Analysis of Ensemble of Neural Networks and Fuzzy Logic

Classification in Process of Semantic Segmentation of Martian

Geomorphological Settings

Kamil Choromański

, Joanna Kozakiewicz

, Mateusz Sobucki

Magdalena Pilarska-Mazurek

and Robert Olszewski

Faculty of Geodesy and Cartography, Warsaw University of Technology, Plac Politechniki 1, 00-665 Warsaw, Poland

Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, prof. Stanisława Łojasiewicza 11,

30-348 Krakow, Poland

Faculty of Geography and Geology, Jagiellonian University, Gronostajowa 7, 30-387 Krakow, Poland

robert.olszewski@pw.edu.pl

Keywords: Deep Learning, Semantic Segmentation, Mars, CNNs, FIS, Aeolian Landscape.

Abstract: Deep learning analysis of multisource Martian data (both from orbiter and rover) allows for the separation

and classification of different geomorphological settings. However, it is difficult to determine the optimal

neural network model for unambiguous semantic segmentation due to the specificity of Martian data and

blurring of the boundary of individual settings (which is its immanent property). In this paper, the authors

describe several variants of multisource deep learning processing system for Martian data and develop a

methodology for semantic segmentation of geomorphological settings for this planet based on the

combination of selected solutions output. Network ensemble with use of the weighted averaging method

improved results comparing to single network. The paper also discusses the decision rule extraction method

of individual Martian geomorphological landforms using fuzzy inference systems. The results obtained using

FIS tools allow for the extraction of single geomorphological forms, such as ripples.

1 INTRODUCTION

Mapping of landforms on Mars using remote sensing

data has become one of the most important issues in

space exploration in recent years. The further

development in Mars exploration requires

preparation of detailed geomorphological maps. The

amount of high-resolution data acquired by Martian

orbiters and rovers increases very quickly, covering

vast regions of the planetary surface. Mapping of

these areas in a short period of time can be done only

using automatic methods. In this work, we present a

novel approach to map aeolian landscape on Mars

using deep learning analysis. We focused on

combining multiple models trained on multisource

https://orcid.org/0000-0002-2047-7434

https://orcid.org/0000-0002-9264-8298

https://orcid.org/0000-0002-2958-8966

https://orcid.org/0000-0001-9494-9863

https://orcid.org/0000-0003-1697-9367

data (namely orbital imagery, derivatives of elevation

models and in situ data from rover camera), taking

advantage of ensemble methods. We also analysed

use of fuzzy inference systems in the process of

decision rule extraction and individual landforms’

classification.

2 RELATED WORKS

2.1 Martian Geomorphological

Landforms

Mars is a desert planet covered by many aeolian

(wind related) landforms, such as dunes or ripples. In

184

Choroma

nski, K., Kozakiewicz, J., Sobucki, M., Pilarska-Mazurek, M. and Olszewski, R.

Analysis of Ensemble of Neural Networks and Fuzzy Logic Classiﬁcation in Process of Semantic Segmentation of Martian Geomorphological Settings.

DOI: 10.5220/0011315200003277

In Proceedings of the 3rd International Conference on Deep Learning Theory and Applications (DeLTA 2022), pages 184-192

ISBN: 978-989-758-584-5; ISSN: 2184-9277

this work, we will focus on ripples as they are the

most common features in the Martian landscape.

Ripples are sand ridges ranging from centimetres to

meters and formed by wind perpendicular to their

crests. Automatic detection of areas covered by large

(> 20 cm in height) ripples are particularly important

for Martian investigation, as ripples often become

traps for wheeled vehicles (e.g., Squyres et al. 2006).

We will focus on the area of Meridiani Planum

(Hynek et al., 2002), which is one of the best-known

regions on Mars due to extensive in situ and orbital

investigations. This is a flat region covered by impact

craters and ripples (see e.g. Fenton et al., 2015). In

this area there are three distinct geomorphological

settings: (i) ripple fields – ripples on sand covers, (ii)

ripples on bedrock - areas where extensive erosion led

to exposing the bedrock in spaces between ripples,

and (iii) sand-gravel covers – extensive sand-gravel

sheets. Two other (not aeolian) landforms

characteristic of this region are impact craters and

structural lineaments.

2.2 Automated Segmentation of

Geomorphological Landforms

First approaches to automated segmentation of

Martian geomorphological landforms were proposed

in the beginning of 21

century (Stepinski et al., 2006;

Stepinski et al., 2009; Gosh et al., 2010). Well-known

machine learning algorithms were utilized for this

task (Stepinski et al., 2006). As Martian data volumes

and computing power increased, Deep learning (DL)

algorithms have begun to be used. Semantic

segmentation based on DL approach was utilized both

for impact craters (Lee, 2019; Bandeira, 2012;

Stepinski et al., 2006; Stepinski et al., 2009) and

landforms (Palafox et al.,2017; Barrett et al.,2022;

Nagle-Mcnaughton et al., 2020). DL techniques have

been employed successfully on the most widely used

imagery and elevation data sources collected from

Mars: Mars Orbiter Laser Altimeter (MOLA)

(Stepinski et al., 2006), High Resolution Stereo

Camera (HRSC) (Lee, 2019), Context Camera (CTX)

(Palafox et al., 2017) and High Resolution Imaging

Science Experiment (HiRISE) (Wilhelm et al., 2020).

There are also works taking advantage of images

taken by Martian roves for the purposes of

segmentation and detection of terrain forms

(Wagstaff et al., 2018).

So far, a study by (Rothrock et al., 2016) is the

only one using orbital and rover data in one

workflow. However, these two data sources were

used in separation and for different purposes (orbital

data was used for search of optimal landing site for

future rovers and rover data for wheel slip

predictions). In this work, we propose an approach

that utilizes multiple data sources for semantic

segmentation of geomorphological settings basing on

deep learning multi-source data fusion methods

proposed by (Cao et al., 2018).

2.3 Decision Fusion

There are numerous works proving that fusing

decision outputs from various neural network models

may improve accuracy and generalizability

comparing to use of a single model. Ensemble of

neural networks was used with success both for

recurrent (Zhou et al., 2018) and convolutional neural

networks (Manna et al., 2021; Han and Jeong, 2020).

Simple methods such as averaging, weighted

averaging or majority voting are being used in many

works. Some researchers are developing also more

sophisticated approaches (Manna et al., 2021).

3 EXPERIMENTAL DESIGN

3.1 Data Sources and Pre-processing

In our investigation we used orbital and in situ data,

simultaneously. We used the high-resolution orbital

images of the Martian surface obtained by HiRISE

onboard the NASA Mars Reconnaissance Orbiter

mission. The orbital data were supplemented by in

situ data obtained by the Opportunity rover, one of

two rovers of the NASA Mars Exploration Rover

(MER) mission. Opportunity explored the western

part of Meridiani Planum between Eagle and

Endeavour craters in years 2004-2018.

The HiRISE and Opportunity Rover data were

downloaded from the Planetary Data System (PDS).

To study aeolian landforms from the planetary

surface we focused on the Navigation Camera

(NAVCAM) data. The NAVCAM system consisted

of two stereoscopic cameras (Maki et al., 2003).

3.1.1 HiRISE Data

We used eight images to produce four stereo pairs and

to create the Digital Terrain Model (DTM) that

covered the entire Opportunity rover traverse:

ESP_018846_1775-ESP_018701_1775,

ESP_051245_1780-ESP_020758_1780,

ESP_016644_1780-ESP_037109_1780,

PSP_001414_1780-PSP_005423_1780.

Analysis of Ensemble of Neural Networks and Fuzzy Logic Classiﬁcation in Process of Semantic Segmentation of Martian

Geomorphological Settings

185

The HiRISE data were processed using NASA Ames

Stereo Pipeline (ASP) (version v2.6.2) and Integrated

Software for Imagers and Spectrometers (ISIS)

(version 3.6.0). From the HiRISE stereopairs four

DTMs were produced. Selected HiRISE images were

orthorectified using the DTMs to remove the impact

of terrain height on the geometry of the images.

Finally, the orthoimages and the DTMs were

mosaicked into continuous raster file, so-called

mosaic, which covered an area of approximately 87

square km and had a spatial resolution of 27 cm.

Using elevation-DTM data from HIRISE images, the

authors also developed derived relief models:

topographic roughness index (TRI), topographic

positioning index (TPI). Various curvature models,

e.g., transverse, longitudinal, were also determined

from the DTM analysis.

3.1.2 NAVCAM Data

We stitched NAVCAM images into spatially

referenced panoramas basing on NAVCAM images

metadata. Radiometric differences between

panorama segments were reduced using histogram

matching technique. The final panoramas were

cylinder-projected. Areas, where images were

overlapping were merged by selecting every second

pixel of each image. The starting orientation for each

panorama is north to ensure consistency for the

analysis of all panoramas used in the research

process. The resolution of a single output panorama

is 2048×6992.

Finally, semantic features from each panorama

were extracted with the use of Places-CNN network

pre-trained on Places365 dataset (Zhou et al., 2017).

Each panorama was converted to 2048-dimensional

feature vector which was reduced to 50 dimensions

by using principal component analysis (PCA)

method. To spatially align in-situ data with orbital

data we interpolated feature vectors onto spatial

domain using Nadaraya-Watson interpolation

algorithm.

3.2 Semantic Segmentation Network

We use a single architecture of a convolutional neural

network (CNN) to train a few independent models in

order to create semantic segmentation of terrain.

Different data sources were used as the input for these

models.

A CNN encoder-decoder network consisting of

two encoders and one decoder was used to train

models employed in this research. Both encoders of

the network were based on VGG-16 architecture

(Simonyan and Zisserman, 2015) with last (fifth)

layer of original VGG-16 replaced by two

convolutional layers. First encoder was used to

extract semantic features from orbital data (imagery

data and derivatives of elevation model concatenated

into multi-layer raster are fed into this part of model).

Second one was utilized to extract in-situ features.

Every last layer of each block of the second encoder

was concatenated with corresponding layer of the first

encoder. The decoder block was also based on VGG-

16 (without the last block, with an up-sampling layer

instead of max-pooling and with reduced number of

parameters). Semantic segmentation of orbital image

is generated as an output from decoder block. The

architecture was implemented using a TensorFlow

framework (Martin, 2015).

3.3 Averaging

Two averaging methods were utilized in this research:

i) simple averaging of selected models decision

certainty, ii) weighted averaging.

In the first case, class decision certainty values of

each model for each data point (pixel) x

were

summed and divided by number of models (n):

𝑥̄ =

∑

𝑥







𝑛

(1)

Weighted averaging x

was performed by

assigning weight w

to each of n models based on their

performance on test dataset (assed by overall

accuracy). The final decision certainty was computed

as the weighted average for each data point x

𝑥̄



∑

𝑤



∗𝑥







∑

𝑤







(2)

Finally, class with the highest fused decision

certainty value was selected as valid for a given data

point.

3.4 Fuzzy Logic

Using deep machine learning methods allows to

obtain reliable classification results, however, the

limitation of this approach is the so-called black box

associated with the use of neural networks. In order

to obtain explicitly defined (yet intentionally fuzzy)

decision rules for classification, the authors of this

paper have applied fuzzy inference systems (FIS).

This approach allows the extraction of decision rules,

but requires prior training of the neural network and

obtaining reliable parameters of membership of

pixels to geomorphological setting classes.

DeLTA 2022 - 3rd International Conference on Deep Learning Theory and Applications

186

4 EXPERIMENTS AND

ANALYSIS

4.1 Individual Models Training

The network architecture described above was used

to train a few semantic segmentation models using

different input data combinations (Table 1).

Table 1: Summary of data sources used for each

experiment.

Experiment no. Data used

1 orbital only

2 orbital + TPI/TRI

3 orbital + curvatures

4 Orbital and in situ fused

5 Orbital and in situ fused +

TPI/TRI

6 Orbital and in situ fused +

curvatures

Each network was trained on the same amount of

data, namely: 523 256x256 tiles of each data type for

training and 108 tiles for testing. As the training

dataset was not large, offline data augmentation

techniques were utilized in order to enlarge dataset.

Moreover, both VGG-16 encoders were pretrained on

the ImageNet dataset.

In our analysis, we used a system of four classes

of Meridiani Planum geomorphological setting:

1) ripple fields,

2) ripples on bedrock,

3) sand-gravel covers,

4) others, neglected in results analysis

4.2 Averaging

Two approaches of results averaging were tested: i)

simple averaging with use of chosen models, and ii)

weighted averaging.

Taking into account individual models results a

couple of variations of models were selected for

simple averaging. Table 2 summarizes experiments

conducted to check the effectiveness of simple

averaging technique.

Second approach to averaging is to use weights

assigned to each model. We used ranked-based

approach to weighting where constant weight values

were assigned to models basing on their individual

accuracy scores (see point 5.1). Table 3 shows

weights assigned to each model.

Table 2: Summary of experiments carried out with use of

simple averaging technique.

Experiments no. used for

avera

(

see Table 1

)

1,2,5,6

5,6

2,5

2,3,4,5

4,5

4,5,6

1,2,3,4,5,6

Table 3: Weight value assigned to each experiment basing

on its individual results.

Experiment no. (see

Table 1)

Weight value

1 0.05

2 0.20

3 0.10

4 0.15

5 0.50

6 0.00

As one can observe, experiment no. 6 was

excluded from multi-model decision process due to

its significantly worse individual performance.

4.3 Fuzzy Logic based Approach

The use of FIS systems allows for the extraction of

fuzzy decision rules and the development of an

efficient inference system based on multiple

variables. In this work, Takagi-Sugeno-Kang fuzzy

inference FIS models (Sugeno, 1985) were used. This

approach uses singleton output membership functions

that are either constant or a linear function of the input

values. Three FIS models were developed to classify

Martian aeolian settings. A fuzzy tree - Aggregated

Structure was also constructed. In this approach, input

values are incorporated as groups at the lowest level,

where each input group is fed into a FIS (Siddique,

2013). The outputs of the lower level fuzzy systems

are aggregated using the higher level fuzzy systems.

In this work, for the simplicity of the model, only two

explanatory variables: image value (IMG) and TRI,

and several simple linguistic variables: low, medium,

high, possible etc. were used.

Analysis of Ensemble of Neural Networks and Fuzzy Logic Classiﬁcation in Process of Semantic Segmentation of Martian

Geomorphological Settings

187

Figure 1: Aggregated Fuzzy Tree.

4.4 Evaluation Metrics

To assess results of the conducted experiments both

global and per-class evaluation metrics were used,

namely: overall pixel accuracy, per-class precision,

recall and F1 score. Also, averaged values of per-

class precision, per-class recall, and per-class F1

score were used to assess overall performance of

selected approaches.

Overall pixel accuracy:

acc=





(3)

Where 𝑡𝑟 is the trace of the matrix, 𝐶𝑀 is the

confusion matrix, and 𝑁 is the number of pixels in all

classes.

Per-class precision, P

∑

j=1

(4)

Per-class recall, r

∑

j=1

(5)

Where c represents the index of a given class in the

confusion matrix, n is the number of all classes, and

is the 𝑖th row and the jth column element in the

confusion matrix.

The per-class F1 score takes precision and recall

metrics into account:

F1=

2*p

(6)

5 RESULTS

Predictions on test dataset of individual and

ensembled models were compared with use of

evaluation metrics described in chapter 4.4.

5.1 Individual Models

Models trained using different data sources

combinations (Table 1) varied between 91.88% and

95.94% in terms of overall accuracy on test dataset.

Best results regarding majority of metrics were

achieved in the experiment which used both in situ

and orbital data along with TPI and TRI rasters

(experiment no. 5).

Figure 2 shows results achieved by the best model

with comparison to the per-metric best and the per-

metric worst result. It can be observed that not in

every case best individual model gives the best result

for each of the tested classes.

Figure 2: Precision, recall and F1-score comparison of best

individual model and best and worst results from all models

for each class.

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5.2 Ensemble Techniques

The results of simple averaging experiments using

different models (Table 2) are visualized below

(Figure 3). Mean value of precision, recall and F1

score was computed basing on results for individual

classes. Best overall simple averaging results were

achieved using combination of two models: 4 and 5.

However, the results were better only in terms of

precision metric when compared to best individual

model (no. 5). Also, overall accuracy of simple

averaging methods is lower than achieved by model

no. 5. (see Figure 5).

Figure 3: Mean precision, recall and F1-score comparison

of best individual model (5) and multiple models combined

with use of simple averaging technique.

Weighted averaging technique was tested using

weights introduced in Table 3 and compared to

selected results from simple averaging and best

individual model. Figure 4 shows comparison of

achieved precision, recall and F1-score. Figure 5

compares overall accuracy of each model.

Figure 4: Mean precision, recall and F1-score comparison

of best individual model (5), selected multiple models

combined with use of simple averaging technique and

models combined with use of weighted averaging

technique.

Weighted approach proved to give better or equal

results when compared to any individual model in

terms of precision, recall and F1-score. Overall

accuracy is also better than any other approach tested

in this research and achieved level of 96.10%.

Figure 5: Overall accuracy of best individual model (5),

selected multiple models combined with use of simple

averaging technique and model combined with use of

weighted averaging technique.

The weighted averaging technique produces results that

visually fit well with manual recognition of the

geomorphological settings. It enables distinction of the

ripples on bedrock class in areas with small share of

bedrock surface. Subsequently, it tends to overlook small,

isolated bedrock outcrops, which prevents creation of

small, misleading artifacts (Figure 6). The weighted

averaging results tend to have lower, however still

conclusive, decision certainty value in ambiguous areas

than some other approaches. It opens a prospect for better

multi-aspect terrain recognition using fuzzy logic.

5.3 Fuzzy Logic Classification

In the present study, an aggregate decision tree was

developed to detect individual Martian

geomorphological landforms. Each of the three

source Sugeno trees allows for classification of a

distinct type of landform (e.g. ripples) and extraction

of decision rules. For example, first FIS (Figure 1)

component of the FIS tree allows classification of

ripples based on two decision variables - IMG and the

morphometric parameter TRI. The nonlinear FIS

decision surface is shown in Figure 7. The operation

of this FIS tree is based on only three fuzzy decision

rules:

- if IMG is medium and TRI is medium then ripple

is certain

- if IMG is low and TRI is low then ripple is

possible

- if IMG is high or TRI is high then ripple is

impossible

Analysis of Ensemble of Neural Networks and Fuzzy Logic Classiﬁcation in Process of Semantic Segmentation of Martian

Geomorphological Settings

189

Figure 6: Exemplary part of classified terrain; orthoimage

(A), manual labelling (B), individual model no.5 (C),

simple averaging: model 4 and 5 (D), simple averaging: all

models (E), weighted averaging (F), decision certainty

value plot for a chosen profile (G), classification result

along the profile for different approaches (H).

The results obtained are (in terms of accuracy)

much worse than the classification based on neural

networks (71.23% classification correctness), but this

is partly due to the way the results are granulated

(Figure 8). The FIS system classifies as "ripple" not

so much the areas of ripple occurrence, but individual

ripples. The areas in between ripples have been

assigned to a different feature class: non-ripples.

Thus, the obtained results allow both to "reveal" the

decision rules and open new research directions in the

field of neuro-fuzzy classification.

6 CONCLUSIONS

This research has shown that use of deep learning

methods combined with multisource data have big

Figure 7: Nonlinear fuzzy decision surface.

Figure 8: FIS classification of ripples using decision

variables: image value and TRI.

potential for the highly accurate, automated

geomorphological Martian settings segmentation.

These results may be improved further with use of

ensemble methods such as weighted averaging.

Fusion of multiple model decisions with varying

accuracy may bring improvement in comparison to

use of one model. Weighted averaging proved to give

better results than simple averaging with regard to

model decision fusion for semantic segmentation of

geomorphological settings. Automated optimization

of weight values may further increase system

accuracy and such approach will be investigated in

future.

The use of deep learning machine learning

methods allows for the correct classification of

aeolian forms on Mars and, consequently, for the

development of an implicit knowledge base acting on

the "black box" principle. The use of fuzzy logic

allows the extraction of decision rules which explain

why a given pixel has been classified into the specific

geomorphological setting class. The decision fuzzy

rules provide an understanding of the multifactorial

reasons for classifying pixels into a given category

and the development of an explicit knowledge base.

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Subsequently, the FIS system enables individual

forms (e.g. ripples) recognition. These issues will be

further investigated by the authors of this paper.

ACKNOWLEDGEMENTS

Funding: The work was funded by the Anthropocene

Priority Research Area budget under the program

"Excellence Initiative – Research University" at the

Jagiellonian University and by POB Research Centre

Cybersecurity and Data Science of Warsaw

University of Technology within the Excellence

Initiative Program - Research University (ID-UB).

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