MR-2011 with IT-2009 - IT-2018).
Fig. 2. Houston, TX study area. (a) predicted impervious fractional cover for
August 28, 2011 where insets refer to the extent of validation images, and (b)
the standard deviation of the random forest’s predictive posterior distribution.
Before prediction, all clouds, cloud shadows, ETM+ SLC-off
gaps, and radiometrically-saturated or contaminated pixels
were algorithmically masked based on quality assessment
bands [20]. Except for these masked areas, which are treated as
data gaps in all predicative modelling, RF regression models
yield posterior predictive distributions based on the votes of all
trees in the RF model [21]. Lacunae are interpolated post-hoc,
based on temporally-adjacent pixels in the prediction time
series. For this interpolation procedure a low pass filter using a
Gaussian kernel in a five-year window was applied to each pixel
in the temporal dimension of the full time series.
Parameter optimization, performed to balance efficiency (run
time) and predictive accuracy based on an external comparison
with independent NLCD maps resulted in the selection of
140,000 pixels as the total sample size (N) and 10 bins (m), with
RF hyperparameters: 300 trees per model, and 1 predictor
sampled at each split. Sensitivity analysis confirmed that model
performance was largely robust to parameter values. Among all
Landsat band combinations and derived indices, the difference
of the blue and near-infrared bands yielded the highest
prediction accuracies in model testing, and was thereby adopted
for all model runs. To prevent the mischaracterization of
temporarily docked waterborne vessels as terrestrial impervious
surface, a mask based on unchanged water pixels in NLCD
2001 and 2011 maps was applied to the full time series.
C. Accuracy assessment
Predictive maps were validated via a three-part accuracy
assessment. First, an in-sample OOB estimate of model
performance (pseudo-R2) was derived for every model run.
Second, all pixels in predictive maps were compared with
NLCD impervious maps for coincident years (i.e. 2001, 2006,
and 2011) and the strength of their agreement was assessed via
adjusted R2. To maintain independence of training and
validation data, training data was constrained to the two NLCD-
Landsat sets not corresponding to the year of prediction, and
their results averaged to produce a single metric of agreement.
Fig. 3. Validation map (MV) classification. (a) 3m resolution validation imagery
(IV); (b) validation classification (CV) at 3m IV native resolution; (c) 3m binary
pervious/impervious CV; (d) resampled impervious cover validation map (MV)
at 30m Landsat spatial resolution.
As a third test of map accuracy, three 3m resolution Quickbird
validation images (IV) from 2005, 2007, and 2013 were used for
independent validation with spatio-temporally coincident map
subsets (Fig. 2a). Cloud masks and regions of interest for five
primary land cover types (forest, grassland, urban, water, and
barren) in the IV were manually delineated, and used to train a
Classes
Impervious
Pervious
Fractional
Impervious
100%
0%
Classes
Forest
Grass
Water
Barren
Impervious
(a) (b)
(c) (d)
0 1 20.5 km
0 1 20.5 km
0 1 20.5 km
0 1 20.5 km
SUBMITTED VERSION. PUBLISHED VERSION AVAILABLE AT: https://ieeexplore.ieee.org/document/8727430
random forest classifier. The resulting validation maps possess
five-class overall accuracies of 0.83, 0.84, and 0.85 for the three
dates, respectively, with the largest confusion occurring
between Barren and Urban classes – a not uncommon result in
urban classification [22]. Thereafter, the five-class validation
classification (CV) was converted to a binary urban-nonurban
classification and resampled to a 30m resolution validation map
(MV) based on the aggregate of all urban (impervious)
subpixels. Aggregated, binary urban-nonurban validation maps
possess overall accuracies of 0.91, 0.91, and 0.92, respectively.
Subpixel impervious fraction in the resampled MV is calculated
as:
(6)
where N is the total number of pixels in CV corresponding to
pixel in the MV. For example, for a 3m binary CV, a single
30m aggregate pixel consists of 100 subpixels, each possessing
a value of 0 (pervious) or 1 (impervious). Summing the
subpixels and dividing by 100 renders an estimated subpixel
impervious fraction in the MV at the coarser 30m resolution
(Fig. 3). Thus devised, AASGr-generated maps (MT) can be
directly compared with corresponding pixels in the validation
subsets in the MV, and assessed for accuracy based on adj-R2.
III. RESULTS
In experiments, internal OOB pseudo-R2 for all 66 image
predictions ranged from 0.76 to 0.90 (= 0.83, =0.03) [23].
Visual observation confirms that AASGr-generated maps
accurately reproduce known patterns in impervious surface
cover (Fig. 2a). The standard deviation of posterior votes serve
as a measure of certainty (Fig. 2b). When compared to
corresponding, but independent NLCD maps from dates not
used for model training, AASGr predictions showed a high
degree of agreement based on adj-R2 (Table 1). As no one map
is authoritative, agreement does not directly correspond with
accuracy and could reflect or obscure errors in any one image
or errors in both [4].
TABLE 1
AGREEMENT & VALIDATION
Validation Data
Year
adj-R2
RMSE
MAE
bias
NLCD
2001
0.82
0.14
0.09
0.01
NLCD
2006
0.77
0.16
0.11
0.02
NLCD
2011
0.77
0.16
0.11
-0.01
Quickbird
2005
0.72
0.15
0.11
-0.05
Quickbird
2007
0.80
0.14
0.11
0.03
Quickbird
2013
0.79
0.14
0.11
-0.01
Independent accuracy assessment using three classified and
resampled fine-resolution images indicate accuracies in line
with NLCD agreement metrics, and comparable to those
observed in other studies [13]–[15], though with the added
benefit of a continuous fields output at a subannual resolution
(Table 1). Scatter charts of agreement show a slight deviation
from the 1:1 line, indicative of some boundary bias (Fig. 4;
Table 1). This compression of the posterior distribution reflects
empirical limitations of ensemble classifiers that, while
optimizing total accuracy, extract predictions from the mean of
the vote posterior and thereby tend to underestimate extreme
values at the poles of the range [24].
Fig. 4. Validation results. AASGr prediction versus NLCD agreement (left
column) and independently classified, 3m resolution Quickbird images.
IV. DISCUSSION
AASGr fully automates model parameterization and
prediction of a continuous fields response variable from time
series imagery, achieving high predictive accuracy in
experiments as it efficiently adapts to inconsistencies in multi-
temporal imagery. Automated signature generalization
algorithms are noteworthy as streamlined workflows enable the
estimation of land surface characteristics at previously elusive
spatio-temporal resolutions. And unlike discrete classifications,
continuous fields regression is optimally suited for producing
confidence intervals critical to secondary applications - such as
estimating unbiased areal land cover change estimates or as
input maps for process-based land surface models - requiring
uncertainty estimates of state values [3], [4].
In this implementation, AASGr was tested on a Landsat
imagery time series to estimate subannual subpixel impervious
fractional cover over a 22-year period in the rapidly urbanizing
city of Houston, TX. The resulting map time series is significant
in that it showcases the utility of AASGr to quantify subannual
land cover dynamics and sub-pixel heterogeneity (Fig. 5).
Therefore, AASGr-enabled time series are capable of
simultaneously characterizing both urban extensification
(conversion of pervious to impervious surface) and
intensification (changing intensity of fractional impervious
cover in any one pixel) – a feat otherwise unattainable with hard
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
NLCD
AASGr
2001
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
Quickbird
AASGr
2005
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
NLCD
AASGr
2006
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
Quickbird
AASGr
2007
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
NLCD
AASGr
2011
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
Quickbird
AASGr
2013
5000 10000 15000
Frequency 2000 4000 6000 8000
Frequency
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classifiers. This level of precision is noteworthy for next
generation urban land cover change applications requiring
precise characterizations of land cover change morphologies
along a continuum of spatio-temporal change. Land cover time
series that are near-continuous in space and time offer several
advantages to coarse spatial resolution, temporally-sparse time
series by more precisely capturing heterogeneity in spatially
complex areas, thereby better lending themselves to the
derivation of indices of continuous surface metrology [25].
Fig. 5. Continuous change in impervious cover for three dates in Houston, TX.
Intermediate colors represent overlap between dates.
V. CONCLUSION
In this letter, we present the automatic adaptive signature
generalization and regression (AASGr) algorithm. AASGr is
fully automated for time series prediction in that it is adaptive
to the spectral and radiometric characteristics of target imagery,
and thereby requires neither atmospheric correction nor data
normalization. Provided a robust reference map paired with an
image from the same date, AASGr can predict highly-accurate
continuous response values and associated uncertainties for
time series imagery before and after the reference date. This
quality makes it attractive for diverse applications requiring
multi-date land surface information where reference data is
otherwise limited. In this implementation, we tested AASGr for
estimating fractional impervious cover in a rapidly urbanizing
city, demonstrating its capacity to characterize heterogeneity
and intensity in spatially complex areas, as well as higher-order
temporal dynamics and change rates. AASGr is not limited to
estimating subpixel land cover fractions, and is amenable to a
range of applications requiring dense, continuous fields raster
map time series with uncertainty estimates including land
surface characteristics like leaf area index, biomass, and albedo.
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