A Tool for 3D Representation of the 2D Thermographic Breast

Acquisitions

Eudoxia L. S. Moura

1,3 a

, Gleidson M. Costa

2 b

, Tiago B. Borchartt

2 c

and Aura Conci

3 d

Federal Institute of Education, Science and Technology of Rond

onia, Ariquemes, Brazil

Department of Informatics, Federal University of Maranh

ao, Brazil

Institute of Computing, Federal Fluminense University, Brazil

Keywords:

3D Breast Models, Thermography Images, Edge Detection.

Abstract:

This study enhances the three-dimensional reconstruction of the breast surface from two-dimensional thermal

images at ﬁve different angles. The process involves the use of a convolutional neural network U-net for image

segmentation, extraction of relevant points and curves, geometric transformations to add a dimension to the

curves, and modeling with Rational Non-uniform B-splines Surface (NURBS). The work aims to improve the

previously proposed algorithm by making modiﬁcations to the rotation points and cutting regions to achieve a

more comprehensive breast contour. In a quantitative evaluation of the results, comparing thermal images and

Structured Light Scanner images with the Costa’s and new algorithm, we observed that, concerning scanning,

the Costa’s algorithm has an average of 37.07% with a standard deviation of 6.27, while the new algorithm

exhibits an average of 14.06% with a standard deviation of 7.28. When compared to thermal images, the

Costa’s algorithm has an average of 37.47% with a standard deviation of 7.24, whereas the new algorithm

shows an average of 14.77% with a standard deviation of 7.37. These results indicate that the new algorithm

signiﬁcantly improves the representation of the breast shape compared to the Costa’s algorithm.

1 INTRODUCTION

Breast cancer is the most common type of cancer

among women and the second most death related

(Bray et al., 2018). With an early diagnosis and

proper treatment in the beginning, it can be curable

(Venkataramani et al., 2015; Koay et al., 2004). There

are many possible exams to detect a breast cancer, but

the mammography is the most popular (Otmani et al.,

2024). Besides being an invasive exam, it is consid-

ered the gold standard (Koay et al., 2004).

The thermography is a non-invasive exam that

analyses the heat distribution over the body (breast

region in this case) (Pricigalli et al., 2023). It is acces-

sible, fast, propitiates very early detection due to the

possibility of detection of the beginning of the huge

cellular multiplication of the cancerous are and its the

usage on dense breast for young woman observations

(Lanisa et al., 2014; Jockers, 2019).An abnormal heat

https://orcid.org/0000-0003-1911-1555

https://orcid.org/0009-0006-0429-6074

https://orcid.org/0000-0002-3709-8385

https://orcid.org/0000-0003-0782-2501

distribution on the images can be related to the cancer

formation, as long as it can increase the metabolism

of the area. But computational tools are necessary to

help specialists on decision about whereas there is a

benign or malignant nodule in a mamothermograpy

examination (Borchartt, 2013).

The diagnosis of thermography exams is made

by analyzing the captured images looking for abnor-

mal features. (Raghavan et al., 2023). Thermogra-

phy images follows the protocol proposed by (Silva

et al., 2014) using static and dynamic data acquisi-

tions. Twenty images are captured after cooling the

patient while the person body surface is returning to

the environmental temperature (natural warm) in the

dynamic data acquisition protocol. Moreover, only

ﬁve images are taken by using the static protocol.

However, static acquisitions are taken positioning

the patient in ﬁve different angle in relation to the

camera frontal direction position. In order to have a

good observation of the breast the angles between the

coronal body frontal plane and the camera must be 0

+45

, -45

, 90

and -90

. These directions form the

named frontal view (0

), positive and negative oblique

views and positive and negative side (90

and -90

)

138

Moura, E., Costa, G., Borchartt, T. and Conci, A.

A Tool for 3D Representation of the 2D Thermographic Breast Acquisitions.

DOI: 10.5220/0012469500003660

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2024) - Volume 4: VISAPP, pages

138-146

ISBN: 978-989-758-679-8; ISSN: 2184-4321

views.

Each speciﬁc direction and view is important to

increase the possibility of identiﬁcation of an breast

abnormalities. Side images are as important as frontal

images are (Jeyanathan et al., 2018), and an abnor-

mality not seen on frontal image can be seen on a side

acquisition. Moreover, they allow not only a best view

but the possibility of combine the information from all

images captured separately (Silva, 2010).

Mainly when for more complex diagnosis one

needs to make correlations among the images. How-

ever in such case for combination of all views, its is

necessary to have a tools for make easier to have a

unique form to visualize all ﬁve images captured in

one static exam. The aim of this work is to present a

methodology developed to unify the 5 views in a 3d

model properly. Using this, specialist can begins to

analyze the model without the need of mental combi-

nation or no longer necessity to correlate the images

manually (Costa et al., 2023).

In this paper, we propose a methodology to make

a tool that automatic constructs three-dimensional

breast models based on the ﬁve images from static

thermography exams (i.e. images of same patient

breasts from different angles). Data used were ac-

quired under a consent of the ethics committee of our

university hospital and ministry of health, being pub-

licly registered. To accomplish the objective, it is nec-

essary to make breast segmentations; extract the key

points and relevant curves from the images; correlate

spatially the key points; correctly positioning and ori-

entation of the curves; increase the dimensional in-

formation of the edge points; create a rational smooth

surface and include texture mapping to render the syn-

thetic tri dimensional model.

In the next section, a review of related works on

breast modeling is explored. After, the approaches

used in this study is presented in Section 3, outlin-

ing the procedures and techniques used for the three-

dimensional modeling of breasts. Section 4 discusses

the results, highlighting the contributions and impli-

cations of our propositions. Section 5 compares the

results, presenting conclusions and suggestions for

future research in this scope.

2 RELATED WORKS

This section presents some works on 3D modelling of

the breast in chronological order.

Silva (2010) developed a three-dimensional re-

construction method for breasts using thermal im-

ages in different positions. The algorithm utilizes

body contours, curves ﬁtted by least squares, and

the NURBS (Non-Uniform Rational B-Splines) tech-

nique to generate 3D meshes. A software was im-

plemented to create three-dimensional models from

infrared exams, highlighting variations between the

actual body and the generated model. However, the

study did not focus on 3D visualization tools for ex-

ams (Silva, 2010) .

Ciechomski et al. (2012) developed a computa-

tional tool for the three-dimensional reconstruction of

the breast from digital photos taken also at three an-

gles (frontal, right lateral, and left lateral). The gener-

ation of the 3D model is based on the identiﬁcation of

points provided by the user in the 2D images. In this

approach some measurements must be manually in-

cluded, as the distance between the nipples and from

the nipple to the infra mammary fold.

As the main goal of Ciechomski et al. (2012)

is surgery planning, the physician carries out the

planning must deﬁne positions and diameters of the

implants for simulation. The software facilitates

the three-dimensional visualization of the breast out-

come. However, it is worth noting that the software

requires user intervention (Ciechomski et al., 2012) .

Viana (2016) created a 3D representation of the

female breast using points from infrared images gen-

erated by a computational program. A MATLAB



program corrected coordinates for breast reconstruc-

tion, and the resulting wireframe was exported for

Computational Fluid Dynamics (CFD) preprocess-

ing. The breast’s internal structure was modeled with

3D volumes, replacing lobes, lactiferous ducts, and

anomalies from patient examinations. Tools such

as Gambit

T M

, DesignModeler

, and MeshingTM

prepared the geometry for temperature calculations,

while Fluent

 software calculated temperature val-

ues at mesh points (Viana, 2016).

Costa (2020) introduced an innovative algorithm

for automated 3D breast model construction, utiliz-

ing ﬁve images per patient: frontal, oblique right lat-

eral, oblique left lateral, total right lateral, and total

left lateral. Automatic segmentation employed the

U-net convolutional neural network across all views.

Nine curves, six corresponding to main images and

three auxiliary, were created considering different an-

gles. These curves were B-spline adjusted, and model

surfaces were generated using Non-Uniform Ratio-

nal B-Splines (NURBS) from the generated points.

While the model received majority approval from 15

experts, some noted shortcomings included lack of

edge smoothing, decentralized nipple texture, model

ﬂattening, and inadequate depth representation in pa-

tients with larger breasts (Costa et al., 2023).

Saha (2023) addresses the challenge of visualizing

the complete 180

mammary region using only 2D

A Tool for 3D Representation of the 2D Thermographic Breast Acquisitions

139

thermal images, reconstructing 3D thermal images of

the breast surface from 2D thermal images captured

at different viewing angles (Saha et al., 2023). The

method consists of ﬁve main steps: foreground seg-

mentation, 3D mammary silhouette generation, 2D

visualization generator, loss function, and overlap

function. The segmentation process is applied using

the Otsu binary segmentation method to each of the

ﬁve thermal views captured at different angles, result-

ing in corresponding 2D mammary silhouettes. These

silhouettes are utilized in a CNN encoder-decoder ar-

chitecture to generate the 3D mammary silhouette,

which is then employed to obtain random projections

of the silhouettes. The loss function minimizes the

distance between the generated 2D projections and

the actual silhouettes of the input 2D thermal images,

and the overlap function maps the input temperature

values onto the generated 3D silhouette.

3 METHODOLOGY

We here present details of how the three-dimensional

breast surface is constructed from ﬁve two-

dimensional thermographic images obtained at

the angles of 0

, 45

, 90

, -45

, and -90

. Basically,

the reconstruction algorithm addresses ﬁve main

steps: (1) segmentation of the 5 original 2d images,

extraction of relevant 2d points and plane curves

(i.e. in the plane of each image), (2) geometric

transformations of these 2d to 3d points and plane

curves to theirs 3d orientation and position; (4)

increasing the dimensional information of the control

points to allow 3d borders , (5) 3d surface modelling

by using Rational Non-uniform B-splines Surface

(NURBS) for breast representation of volunteers, and

its rendering.

This works is dedicated mainly to correct some

previous drawn-back of the NURBS construction, it

is in step 2. We here suggest a set of modiﬁcations

in the rotations points and cutting regions to achieve

more complete and smooth breast representations.

3.1 Image Acquisition

This work uses a public data from (Silva et al., 2014)

and available online at Visual Lab DMR website (vi-

sual.ic.uff.br/dmi). The images have a resolution of

640x640 pixels , and are achieved with a thermo-

graphic camera FLIR

 SC620. The acquisition pro-

tocol captures 25 images for each patient, 20 are un-

der induced superﬁcial temperature modiﬁcation (dy-

namic protocol), and 5 under constant temperatures

(static protocol) (Silva et al., 2014). Only the static 5

images are used on this work methodology.

Each image represents a different angle between

the camera frontal direction and the patient coronal

plane. Frontal view captures the body plane in the

same direction of the frontal camera plane, that is the

angle between them is 0

. Figure 1 ﬁrst image shows

this view. The oblique on the right lateral view cap-

tures the body rotated to 45

to the right around the

cranium- caudal body axis: Figure 1 second image

shows this view. Oblique on the left lateral view , ori-

entated for acquisition the body rotated around 45

the left in this axis (Figure 1 fourth image shows this

view). The right lateral view puts the body rotated to

to the right before acquisition (Figure 1 third im-

age shows this view) . The left lateral view rotated to

to the left the body as can be observed in the ﬁnal

image of Figure 1).

The proper functioning of the image processing

and edge detection algorithm depends on ensuring

that the 5 input images meet speciﬁcations, being cap-

tured without blur or other errors. In lateral images,

it is crucial that the contour of the breasts is visible.

Examinations revealing anomalies in breast shape are

considered only if the visibility of one breast’s silhou-

ette is not impaired by the other. A preprocessing step

is incorporated to eliminate inputs and preserve the

accuracy and reliability of the algorithm’s output.

3.2 Preprocessing

Initially, a simple conversion is performed from tem-

perature data stored for the images to the gray scale,

which operates with only one channel per image. The

conversion is expressed by Equation 1, where, for an

image P, P

i j

represents the temperature value of a

point (i, j) of the stored image array. The minimum

and maximum temperatures in a matrix are denoted

by min and max, respectively. The result, m

i j

, cor-

responds to the new gray scale value of each pixel,

allowing good contrast and visibility of the tempera-

tures:

i j

= 255 ×

Pi j − min

max − min

(1)

In the prepossessing step, the dimension of the

gray scale images is also transformed from 640×480

to 256x256. These new images will be used in the

automatic segmentation process.

The frontal view images of the exams will be used

exclusively for the texture mapping in the rendering

step of the three-dimensional model. To obtain a color

representation of this view, their pixels are converted

from gray scale to the RGB (Red, Green, Blue) color

system, following the Look Up Table (LUT) of the

FLIR Rain palette color levels.

VISAPP 2024 - 19th International Conference on Computer Vision Theory and Applications

140

Figure 1: Five images of an thermography exam with the body and camera at ﬁve positions. Frontal (0

), oblique on the right

lateral (45

), right lateral (90

), oblique on the left (-45

) and left lateral (-90

) (ﬁrst line). Example of automatic segmentation

output using a U-Net architecture and the learned hyper-parameters (second line).

3.3 2D Border Segmentation

The segmentation of the region of interest (ROI) of

the breasts is performed using a deep learning tech-

nique, speciﬁcally the architecture of a Convolutional

Neural Network (CNN) named U-Net (Ronneberger

et al., 2015) (Dalmia et al., 2018).

Considering all the data set of patients, a subset

used, 109 (78%) exams were used for training the nets

and 31 (22%) were separated from the database for

testing. The training used 100 epochs in batches of

2 with 50 epochs. Net weights are initialized with

normal distribution of random values. Each convo-

lution uses the rectiﬁed linear unit activator (ReLU)

function to allow passing values that are greater than

zero (0). Adam optimizer with learning rate 1x10

−4

used (zhixuhao, 2023). This allows the region of the

breasts to be separated (i.e. segmented) from the rest

of the image, as shown in Figure 1. In this ﬁgure the

ﬁrst line of images represents the gray scale input to

the U-net and the second line the segmented results.

After segmentation with the U-net, it is necessary

to perform a ﬁltering step to remove unnecessary ar-

eas. This is achieved by applying a grayscale thresh-

old using the Suzuki approach, transforming the im-

age into binary (Suzuki et al., 1985). Subsequently,

only the area with the highest number of pixels in

each direction is retained. The Canny edge detection

method is then applied to obtain only the largest con-

nected edges in each direction. This process is de-

tailed in (Costa et al., 2023).

3.4 Relevant Edge

Identifying relevant edges and points in each view

(Figure 2) is crucial for understanding breast shape in

width (front views) and depth, thickness, and height

(lateral obliques and side views). These elements are

later used to generate 3D information, transforming

plane curves into spatial ones for surface modeling.

The infra-mammary curve holds particular impor-

tance in this process and serves as a reference to po-

sition other curves. Through the identiﬁcation of rel-

evant edges and points in each view, a uniﬁed 3D co-

ordinate system is established. The four-step process

is employed to identify these relevant edges.

Initially, the algorithm locates points in the lower

region of each edge by searching for the ﬁrst pixels

from bottom to top in the output of the previous step.

This ensures that only the pixels closest to the bottom

of each of the ﬁve edges are stored. Then, a verti-

cal search is conducted, starting from the right side

of each image. Unlike the bottom search, the lateral

search involves scanning each ﬁnal edge pixel from

the right end to ﬁnd the closest pixels on this side.

The same approach is applied to deﬁne the left edge,

ﬁnding the closest pixels on this side.

In the ﬁnal step, pixels from the ﬁrst step that are

found three times in steps 2 and 3 are removed. This

ensures the exclusion of points present in the relevant

edges on the right and left sides. The resulting points

constitute the basis for subsequent 3D modeling. This

process is detailed in (Costa et al., 2023).

A Tool for 3D Representation of the 2D Thermographic Breast Acquisitions

141

Figure 2: Identiﬁcation of the relevant edges and key points of each direction.

Figure 3: Relevant edges in a two-dimensional plane: Red

color represents the points from the frontal view; the two

tones of Green color represent the points from the oblique

views; magenta and blue colors represent the points from

the side view.

3.5 Key Points of Breast Edges

Extraction of each view relevant breast edges points

for each examination angle (or for each view) must be

done. For each 2d curve of the last step, this process

consists of the identiﬁcation of three points named P1,

P2 and P3. Figure 2 shows these points in the images

resulting from segmentation of relevant edges in order

to better identify their meanings. These points belong

to the lower single edge of the 5 views, that is, from

ﬁnal step of the previous subsection.

On the 0

, 45

and -45

images, a point is found

at the junction of the infra-mammary curves, in the

center of the body, this is named P2, Other two points

correspond to the inﬂections of the infra-mammary

curves on the right (named P1) and left (P3). For side

images of 90

and -90

, the beginning and end of the

curve are identiﬁed, they are named P1 and P3, and

presented on Figure 2(d). For these view, a third point

(named P2) is deﬁned by lowest point of these curves.

3.6 Geometric Transformation and 3D

Representations

After segmenting the breast limits in various direc-

tions in the 2D plane, key points identiﬁed in the pre-

vious step play a crucial role in translating and rotat-

ing the 2D curves to their correct positions in a three-

dimensional space.

A 3D coordinate system is employed, where the X

and Y axes align with the 2D image’s horizontal and

vertical directions, respectively, and the Z-axis is de-

termined by the cross product of X and Y. The trans-

lation of curves involves moving them to the identi-

ﬁed key points, and subsequent rotation is based on

the view directions, creating a 3D representation for

surface generation.

Curves, such as those from 45

and -90

views,

undergo rotation by their respective angles. For in-

stance, curves from 45

and 90

views are translated

to point P3, while curves from -45

and -90

views

are moved to point P1 on the frontal contour (see

Figure 4). This results in rotated curves with di-

verse 3D coordinates based on their rotation angles.

To enhance the 3D representation, auxiliary contours

are created by replicating contours from 45

and -

views to new positions, forming curves rotated

by 135

and -135

(which rotate at around P3 and P1,

respectively). These contribute to the formation of an

internal curve resembling a valley between two moun-

tains relief. Figure 4 displays these curves. After this

step, the algorithm eliminates all points located above

the zero point on the Z axis, revealing only the surface

of the breast (see Figure 5).

Figure 4: The main curves after their translation and rota-

tion and the auxiliary curves at 135

and -135

, in yellow

and red, included for modeling the surface of the breast re-

gions.

VISAPP 2024 - 19th International Conference on Computer Vision Theory and Applications

142

3.7 Surface Modelling

So far, six curves that play a crucial role in determin-

ing the breast shape have been identiﬁed. In addition

to these, three more curves are incorporated to com-

pose the model, representing the lateral and central

proﬁle of the body. These curves are derived from the

image, with the ﬁrst capturing the left contours,

the second capturing the right contours, and the cen-

tral curve generated by connecting the P1 points to a

straight line to the top of the image. This process re-

sults in a total of nine curves: (1) right frontal curve,

(2) left oblique lateral curve, (3) total lateral (right 90

angle) curve, (4) left oblique auxiliary curve, (5) cen-

tral auxiliary curve, (6) right oblique auxiliary curve,

(7) total lateral (left 90

angle) curve, (8) right oblique

curve, (9) left frontal curve. Figure 5 shows all these

curves.

Figure 5: The set triangular mesh limit points of generated

curves parallel to the cranium caudal body direction used

for rendering the ﬁnal surface.

These nine 3D curves are initially described by all

their points (raster format). However, for better de-

scription and surface generations, they must be trans-

formed into vector form, i.e., through mathematical

expressions.

As the number of points on each of these curves is

different, an adjustment is used before these. They are

normalize for represent the same number of control

points for each curve. The B-spline function imple-

mented in (Bingol and Krishnamurthy, 2019) is em-

ployed for this purpose.

The nine (9) B-Splines curves (in blue) and

NURBS Surface created are shown in Figure 5 by

green dots. They are represent the vertices of the tri-

angles that generated the mesh, obtained after apply-

ing a generator of the surface by NURBS (Azevedo

and Conci, 2003) and delete all positive points (Costa

et al., 2023). The ﬁnal red shaded surface of these

process can be observed in Figure 6.

Figure 6: Output of Costa’s algorithm showing smaller

breast volume than the patient’s breast.

4 SURFACE IMPROVEMENTS

For the surface, only the curves representing the

breast shape are necessary. For this reason, Costa’s

original algorithm discards points that have positive

Z-axis coordinates (Costa et al., 2023). The result is a

surface that does not fully represent the breast shape

on 90

lateral views and includes some irregular ap-

pearing like folders, protrusions and superﬁcial pleats

in the upper parts.

In the quest to reﬁne the model, the decision was

made to display the complete curvature of the breast

in the 90

images. The new approach involves exclud-

ing points with Z coordinates greater than the Z coor-

dinate of P3 (representing the end of the infra mam-

mary region and being the point closest to the body’s

center, as shown in the Figure 2). Due to variability

in the position of these points, a strategy was adopted

to calculate the Z average between the two P3 points

from the 90

and -90

curves (referred to as PM3).

This has the effect of slightly shifting the curve end

to include some ascendant curve points, providing a

more accurate representation of breast anatomy.

Figure 7: New algorithm result: the complete shape of the

side of the breast is represented.

Another modiﬁcation to the previous model is

made by translating all Z points of the right frontal

curve and the left frontal curve to PM3, that is re-

sponsible for deﬁning the trunk shape. This change

ensures a more rounded proﬁle for the body. Figure 7

show the result achieved with this modiﬁcation. Com-

A Tool for 3D Representation of the 2D Thermographic Breast Acquisitions

143

Figure 8: Blue: Structured Light Scanner; Gray: FLIR camera; Green: New algorithm; Red: Costa’s algorithm.

paring the lateral breast contours of both results (i.e

Figure 7 and Figure 6), it is possible to see that now

the resulting surface is more realistic.

5 COMPARING RESULTS

In the present study, a qualitative and quantitative

comparison was carried out between the surfaces cre-

ated by Costa’s algorithms and the new algorithms, as

well as 3D images acquired using the structured light

scanner and 2D images captured by the FLIR camera

at angles of 90

and -90

degrees, through image anal-

ysis, using data from 3 volunteers. The objective was

to contrast the models generated by the previous al-

gorithm with those produced by the new algorithm, as

well as to analyze the Symmetric Difference between

the data coming from the structured light scanner scan

and FLIR (Conci and Kubrusly, 2017).

Using Blender

 software, all 3D models and

2D images were superimposed respecting the same

limits, see ﬁgure 8. The proposed image com-

parison algorithm uses a visual approach, binariz-

ing each image of interest and then calculating the

symmetric difference between each corresponding

pixel in the two models, see the example in the ﬁg-

ure 9. More images available online on the web-

site (https://sites.google.com/view/three-dimensional-

breast-model).

Figure 9: Binarized images of the New model (left) and

Structured Light Scanner reconstruction (center) of volun-

teer 1 at 90 degree angle. In the last image on the right, the

symmetric differences between the two images is displayed

in white.

Table 1 displays the percentage of difference be-

tween each volunteer’s models for the 90 and -90

degree angles. These values allow comparisons be-

tween thermal images (FLIR) and Scanner acquisi-

tions (Scan) with the Costa’s algorithm (Old) and new

algorithm (New). This table shows, in the bottom line,

the Standard Deviation (SD) of the 6 views used: the

biggest difference in the average values (line 8) is in

VISAPP 2024 - 19th International Conference on Computer Vision Theory and Applications

144

Table 1: Between breast relative symmetric differences, means and standard deviations (SD).

Volunteer–angle New/Old Scan/Old Flir/Old Scan/New Flir/New Flir/Scan

1–(-90

) 20.75% 34.90% 38.66% 16.39% 19.45% 4,63%

1–(90

) 19.92% 39.79% 37.43% 20.30% 18.87% 5,74%

2–(-90

) 28.41% 29.67% 27.86% 4.39% 6.10% 5.34%

2–(90

) 47.50% 47.97% 49.75% 5.58% 5.19% 2.96%

3–(-90

) 17.36% 33.86% 33.31% 16.74% 16.23% 1,91%

3–(90

) 18.31% 36.21% 37.82% 20.97% 22.78% 3.26%

Mean 25.38% 37.07% 37.47% 14.06% 14.77% 3.97%

SD 11.52 6.27 7.24 7.28 7.37 1.50

the Scan/Old and Flir/Old columns. Considering the

DP (line 9), the most critical variation occurs between

the New and Costa’s algorithm.

6 CONCLUSIONS

We can see that the new model represents the breast

with a more pronounced lateral contour, more faith-

fully reﬂecting the anatomy of the body. The compar-

ison between the previous model and the new model

highlights that there were no signiﬁcant changes in

the shape of the model’s surface, but rather in the to-

tal volume of the surface included in the breast.

In a quantitative evaluation of the results, compar-

ing FLIR acquisitions (thermal images) and Scanner

with the Costa’s algorithm and New algorithm, we

observed that, concerning scanning, the Costa’s algo-

rithm has an average of 37.07% with a standard de-

viation of 6.27, while the New algorithm exhibits an

average of 14.06% with a standard deviation of 7.28.

When compared to thermal images, the Costa’s algo-

rithm has an average of 37.47% with a standard de-

viation of 7.24, whereas the New algorithm shows an

average of 14.77% with a standard deviation of 7.37

(see Table 1). These results indicate that the New al-

gorithm signiﬁcantly improves the representation of

the breast shape compared to the Costa’s algorithm.

However, improvements are still possible in the

frontal representation, as well as in adjusting the

alignment of the curves in the upper region of each

breast.

It is important to highlight that textures were not

incorporated in this work. Therefore, this is the ob-

jective of future research, which is the development

of merging all ﬁve images into a single textured 3D

object, enabling an overview of infrared scans.

ACKNOWLEDGEMENTS

E.L.S.M. is supported by Federal Institute of Educa-

tion, Science and Technology of Rond

onia (IFRO).

A.C. is supported in part by the National Institutes

of Science and Technology (INCT - MACC project),

National Council for Scientiﬁc and Technological

(CNPq) under grant 307638/2022-79, the Research

Support Foundation of Rio de Janeiro State (FAPERJ)

over CNE, e-Health Rio and Digit3D (”tem

aticos”)

projects (Digit3D projects, 2023).

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