3D Reconstruction and Characterization of Human External Shapes
from 2D Images using Volumetric Methods
Teresa C. S. Azevedo, João Manuel R. S. Tavares 1, Mário A. P. Vaz
Faculdade de Engenharia da Universidade do Porto (FEUP)
Instituto de Engenharia Mecânica e Gestão Industrial (INEGI)
Rua Dr. Roberto Frias, s/n
4200-465 PORTO
PORTUGAL
Telephone: +351 22 508 1487
Fax: +351 22 508 1445
Email: {teresa.azevedo, tavares, gmavaz}@fe.up.pt
1
Corresponding author. Email: [email protected]
3D Reconstruction and Characterization of Human External Shapes
from 2D Images using Volumetric Methods
Abstract
This work presents a volumetric approach to reconstruct and characterize threedimensional (3D) models of external anatomical structures from two-dimensional
(2D) images. Volumetric methods represent the final volume using a finite set of 3D
geometric primitives, usually designed as voxels. Thus, from an image sequence
acquired around the object to reconstruct, the images are calibrated and the 3D models
of the referred object are built using different approaches of volumetric methods. The
final goal is to analyze the accuracy of the obtained models when modifying some of
the parameters of the considered volumetric methods, such as the type of voxels
projection (rectangular or accurate), the way the consistency of the voxels is tested
(only silhouettes or silhouettes and photo-consistency) and the initial size of the
reconstructed volume.
Keywords: Bioengineering, Biomedical Engineering, Computational Vision, 3D
Reconstruction, Volumetric Methods, Human Body Reconstruction.
1 - Introduction
Three-dimensional (3D) models generated by computational systems are an intensive
and long-lasting research problem in the Graphics and Computer Vision scientific
communities. One of the key challenges for 3D content production is the creation of
visually realistic models of humans.
Currently, the demand for 3D models of the human body has significantly increased
and the application fields vary from cinematographic industry (e.g. [1], [2]), to virtual
reality (e.g. [3], [4]), clothing industry (e.g. [5], [6]), or biomedical applications (e.g.
[7], [8]), among others.
However, in spite of all the effort it is still an open research area with considerable
arduous work to be done. There are many methods for human body 3D
reconstruction. In some of these methods good results have been obtained. However
simplification, automation, practicality and speed are still important problems which
need to be solved before wide application.
In this work we use volumetric methods for 3D reconstruction of objects. Recently,
volumetric methods have been successfully used in 3D reconstruction of objects with
complex shapes (e.g. [9], [10], [11], [12]), but a complete and deep analysis on them
still needs to be addressed. These methods work in the object volumetric space and do
not require a matching process between the images used, which is usually very
complex with smooth objects. Thus, typically, the 3D models are built from a
sequence of images, acquired using a turntable device and an off-the shelf camera.
The volumetric methods considered in this work use octrees, [13], to represent the
volume occupied by the object to be reconstructed. This reduces the reconstruction
time since the voxels that do not belong to the object volume are removed at an early
stage.
Our final goal is to analyze the accuracy of the obtained models when modifying
some of the parameters of the considered volumetric methods (such as the type of
voxels projection, the way the voxels consistency is tested and the initial size of the
reconstructed volume). Therefore, the obtained 3D models are compared both
qualitatively and quantitatively.
This paper is organized in the following away. First, a review on several
reconstruction methods of anatomical shapes is given in the next section. Then, the
volumetric methods are described in detail. Afterwards, an explanation of the
methodology followed is given. Then, the conducted experiments, results and their
analysis are presented. Finally, in the last section, main conclusions and future
directions of this work are addressed.
2 - Related work
The available methods for the 3D reconstruction of objects are usually classified into
contact or non-contact methods, [14], Figure 1.
2.1 - Contact-based methods
In the contact-based methods some kind of devices, that are in touch with parts of the
human body, are used. Some examples of these methods can be found in [15], [16],
[17], among others. The main disadvantage of these methods is that, because of the
referred mechanical contact, some deviation in the results can appear. Moreover, they
can be biologically unsafe; for example, a contact with damaged skin can cause an
infection.
2.2 - Range-based methods
Range or depth images are a collection of distance measurements from a well known
reference coordinate system to points on the surface of the object to be reconstructed.
They are very common when highly detailed models are required; however, they are
high-priced (at least for now), they are spatially limited and most of the systems
available do not provide colour information about the reconstructed object, [18].
Laser scanning, (e.g. [19-21]), and structured light pattern methods, (e.g. [22-24]),
are the range-based technologies most widely used to build 3D human body models.
The main contribution factors of these methods are their precision and simplicity of
use. Acquisition time depends on the size of the object and technology used, during
which the object of interest must remain stationary. Thus, it is difficult to obtain stable
results as humans always move slightly during the data acquisition, [25]. Other
drawbacks of these systems are missing data points; namely, where the laser or
projected pattern is occluded and erroneous reconstruction data due to specularities of
the objects surface, [26].
2.3 - Image-based methods
Another class of usual 3D static human reconstruction methods are image-based.
They are easy and flexible methods, based on image measurements. The required
images can be acquired from video sequences or from image-cameras, which are
currently inexpensive acquisition systems.
2.3.1 - Shape-from-silhouettes
One of the most commonly used methods in human body reconstruction is shapefrom-silhouette, (e.g. [14, 27-30]). Silhouettes in a 2D image directly reflect the 3D
shape of an object. The images are usually acquired around a static person and image
segmentation is performed in order to obtain the human body silhouettes. Intersecting
the projection centres of each image and the visual cones generated by the silhouettes,
a 3D model is determined, Figure 2. This 3D model is named visual hull, [31], a
locally convex over-approximation of the volume occupied by an object. Therefore,
shape-from-silhouette methods are widely used to provide a coarse 3D shape estimate,
which can serve as an initialization for more sophisticated 3D shape reconstruction
algorithms, like in [32], for example. Obtaining continuous silhouette images is
usually a computationally simple task if the images are acquired in a controlled
environment. However, it is a very challenging task to apply silhouette-based
reconstruction methods in uncontrolled or outdoor environments, where occlusions
may occur, [33].
2.3.2 - Multi-view geometry
Multi-view geometry consists on reconstructing the 3D shape of an object from
correspondences on a sequence of images, taken from different viewpoints, Figure 3.
It is considered an evolution of stereo-based methods, where only two images are
used: first, correspondences between points in both images are established (matched)
and then their position in 3D space is determined by triangulation, [34].
Unfortunately, the first matching step is far from having an easy solution. Firstly, if
the object to reconstruct has a smooth surface and low or constant texture, feature
extraction may be incorrect, or even impossible to be established, since the local
appearance is the same for every neighbourhood of the possible features to be
matched. Secondly, matching correspondence cannot be established by just
comparing local image measurements unless the object has a lambertian surface; that
is, its appearance does not change significantly along the consecutive viewpoints
considered. To overcome these difficulties, variations and improvements to the
original method are considered. The most common approach is based on stereophotogrammetry, in which the human body is “marked” with artificial fiducials (such
as, points) (e.g. [35, 36]).
2.3.3 - Model-based methods
Model-based approaches are now very common, in particular for monocular image
sequences or range-based methods. For example, the use of these model-based
approaches is widespread in graphic communities, especially for animation purposes,
where the goal is to build dynamic 3D models or for tracking a moving person.
Generically, model-based methods use a prior knowledge of the objects geometry in
order to constrain the shapes recovery process in the presence of visual ambiguities.
Thus, they can reduce the influence of noisy, sparse or outlier data in shape 3D
reconstruction, providing by this way more accurate 3D models, [37].
For human 3D reconstruction, these approaches use a pre-defined human model or
training data as a reference in order to constraint or guide the interpretation of the
image data acquired. Such models should support a broad variety of possible poses,
while being adaptable to different human shapes. At the same time, the set of
parameters to describe the models pose should be kept as small as possible, because
each additional parameter increases the dimensionality of the problem involved, [38].
2.4 - Volumetric methods
Previous image-based methods often fail to reconstruct objects with complicated
shapes, like the human body, essentially because of its high level of smoothness, [39].
Volumetric methods appeared recently as a versatile alternative for smooth object 3D
reconstruction, [40]. The 3D space volume is divided into discrete 3D volume
elements (voxels or 3D pixels) which are then classified into two categories: inside or
outside. The union of all the inside voxels is an approximation of the visual hull.
Some volumetric methods use a hierarchical form of voxel representation: octrees,
[13]. Octrees are based on a recursive subdivision of the space into eight octants,
Figure 4. Thus, they are a computationally efficient way to represent objects in the 3D
space, especially if the objects are highly connected, as the case of the human body.
The first 3D volumetric representations were proposed for shape-from-silhouettes
methods, in order to describe the 3D reconstructed models by using voxels rather than
2D surface patches, [41]. Then, volumetric methods evolved by testing if each voxel
belongs to the object of interest by using photo-consistency tests, like in Space
Carving, [42]. With this method, the resulting 3D model is the photo hull, defined as
the biggest volume of voxels that are photo-consistent with all viewpoints, Figure 5.
Photo-consistency is checked statistically: a voxel is considered consistent if the mean
deviation of the pixels colour, which results from the voxel image projection, is under
a predefined threshold. One problem with photo-consistency is the determination of
the referred threshold value, which is often obtained through experimentation until
reasonable results are obtained. Usually, a low threshold level is suitable for areas
with low texture, while highly textured areas or with sharp edges need higher
threshold values.
Some examples for 3D human body reconstructions using volumetric methods can be
found in [38, 43-46].
3 - Followed methodology
The first step in the methodology followed in this work is to calibrate the camera used
for image acquisition. The calibration process was based on Zhang’s calibration
algorithm, [47]. It requires an image sequence with the object to be reconstructed
placed on a planar chessboard pattern. Thus, for each viewpoint to be used in the
reconstruction process, the associated pose is determined.
Even when the scene background has low colour variation, the photo-consistency
criterion may not be sufficient for correct 3D reconstructions, [48]. Also, since the
used calibration pattern rotates together with the object to be reconstructed, it will not
be considered as background and, consequently, will be reconstructed as if it belongs
to the object. Thus, image segmentation between the background and the object is
performed. This is accomplished by first removing the red and green channels from
the original RGB images and, finally, using image binarization through threshold
value. The silhouette information obtained will allow for all voxels, which do not
reproject inside all silhouette images, to be removed from the reconstruction volume.
Finally, using the image sequence and associated silhouette images, combined with
the calibration parameters determined, the 3D models are built using two volumetric
methods: one based on silhouettes and a second one that combines silhouettes and
photo-consistency tests. The goal is to compare the obtained accuracy of the obtained
3D models when some parameters of the volumetric methods are modified, such as
the type of voxels projection (rectangular or accurate) and the initial reconstructed
volume size.
3.1 - Voxel projection
The simplest voxel projection onto an image plane (footprint) is a single point. Here,
only the center of the voxel is projected, which leads to some problems such as: the
rounding operation used to identify the pixel and artifacts on the 3D reconstruction
due to the excessive simplification of the projection.
The accurate footprint of a voxel has to consider its cubic shape. The projection leads
to a convex 2D polygon in the image plane, either 4-sided or 6-sided. In order to
obtain the accurate outline of the projected voxel, the eight corner points must be
projected into the image plane and then their closed convex hull is computed.
One computationally attractive technique to approximate the accurate footprint is to
use the bounding rectangle that can be computed from the projection of the eight
corner points of a voxel, Figure 6.
4 - Experimental results
In this work the experimental tests are performed considering three objects: a
parallelepiped, a human hand model and a human torso model. Due to its shape
simplicity, the parallelepiped is used for accuracy evaluation of the considered
volumetric methods. The hand and torso models allow for a capability analysis of the
volumetric methods to built 3D models of complex objects. Figures 7, 8 and 9 show
some examples of the acquired image sequences used to reconstruct the three
considered objects and the obtained silhouette images.
Figures 10 and 11 show two sets of reconstruction results for the parallelepiped
object, using the volumetric method based only on silhouettes. The sets differ on the
octrees voxels projection criterion. Figure 12 shows some of the reconstruction results
for the same object, using the volumetric method based on silhouettes and photoconsistency. This set uses accurate voxel projection.
Figure 13 compares the time consumed to build the parallelepiped 3D models. Using
accurate voxel projection, Figure 11, it is verified that voxels are classified as
completely inside or outside the object at lower levels of refinement; thus, the 3D
reconstruction process becomes faster, because it decreases the number of ambiguous
voxels at the first levels of the octree. An important observation is that computational
complexity of the developed volumetric methods is O(n), with n the number of voxels
of the reconstructed volume. Thus, reconstruction time grows exponentially with the
octrees final level L, because the maximum number of voxels is 8L.
Figure 14 compares the volume of the reconstructed 3D models with the
parallelepiped real volume, accurately measured using a calliper. All built models
have bigger volumes than the real parallelepiped object because both the visual and
photo hulls tend to be larger than the real object; this is even more evident in the
lower octree levels, where voxels have larger dimensions.
Figures 15 and 16 show two sets of reconstruction results for the hand model object,
using the volumetric method based only on silhouettes. The sets differ on the octree
voxels projection criterion. In order to visualize the octree volumetric representation,
Figure 17 shows half of a reconstructed hand model, obtained using the volumetric
method based only on silhouettes. It is noticeable that voxels that are inside the object
volume are less refined (bigger) than voxels that are closer to the object surface.
Figure 18 shows some of the reconstruction results for the same object, but at this
time using the volumetric method based on silhouettes and photo-consistency. Again,
this set uses accurate voxel projection. Figures 19 and 20 respectively compare the
reconstruction time and volume of all 3D models for the hand object. Since the hand
model was manufactured by a rapid prototyping technique, its real volume is acquired
directly from its stereolithography CAD (computer-aided design) file.
As both considered objects have a uniform colour throughout all their surfaces, the
results obtained with the photo-consistent-based volumetric method are very similar
to the ones obtained with the volumetric method based only on silhouettes.
Figure 21 shows some reconstruction results for the hand model object, using the
silhouette-based volumetric method and accurate voxels projection. This set differs
from the one presented on Figure 16, because the initial volume size is 20x20x10 cm,
whereas before it was a cube of 20x20x20 cm. When the initial volume is nearer to
the real bounding volume, for the same refinement level of the octree, the
reconstructed 3D model volume is closer to the real one, Figure 22.
Figure 23 shows some reconstruction results for the torso model, using the volumetric
method based on silhouettes and photo-consistency and accurate voxels projection.
The initial volume size is 100x40x40 cm and the final refinement level of the octree is
7. Since the torso model has a specular surface, it reflects the calibration pattern.
Consequently, some minor errors can be observed on the reconstructed 3D model,
mainly due to an inaccurate image segmentation process.
In order to evaluate how the noise in image affects the reconstruction results, 10% of
Gaussian noise was introduced in the original images of the torso model and a 3D
model was reconstructed using the volumetric method based on silhouettes and photoconsistency. No changes were observed when comparing these results with the
previous ones: the number of voxels of both 3D models and their geometrical
measures were exactly the same. Therefore, it is possible to conclude that the image
noise is not a determinant factor on the accuracy of the obtained reconstructions
because the considered object has a constant colour on all its surface and also because
the noise is somewhat eliminated by averaging the RGB values of the projected
voxels on all acquired images.
Finally, from the voxelized 3D models obtained, some geometrical measures can be
determined, such as height, length and width. Figure 24 compares these values with
the real ones, for all reconstructed objects. This comparison confirms the
approximated reconstruction results of the considered objects, using volumetric
methods.
5 - Conclusions and future work
It is not easy to build an accurate 3D model of an object only from 2D images. It is
even worst when the object presents complex surfaces, as seen in external anatomical
structures.
The 3D models built with the implemented volumetric methods were quite similar to
the real objects. These methods present high application potential due to their
straightforward implementation and few requirements on a setup level (only one CCD
camera and a suitable calibration process).
Silhouette-based volumetric methods require scenes where it is easy to perform
object/background segmentation. On the other hand, volumetric methods based on
photo-consistency require constant illumination conditions. However, it is fruitful to
combine both techniques in order to enhance the 3D reconstruction process.
Future work will concentrate on the implementation of auto-calibration processes and
on the 3D reconstruction of deformable objects.
Acknowledgements
The
first
author
would
like
to
thank
her
PhD
grant
with
reference
SFRH/BD/27716/2006 from FCT – Fundação para a Ciência e a Tecnologia from
Portugal.
References
Beard, J. (2001). Clones, Bones and Twilight Zones: Protecting the Digital Persona
of the Quick, the Dead and the Imaginary. Berkeley Technology Law Journal,
University of California, Simon Hall, Berkeley, California, CA, USA, vol. 16, no. 3.
Nebel, J.-C. (2001). Generation of True 3D Films. International Conference on
Virtual Storytelling: Using Virtual Reality Technologies for Storytelling, Avignon,
France, vol. 2197, 10-19.
Nebel, J.-C., Sibiryakov, A., et al. (2003). V-Man Generation for 3-D Real Time
Animation. A Symposium on Intelligent Motion and Interaction Within Virtual
Environments, London, UK.
Allard, J., Franco, J.-S., et al. (2006). The GrImage Platform: A Mixed Reality
Environment for Interactions. IEEE International Conference on Computer Vision
Systems, New York City, NY, USA, 46.
Vassilev, T. (2000). Dressing Virtual People. Systemics, Cybernetics and Informatics,
Orlando, FL, USA.
Volino, P., Cordier, F., et al. (2005). From early virtual garment simulation to
interactive fashion design. Computer-Aided Design, vol. 37, no. 6, 593-608.
Pednekar, A. and Kakadiaris, I. (2000). Applications of Virtual Reality In Surgery.
Indian conference on Computer Vision, Graphics and Image Processing, Graphics and
Applications session, Bangalore, India.
Benton, L. and Nebel, J.-C. (2002). Study of the breathing pattern based on 4D data
collected by a dynamic 3D body scanner. 7th Numérisation 3D/Scanning, Paris,
France.
Montenegro, A., Carvalho, P., et al. (2004). Space Carving with a Hand-Held
Camera. International Symposium on Computer Graphics, Image Processing and
Vision, Curitiba, Brasil.
Adipranata, R. and Soo, Y. (2007). 3D Object Reconstruction using Voxel Coloring
with Mean Charts Color Consistency Checking. IASTED International Conference in
Advances in Computer Science and Technology, Phuket, Thailand, 206-211.
Lin, F., Seah, H., et al. (2007). Voxelization and fabrication of freeform models.
Virtual and Physical Prototyping, vol. 2, no. 2, 65-73.
Furukawa, Y. and Ponce, J. (2009). Carved Visual Hulls for Image-Based Modeling.
International Journal of Computer Vision, vol. 81, no. 1.
Chien, C. and Aggarwal, J. (1984). A Volume/Surface representation. International
Conference on Pattern Recognition, Montreal, Canada, 817-820.
Takahashi, K., Sakaguchi, T., et al. (2000). Remarks on a real-time, noncontact,
nonwear, 3D human body posture estimation method. Systems and Computers in
Japan, vol. 31, no. 14, 1-10.
Ge, Y. (1994). Noncontact 3D biological shape measurement from multiple views.
MSc Thesis, Department of Computer Science, University of Western Australia,
Australia.
Naik, S. (2002). Real-time Avatar Construction Using Shape Tape. Technical Report
Number 02-036, Effective Virtual Environments Research Group, Department of
Computer Science, University of North Carolina, Chapel Hill, NC, USA.
Kalkhoven, T. and Naber, N. (2003). 3D measurement methods. Research project,
Computer-Aided Design and Engineering, Faculty of Industrial Design, University of
Technology, Delft, The Netherlands.
Remondino, F. and El-Hakim, S. (2006). Image-Based 3D Modelling: A Review. The
Photogrammetric Record, vol. 21, no. 115, 269-291.
Tukuisis, P., Meunier, P., et al. (2001). Human body surface area: measurement and
prediction using three dimensional body scans. European Journal of Applied
Physiology and Occupational Physiology, vol. 85, no. 3-4, 264-271.
Kovacs, L., Zimmermann, A., et al. (2006). Three-dimensional recording of the
human face with a 3D laser scanner. Journal of Plastic, Reconstructive and Aesthetic
Surgery, vol. 59, no. 11, 1193-1202.
Xi, P., Lee, W.-S., et al. (2007). Analysis of segmented human body scans. Graphics
Interface, Montreal, Canada, vol. 234, 19-26.
Zhang, L., Curless, B., et al. (2002). Rapid Shape Acquisition Using Color Structured
Light and Multi-pass Dynamic Programming. 1st International Symposium on 3D
Data Processing, Visualization, and Transmission, Padova, Italy, 24-36.
Tsalakanidou, F., Forster, F., et al. (2005). Real-time acquisition of depth and color
images using structured light and its application to 3D face recognition. Real-Time
Imaging, special issue on multi-dimensional image processing vol. 11, no. 5-6, 358369.
Čarnický, J. and Jr., D. (2006). Three-dimensional measurement of human face with
structured-light illumination. Measurement Science Review, vol. 6, no. 1, 1-4.
Marshall, S. and Gilby, J. (2001). New Opportunities in Non-Contact 3D
Measurement. National Measurement Conference, Harrogate, United Kingdom.
Forsyth, D. and Ponce, J. (2003). Computer Vision: A Modern Approach. Prentice
Hall Series in Artificial Intelligence.
Kakadiaris, I. and Metaxas, D. (1995). 3D Human Body Model Acquisition from
Multiple Views. International Conference on Computer Vision, Boston, MA, USA,
618-623.
Hilton, A., Beresfors, D., et al. (2000). Whole-body modeling of people from
multiview images to populate virtual worlds. The Visual Computer, Springer-Verlag,
Berlin, Germany, 411-436.
Wong, K.-Y. and Cipolla, R. (2001). Structure and Motion from Silhouettes.
International Conference on Computer Vision, Vancouver, Canada, 217-222.
Franco, J.-S. (2005). Modélisation à partir de silhouettes. PhD Thesis, Institut
National Polytechnique de Grenoble, France.
Laurentini, A. (1994). The visual hull concept for silhouette-based image
understanding. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.
16, no. 2, 150-162.
Faugeras, O. and Keriven, R. (1999). Variational principles, Surface Evolution,
PDE's, level set methods and the Stereo Problem. IEEE Transactions on Image
Processing, vol. 7, no. 3, 336-344.
Guan, L., Franco, J.-S., et al. (2007). 3D Occlusion Inference from Silhouette Cues.
IEEE Computer Vision and Pattern Recognition, Minneapolis, Minnesota, MN, USA,
1-8.
Hartley, R. and Sturm, P. (1995). Triangulation. Lecture Notes in Computer Science,
vol. 970, 190-197.
Siebert, J. and Marshall, S. (2000). Human body 3D imaging by speckle texture
projection photogrammetry. Sensor Review, vol. 20, no. 3, 218-226.
D'Apuzzo, N. (2002). Modeling human faces with multi-image photogrammetry. SPIE
Conference on Three-Dimensional Image Capture and Applications, San Jose, CA,
USA, vol. 4661, 191-197.
McInerney, T. and Terzopoulos, D. (1996). Deformable models in medical image
analysis: a survey. Medical Image Analysis, vol. 1, no. 2, 91-108.
Kehl, R. and Gool, L. (2006). Markerless tracking of complex human motions from
multiple views. Computer Vision and Image Understanding, vol. 104, no. 2-3, 190209.
Zeng, G., Lhuillier, M., et al. (2005). Recent Methods for Reconstructing Surfaces
from Multiple Images. Lecture Notes in Computer Science, Springer Verlag, vol.
3519, 429-447.
Kutulakos, K. (1997). Shape from the Light Field Boundary. IEEE Computer Vision
and Pattern Recognition, San Juan, Puerto Rico, 53-59.
Massone, L., Morasso, P., et al. (1985). Shape from occluding contours. SPIE
Conference on Intelligent Robots and Computer Vision, Cambridge, MA, USA, vol.
521, 114-120.
Kutulatos, K. and Steiz, S. (1998). A Theory of Shape by Space Carving. Technical
Report TR692, Computer Science Department, University of Rochester, New York,
NY, USA.
Ahmed, M., Eid, A., et al. (2001). 3-D reconstruction of the human jaw using space
carving. International Conference on Image Processing, Tessaloniki, Greece, vol. 2,
323-326.
Mikić, I., Trivedi, M., et al. (2003). Human Body Model Acquisition and Tracking
using Voxel Data. International Journal of Computer Vision, vol. 53, no. 3, 199-223.
Zeng, G., Paris, S., et al. (2003). Study of Volumetric Methods for Face
Reconstruction. IEEE Intelligent Automation Conference, Hong Kong.
Azevedo, T., Tavares, J., et al. (2007). 3D Volumetric Reconstruction and
Characterization of Objects from Uncalibrated Images. 7th IASTED International
Conference on Visualization, Imaging, and Image Processing, Palma de Mallorca,
Spain, 141-146.
Zhang, Z. (2000). A Flexible New Technique for Camera Calibration. IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 11, 13301334.
Sande, K. (2004). A Practical Setup for Voxel Coloring using off-the-shelf
Components. BSc Project, Universiteit van Amsterdam, Netherlands.
FIGURE CAPTIONS
Figure 1. Usual classification of 3D reconstruction methods.
Figure 2. Visual hull defined by two different viewpoints.
Figure 3: Multi-view geometry: a 3D point P can be reconstructed by intersecting the
optical rays that pass through the camera centres and respective image points, p n
(image projections of the 3D point).
Figure 4: Octree: on the right, data structure, organized hierarchically, used to
represent objects in the 3D space, as represented on the left.
Figure 5: Relation between photo and visual hull: real object ⊆ photo hull ⊆ visual
hull.
Figure 6: Accurate and rectangular projection of a voxel onto an image plane.
Figure 7: Four examples of the acquired image sequence used to reconstruct the
parallelepiped object (top) and the obtained silhouette images (bottom).
Figure 8: Four examples of the acquired image sequence used to reconstruct the
human hand model object (top) and obtained silhouette images (bottom).
Figure 9: Four examples of the acquired image sequence used to reconstruct the
human torso model object (top) and obtained silhouette images (bottom).
Figure 10: 3D reconstructed models of the parallelepiped object, obtained with the
silhouette-based volumetric method and rectangular projection of voxels, with (from
the left to the right) 2, 3, 4, 5 and 6 refinement levels of the octree.
Figure 11: 3D reconstructed models of the parallelepiped object, obtained with the
silhouette-based volumetric method and accurate projection of voxels, with (from the
left to the right) 2, 3, 4, 5 and 6 refinement levels of the octree.
Figure 12: 3D reconstructed models of the parallelepiped object, obtained with the
volumetric method based on silhouettes and photo-consistency and accurate
projection of voxels, with (from the left to the right) 2, 3, 4, 5 and 6 refinement levels
of the octree.
Figure 13: Reconstruction time (in seconds) versus refinement levels of the octree, for
the parallelepiped object, using the three considered volumetric methods.
Figure 14: Reconstruction volume (in cm3) versus refinement levels of the octree, for
the parallelepiped object, using the three considered volumetric methods.
Figure 15: 3D reconstructed models of the hand model object, obtained with the
silhouette-based volumetric method and rectangular projection of voxels, with (from
the left to the right) 2, 3, 4, 5, 6 and 7 refinement levels of the octree.
Figure 16: 3D reconstructed models of the hand model object, obtained with the
silhouette-based volumetric method and accurate projection of voxels, with (from the
left to the right) 2, 3, 4, 5, 6 and 7 refinement levels of the octree.
Figure 17: Half of a reconstructed hand model obtained using the volumetric method
based only on silhouettes and accurate projection of voxels.
Figure 18: 3D reconstructed models of the hand model object, obtained with the
volumetric method based on silhouettes and photo-consistency and accurate
projection of voxels, with (from the left to the right) 2, 3, 4, 5, 6 and 7 refinement
levels of the octree.
Figure 19: Reconstruction time (in seconds) versus refinement levels of the octree, for
the hand model object, using the three considered volumetric methods.
Figure 20: Reconstruction volume (in cm3) versus refinement levels of the octree, for
the hand model object, using the three considered volumetric methods.
Figure 21: 3D reconstructed models of the hand model object, obtained with the
silhouette-based volumetric method, accurate projection of voxels and initial cube
size of 20x20x10 cm, with (from the left to the right) 2, 3, 4, 5, 6 and 7 refinement
levels of the octree.
Figure 22: Reconstruction volume (in cm3) versus refinement levels of the octree, for
the hand model object, for different initial cube sizes, using the silhouette-based
volumetric method and accurate projection of voxels.
Figure 23: Six different viewpoints of the 3D reconstructed model of the torso model
object, obtained with the volumetric method based on silhouettes and photoconsistency and accurate projection of voxels, with 7 refinement levels of the octree.
Figure 24: Comparison of the obtained measurements from the reconstructed 3D
models with the real objects measures.
FIGURES
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24