#  SAGE-NDVI: A Stereotype-Breaking Evaluation Metric for Remote Sensing Image
Dehazing Using Satellite-to-Ground NDVI Knowledge

Zepeng Liu1,2,†, Zhicheng Yang3,‡, Mingye Zhu1,2,†, Andy Wong3, Yibing
Wei4,3,†, Mei Han3,
Jun Yu1,‡, Jui-Hsin Lai3,‡ †This work was done when Zepeng Liu and Mingye Zhu
were interns at Ping An Technology, Shenzhen, Guangdong, China, and when
Yibing Wei was an intern at PAII Inc., Palo Alto, CA, USA.‡Corresponding
authors: Zhicheng Yang ($\mathtt{zcyangpingan@gmail.com}$); Jun Yu
($\mathtt{harryjun@ustc.edu.cn}$); Jui-Hsin Lai
<EMAIL_ADDRESS>1University of Science and Technology of
China, China
2Ping An Technology, China
3PAII Inc., USA
4University of Wisconsin - Madison, USA

###### Abstract

Image dehazing is a meaningful low-level computer vision task and can be
applied to a variety of contexts. In our industrial deployment scenario based
on remote sensing (RS) images, the quality of image dehazing directly affects
the grade of our crop identification and growth monitoring products. However,
the widely used peak signal-to-noise ratio (PSNR) and structural similarity
index (SSIM) provide ambiguous visual interpretation. In this paper, we design
a new objective metric for RS image dehazing evaluation. Our proposed metric
leverages a ground-based phenology observation resource to calculate the
vegetation index error between RS and ground images at a hazy date. Extensive
experiments validate that our metric appropriately evaluates different
dehazing models and is in line with human visual perception.

###### Index Terms:

dehazing, evaluation metric, remote sensing, satellite-to-ground

##  I Introduction

As an integral part of low-level computer vision (CV) tasks, image dehazing is
utilized to remove the influence of weather factors and improve the visual
effects of the images. Image dehazing can be applied to a wide range of
scenarios, including game production and vision systems for autonomous
driving, video surveillance, military reconnaissance, etc. Another major
dehazing scenario is in the field of _remote sensing_ (RS) imagery, with both
government-level and commercial-level applications, such as change detection
and crop identification.

In our industrial scenario, our customers’ demands are crop identification and
growth monitoring using RS images [1, 2, 3]. These demands heavily rely on the
calculation of the Normalized Difference Vegetation Index (NDVI) [4], a widely
used RS index to assess vegetation growth. However, RS images with fog and
haze can cause significant errors in NDVI calculation, leading to the
unsatisfactory results we deliver to our customers. Therefore, image dehazing
assessment is essential to convey the proper RS image product to our clients.

In order to evaluate the dehazing effects, a dehazed image and a clear ground
truth image are required to estimate their similarity. This can be easily
achieved in the natural image domain, because many dehazing datasets employ
clear images to artificially generate the corresponding hazy images. However
in the RS domain, a hazy image does not have a clear counterpart at the same
time stamp. Although haze synthesis on a clear RS image is passable, our model
trained with artificial hazy images suffers from unsatisfying performance on
real haze. Alternatively, recent studies provide a new perspective that
jointly employs ground-level and satellite images for various satellite-to-
ground cross-reference applications when either image source is insufficient
[5, 6].

Figure 1: (a): Geographic location (cyan dot) of the PhenoCam observation site
bouldinalfalfa [7] on an S2 image. (b)-(d): Example images of the ground-based
imagery source, showing the visual appearance changes within only a one-month
span. (e): Example near-infrared image on the same date of (d). (f): Refined
mask based on the given one.

Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) are
two commonly used metrics for dehazing evaluation [8, 9, 10], however, they
are hardly interpreted or deployed in practice as an indicator of the dehazing
model upgrade. Our clients’ feedback indicates that the increment in the value
of PSNR or SSIM does not necessarily bring out quality improvement in human
perception. Recent studies also confirm this misalignment in evaluating low-
level CV tasks such as the super-resolution task [11, 12]. Therefore,
designing a stereotype-breaking metric is necessary [13, 14, 15].

To address the pain points in terms of the data and metrics above, we propose
a new evaluation metric for RS image dehazing assessment based on _satellite-
to-ground_ multimedia image sources, called “SAtellite-to-Ground Error of
NDVI” (SAGE-NDVI). Our key contributions are listed as follows.

  * •

To tackle the unavailability of a clear ground truth RS image, we leverage a
sharp ground image dataset of vegetation phenology, which daily monitors
multiple crop types worldwide using outdoor cameras. The error between the
NDVI values of this clear ground image source and the dehazed RS image source
contributes to the proposed SAGE-NDVI.

  * •

Extensive experiments demonstrate that our objective SAGE-NDVI is capable of
appropriately evaluating different dehazing models and more consistent with
human perception than the conventional PSNR metric.

##  II Related Work

Natural Image and Remote Sensing Image Dehazing. For natural images,
traditional methods mainly utilized different priors for image restoration and
improve the image contrast and saturation [16, 17, 18]. Recently deep
learning-based methods aimed to generate a dehazed image from a hazy one [19,
9, 10]. FFA-Net [9] exploited channel and pixel attention modules to
incorporate features on different channels to accomplish robust dehazing
performance. DehazeFormer [10] adopted reflection padding and modified
normalization layers built upon Swin Transformer [20] to achieve state-of-the-
art performance on various datasets. For RS scenarios, image dehazing is a
rigid demand for various civilian purposes, like land planning and crop yield
surveys [8, 21, 22].

Evaluation Metrics. Peak Signal-to-Noise Ratio (PSNR) and Structural
Similarity Index (SSIM) are the two main objective metrics to evaluate the
dehazing effects [19, 8, 9, 10]. The former gauges the pixel-wise error using
Mean Squared Error (MSE), and the latter measures the structural similarity of
pictures to estimate the quality of pictures after compression [23]. However,
they are not entirely consistent with human perception [12] or even
interpretable for clients who lack domain knowledge. In the context of our
deployment scenario using RS imagery, our design of the proposed objective
evaluation metric SAGE-NDVI benefits from the satellite-to-ground multimedia
image reference sources and breaks the stereotype of the difficulty to measure
low-level image tasks in RS images.

##  III Materials and Methods

###  III-A Data Acquisition and Pre-Processing

Satellite Image Data. Instead of using Google Earth or other sources that are
limited to academic use only, we utilize the Sentinel-2 (S2) satellite imagery
with a 10m spatial resolution [24], which is _commercial use free_ , to
construct our satellite image database. It is worth noting that our database
pipeline prioritizes the clients’ demands rather than this specific evaluation
metric design. As required by our clients, the production of S2 images for a
given time interval (e.g. every 8 days) must be guaranteed. However, the
original revisiting period of S2 satellites (around 4-5 days) is not fixed and
an S2 image for each period is sometimes corrupted or defective, definitely
conflicting with the clients’ requirements. To this end, we exploit temporally
adjacent images to composite an S2 image with a fixed time interval of every 8
days. Fig. 1a provides an S2 image example from our satellite image database
with the pinned geographic location of the observation site.

Ground Image Data. We leverage the PhenoCam database as our ground data source
[25]. This database of monitoring vegetation phenology covers over 800 global
observation locations using outdoor ground-based cameras. Due to the impact of
diverse climates across worldwide locations on camera image availability,
especially in rainy and snowy seasons, our focus is the cropland areas in the
middle Central Valley of California, USA. The reasons are twofold: 1) this
area enjoys a hot Mediterranean climate that rarely has snowy days; 2) the
long-running camera deployment acquires abundant images. Specifically, we
select an observation site that grows _alfalfa_ at Bouldin Island, CA [7],
where the image data is available from 2016 to the present. Since alfalfa is
harvested several times a year, its vegetation appearance can change more
frequently than other plants. This property is challenging but beneficial to
our metric design and evaluation. Fig. 1b-1d exemplify the images captured at
this site, showing the visual changes within only one month.

The deployed camera contains four RGBN channels: red, green, blue, and near-
infrared (NIR) (shown in Fig. 1e). The frequency of image production of a
camera is around every 30 minutes in the daytime every day. We refine the
originally given binary mask to eliminate the region of the camera stand and
the sky (shown in Fig. 1f). Thanks to our careful selection of the observation
site and time span, the masked regions can be regarded as cloud-free and haze-
free image sources, serving as a reliable reference for S2 image counterparts.

Input: Satellite imgs:
$\mathbf{I}=[\mathbf{I}_{1},\mathbf{I}_{2},\dots,\mathbf{I}_{n}]$;
Ground imgs:
$\mathbf{G}=[\mathbf{G}_{1,1},\mathbf{G}_{1,2},\dots,\mathbf{G}_{l,t_{l}}]$;
NDVI threshold: $h$.

Funcs: ➊ $\psi$: Cloud detector; ➋ $\phi$: Dehazing;
➌ $\lambda^{\mathbf{I}}$: NDVI for $\mathbf{I}$; ➍
$\tilde{\lambda}^{\mathbf{G}}$: NDVI and post-proc for $\mathbf{G}$; ➎
$\mathtt{d}$: DTW.

Output:
$\mathrm{\overline{e}}\in\mathbb{R},~{}~{}\mathrm{\overline{e^{\phi}}}\in\mathbb{R}$.

1 for  _$i\leftarrow 1$ to $n$_ do

2 $\mathbf{M}^{\psi}_{i}\leftarrow\psi(\mathbf{I}_{i})$;

3
$\mathbf{I}_{i}^{\psi}\leftarrow\mathbf{I}_{i}~{}\&~{}(\mathbf{1}-\mathbf{M}^{\psi}_{i})$;

4 $\mathbf{I}_{i}^{\phi}\leftarrow\phi(\mathbf{I}_{i}^{\psi})$;

5

6 end for

7$\mathbf{u}\leftarrow\lambda^{\mathbf{I}}(\mathbf{I}^{\psi});~{}~{}\mathbf{u}^{\phi}\leftarrow\lambda^{\mathbf{I}}(\mathbf{I}^{\phi});~{}~{}\mathbf{v}\leftarrow\tilde{\lambda}^{\mathbf{G}}(\mathbf{G})$;

8

9Normalize $\mathbf{u}\in\mathbb{R}^{n}$,
$\mathbf{u}^{\phi}\in\mathbb{R}^{n}$, and $\mathbf{v}\in\mathbb{R}^{m}$;

10

11$\mathbf{A}\leftarrow\mathtt{d}(\mathbf{u},\mathbf{v})\in\\{0,1\\}_{(n\times
m)}$;

12
$\mathbf{A}^{\phi}\leftarrow\mathtt{d}(\mathbf{u}^{\phi},\mathbf{v})\in\\{0,1\\}_{(n\times
m)}$;

13

14Initialize $\mathrm{e}$, $\mathrm{e^{\phi}}$, and $k$ with $0$s;

15

16for  _$i\leftarrow 1$ to $n$_ do

17

18 if  _$|u_{i}-u_{i}^{\phi}| >h$_ then

19 $\mathbf{q}\leftarrow\\{j|A_{ij}==1;j\in\\{1,\dots,m\\}\\}$;

20 $\mathbf{q}^{\phi}\leftarrow\\{j|A^{\phi}_{ij}==1;j\in\\{1,\dots,m\\}\\}$;

21
$\mathrm{e}\leftarrow\mathrm{e}+\frac{1}{|\mathbf{q}|}\sum_{q\in\mathbf{q}}|u_{i}-v_{q}|$;

22
$\mathrm{e^{\phi}}\leftarrow\mathrm{e^{\phi}}+\frac{1}{|\mathbf{q}^{\phi}|}\sum_{q^{\phi}\in\mathbf{q}^{\phi}}|u_{i}^{\phi}-v_{q^{\phi}}|$;

23 $k\leftarrow k+1$;

24

25 end if

26

27 end for

28$\mathrm{\overline{e}}=\mathrm{e}/k;~{}~{}~{}~{}\mathrm{\overline{e^{\phi}}}=\mathrm{e^{\phi}}/k$;

Algorithm 1 SAGE-NDVI

###  III-B Design of SAGE-NDVI

Background of NDVI. The Normalized Difference Vegetation Index (NDVI) [4] is
an technique to assess vegetation growth and condition by measuring the
difference between NIR and red channels of an image, calculated as
$\mathrm{NDVI}=(\mathrm{NIR}-\mathrm{Red})/(\mathrm{NIR}+\mathrm{Red})$. NDVI
values range from -1 to +1. The higher values indicate more green and healthy
vegetation and negative values often indicate water bodies. NDVI is widely
used in environmental monitoring to assess vegetation cover, monitor changes
in land use and land cover, and track the effects of climate change on
ecosystems.

Algorithm Details. Alg. 1 reveals our algorithm design of SAGE-NDVI. Let
$\mathbf{I}=[\mathbf{I}_{1},\mathbf{I}_{2},\dots,\mathbf{I}_{n}]$ denote the
$n$-length sequence of 8-day composite S2 satellite images in one year, where
$n$ is the number of valid satellite images. The ground image year-round
sequence is
$\mathbf{G}=[\mathbf{G}_{1,1},\mathbf{G}_{1,2},\dots,\mathbf{G}_{l,t_{l}}]$,
where $l$ refers to the number of valid days and $t_{l}$ is the number of
available images on the $l$-th day. For each
$\mathbf{I}_{i},i\in\\{1,\dots,n\\}$, a cloud detector $\psi(\cdot)$ is first
used to void pixels occluded by cloud, and the remaining valid pixels are then
dehazed by a dehazing model $\phi(\cdot)$. The corresponding NDVI sequences
($\mathbf{u}$ and $\mathbf{u}^{\phi}$) of the cloud-cropped hazy satellite
images $\mathbf{I}^{\psi}$ and the dehazed satellite images
$\mathbf{I}^{\phi}$ are next calculated, respectively.

Note that the original NDVI values of ground images have a length of $l$,
since they are calculated on a daily average basis. We then denoise them and
conduct peak detection to remove minor fluctuation and maintain the key
patterns, consequently achieving an $m$-length NDVI sequence $\mathbf{v}$ for
ground images $\mathbf{G}$, where $m$ is the number of detected peaks and
troughs.

Due to the inherent distance in the color space between the satellite imaging
sensors and the ground camera sensors, we normalize the three NDVI sequences
using a min-max scaling strategy. Note that a hazy NDVI value can be a salient
outlier of a regular figure, hence applying the min-max scaling scheme on such
time series data can cause serious offset errors. Those inappropriate offsets
further damage the real relative distances between hazy $\mathbf{u}$ and
dehazed $\mathbf{u}^{\phi}$. We normalize $\mathbf{u}$ using the parameters of
$\mathbf{u}^{\phi}$ instead.

Next, we measure the similarity between the NDVI temporal sequences of
satellite images and ground images. Owing to the different lengths ($n$ vs.
$m$) of NDVI values, the dynamic time warping (DTW) algorithm [26] is
exploited to dynamically associate similar values of two time series with
different temporal resolutions. We let $\mathbf{A}$ denote the binary
adjacency matrix to present the DTW path. For the $i$-th of $n$ time stamps,
we compare the difference between hazy $u_{i}$ and dehazed $u_{i}^{\phi}$. If
the difference is greater than a given threshold, the dehazing effect is
_significant_ at this time spot. We define $\mathrm{\overline{e}}$ and
$\mathrm{\overline{e^{\phi}}}$ as the mean errors for hazy and dehazed NDVI
values at all these significant time stamps, respectively.

###  III-C Use Description of SAGE-NDVI

For the use of SAGE-NDVI, the hazy images of the PhenoCam observation site are
provided as the gold standard reference dataset. To evaluate a dehazing model,
we run the model on those hazy images and generate the dehazed ones. The
dehazed images are used to calculate the values of
$\mathrm{\overline{e^{\phi}}}$.

##  IV Performance Evaluation

TABLE I: SAGE-NDVI results at the observation site bouldinalfalfa [7] from
2018 to 2022. Green: difference between $\mathrm{\overline{e}}$ and
$\mathrm{\overline{e^{\phi}}}$. Bold: the better dehazing performance between
FFA-Net and DehazeFormer.

Alfalfa |  $\mathrm{\overline{e}}$ ($\downarrow$) |  $\mathrm{\overline{e^{\phi}}}$ ($\downarrow$) (FFANet[9]) |  $\mathrm{\overline{e^{\phi}}}$ ($\downarrow$) (DehazeFormer[10])
---|---|---|---
2018 | 0.4457 | 0.2312 (${-}$0.2145) |  0.1865 (${-}$0.2592)
2019 | 0.3259 | 0.3181 (${-}$0.0077) |  0.3032 (${-}$0.0227)
2020 | 0.3190 | 0.2351 (${-}$0.0839) |  0.2259 (${-}$0.0931)
2021 | 0.4385 | 0.2773 (${-}$0.1612) |  0.2243 (${-}$0.2142)
2022 | 0.4370 | 0.2140 (${-}$0.2230) |  0.1696 (${-}$0.2674)
Mean | 0.3764 | 0.2719 (${-}$0.1045) |  0.2219 (${-}$0.1545)

###  IV-A Implementation Details

For the satellite side, we collect 18,776 S2 image pairs of a hazy and a clean
image at the proximate date. The Dark Channel Prior (DCP) [16] is used to
determine whether one image is hazy or not. The default DCP threshold is set
to 20. We choose the FFA-Net [9] and the DehazeFormer-B [10] since they
demonstrated superior performance on various datasets in [10] and they are
deployed in our production environment. The images were cropped into patches
with a size of 1024$\times$1024 and equipped with rotation and flip
augmentations. We keep the default setting of both FFA-Net and Dehazeformer-B,
respectively trained for 300 epochs. The threshold of NDVI difference $h$ is
set to 0.1 by default.

For the ground side, we download the image data of this observation site
spanning from 2018 to 2022. To avoid the camera being affected by the sunrise
and sunset, we use the images from 11:00 to 13:00 when the sun is not in
camera images, collecting approximately 4 images per day.

###  IV-B Experiment Results

Evaluation of Dehazing Models Using SAGE-NDVI. Table I lists the evaluation
results of dehazing models using SAGE-NDVI at the alfalfa observation site
from 2018 to 2022. The significantly decreased error values
$\mathrm{\overline{e^{\phi}}}$ compared with $\mathrm{\overline{e}}$
demonstrate the usability of our newly designed metric. Furthermore, the bold
results indicate the stable superiority of DehazeFormer-B over FFA-Net. This
observation is consistent with the results in [10] that DehazeFormer-B overall
outperformed FFA-Net on a remote sensing dataset and other datasets using the
traditional PSNR and SSIM metrics.

TABLE II: Averaged SAGE-NDVI on other observation sites [7]. Green: difference
between $\mathrm{\overline{e}}$ and $\mathrm{\overline{e^{\phi}}}$.

Mean |  $\mathrm{\overline{e}}$ ($\downarrow$) |  $\mathrm{\overline{e^{\phi}}}$ ($\downarrow$) (FFANet[9]) |  $\mathrm{\overline{e^{\phi}}}$ ($\downarrow$) (DehazeFormer[10])
---|---|---|---
Corn | 0.3085 | 0.2374 (${-}$0.0711) |  0.2285 (${-}$0.0837)
Rice | 0.1602 | 0.1232 (${-}$0.0370) |  0.1157 (${-}$0.0445)

Comparison of SAGE-NDVI and PSNR. Although the general conclusions drawn from
evaluating the dehazing models using either SAGE-NDVI or PSNR seem aligned as
aforementioned, we next illustrate the shortcomings of PSNR. Fig. 2 depicts
the NDVI errors (the second addend on Line 15 and 16 in Alg. 1) and the PSNR
values calculated at the alfalfa observation site on a hazy date. Aside from
the obviously poor PSNR value and large NDVI error of the original hazy image,
we observe that even though PSNR values of FFA-Net are higher than those of
DehazeFormer-B, the visualized results are not quite in accordance with the
human perception. The image’s color and texture reconstructed by
DehazeFormer-B from the original hazy image are better. Instead, our objective
NDVI error is able to match the subjective visual consistency better. We also
conduct preliminary subjective evaluation from both our technical and client
sides, and the results align with the SAGE-NDVI.

SAGE-NDVI at Other PhenoCam Locations. We also test SAGE-NDVI at different
PhenoCam locations, focusing on the crop types with few phenological periods
than alfalfa, such as corn and rice [7]. The NDVI values at those locations do
not have dramatic changes throughout the year. Table II shows similar observed
relationships among $\mathrm{\overline{e}}$ and two
$\mathrm{\overline{e^{\phi}}}$ values. However, due to the few phenological
periods and available hazy dates, the differences in NDVI values are not
noticeable as those at the alfalfa observation site.

Figure 2: Visualization of different PSNR and SAGE-NDVI results at the
observation site bouldinalfalfa [7] (red dot). Top: One clean ground image at
a _hazy_ date and two clean satellite images at the _adjacent_ dates. Bottom-
Left: Original hazy image. Bottom-Center: FFA-Net [9]. Bottom-Right:
DehazeFormer [10]. PSNR values and our new satellite-to-ground NDVI-based
errors of three bottom images are provided. For better visualization, the
brightness of all satellite images is increased with a fixed value.

##  V Conclusions

In this paper, we leverage the satellite-to-ground philosophy to propose a new
objective metric, SAGE-NDVI, for RS image dehazing evaluation. A public
phenology observation resource containing ground images is exploited to
calculate the vegetation index error between RS and ground images at a hazy
date. Our metric’s capability of appropriately evaluating various dehazing
models and conforming to human visual perception is demonstrated by extensive
experiments.

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