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Similarity
Curvature Evaluation
Computational Topology
Skeletal Structures
Meshing/Remeshing
Computer Aided Design
Past Research
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Graph Comparison
A skeletal structure is
a one-dimensional representation, which encodes the decomposition of a
shape into relevant parts that may have either a geometric or an
application-dependent meaning. The shape comparison approach based on a
graph matching technique allows a structured process for identifying
matched areas on the input objects so that the matching results are
intuitive and visually meaningful.
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Polygon Morphing
The first step in
polygon morphing consists in automatically finding on the source and
target polygons couples of corresponding vertices to guide the blend.
We tried to solve this problem through a morphological characterization
of the shape. An approximated skeleton is suggested for coding the
shape as a graph of meaningful areas, and the correspondence problem is
therefore reduced to a skeleton matching process. The correspondences
are found taking into account the global structure of the shapes and
also local similarity criteria are used to further refine the matching.
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Tailor
Shape analysis and
coding are challenging problems in Computer Vision and Graphics. To
characterize a shape we have used the paradigm of Blowing Bubbles: a
set of spheres of increasing radius is drawn, whose centers are at each
vertex of the mesh, and whose radius represent the scale at which the
shape is analyzed. The number of connected components of the
intersection curve between each bubble and the mesh gives a first
qualitative characterization of the shape in a 3D neighborhood of each
vertex. Then geometric properties, such as an approximated curvature
estimation, are used to refine the classification and detect specific
features like sharp protrusions or wells, mounts or dips, blends or
branching parts.
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Plumber
The Plumber algorithm
is finalized at the identification of tubular features of 3D objects
represented by triangular meshes. Plumber is developed on the basis of
the multiscale morphological characterization produced by "Tailor". For
each tubular part found at a given scale, its approximated axis and
cross sections are determined. The final goal is to segment a 3D model
into main bodies and tubular parts and to encode the tube/body
connectivity and the spatial arrangement of the tube attachments onto
the body.
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Reeb Graphs
The main features of a
shape and their configuration are important to devise a surface
understanding mechanism that discards irrelevant details without
loosing the overall surface structure. Our approach is based on the
classical Morse theory and would seem to be suitable for analysing any
data that can be modelled as a surface. Through the analysis of the
evolution of the contour levels of a surface, we obtain a discrete
description which effectively represents the shape. Such a description
can be encoded into a topological graph, called a Reeb graph. In
particular, the notion of Extended Reeb Graph (ERG), we have
introduced, is based on a characterisation strategy that recognizes
critical points and areas by evaluating the behaviour of the contour
levels on a shape, including also the so-called degenerate
configurations. Finally, we have proposed an algorithm for the
construction of the ERG extraction both for terrain models and 3D
closed surfaces.
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Apparent Contours
An important visibility
feature of a smooth object with respect to a direction is its outline
(or profile or contour generator), that is the curve on the surface
that separates front face regions from the back ones. This curve is
correlated both to the view direction and the object embedding;
furthermore, it may reflect some of the shape properties.
Instead, the apparent contour of a shape is the projection of the
outline onto a plane perpendicular to the view direction. By their
properties, apparent contours have been extensively studied in computer
vision and computer graphics; in particular, they are used for
non-photo-realistic and silhouette rendering, camera motion estimation
and partial reconstruction of surfaces. Moreover, it has been
demonstrated that the knowledge of the apparent contour and its
singularities is enough for estimating the genus of the surface.
Currently our research efforts are in the direction of adapting to
discrete context some theoretical results and studying the evolution of
the apparent contour of a shape when the view direction changes with
time.
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Dual Meshes
This research focus on
duality considering basic relationships between a 2-manifold triangle
mesh M and its dual representation M'. The achieved combinatorial
properties define a discrete homeomorphism between M and M', and the
"dual Laplacian smoothing" which combines the application to the dual
mesh M' of well-known smoothing algorithms with an inverse
transformation for reconstructing the regularized triangle mesh. The
use of M' instead of M exploits a topological mask different from the
1-neighborhood one, related to Laplacian-based algorithms, guaranteeing
good results and optimizing storage and computational requirements.
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Medial Axis
An intuitive definition
of the skeleton in the continuum was given by Blum in 1967, who
described the skeleton by analogy with a fire front which starts at the
boundary of the shape and propagates isotropically towards the
interior. The medial axis is defined by the locations at which the fire
fronts collide. The medial axis, together with the radius function,
i.e. the distance from each point on the axis to the nearest point on
the boundary, define the medial axis transformation (MAT). The power of
this representation is that the shape's boundary and its MAT are
equivalent and one can be computed from the other, therefore a
two-dimensional object is effectively transformed into a
one-dimensional graph-like structure. We have investigated the MAT
properties and drawbacks, and developed an approximated MAT for planar
shapes for use in matching for polygon blending and surface
reconstruction.
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Curvature-based Skeleton
The Multiscale
Curvature Evaluation proposed exploited in Tailor, also paved the way
to the extraction of a skeletal structure of a triangle mesh starting
from high-curvature regions of its surface. Since a high curvature
region is usually located at the end of a protrusion, the achieved
skeleton strictly reseambles the object shape and, beeing curvature an
intrinsic characteristic of the surface, the skeleton is indeed an
affine-invariant representation of the object.
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Compression
Here we focus on the
lossy compression of manifold triangle meshes. Our approach, called
SwingWrapper, performs a retiling of the mesh to be compressed. In the
retiled mesh, all the triangles are isosceles and the locations of the
vertices are compactly encoded with our new prediction technique, which
uses a single correction parameter per vertex. SwingWrapper strives to
reach a user-defined output file size rather than to guarantee a given
error bound. This makes it particularly useful when transmitting meshes
over networks with time and band constraints.
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Reconstruction
This research tackles
the problem of creating a triangle mesh out of a data source, which may
be in the form of an unorganized point cloud, but also a parametric
definition of a manifold. Our contribution in the surface
reconstruction context is a sculpturing algorithm which is able to
produce boundary representations of solids with through holes. When
approximating parametric surfaces, we show how to design a tessellation
primitive that is independent of the particular mapping used to
describe the surface. Moreover, we show how to create both isotropic
and anisotropic meshes through our triangulation approach endowed with
a remeshing strategy.
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Sharp Feature Enhancement
This research studies
the 3D "aliasing" of triangle meshes obtained by feature-insensitive
samplings. Our contribution is a new Edge-Sharpener filter which
identifies the aliased regions and performs a local refinement.
Information in the neighborhood is used to sharpen the alised regions,
so that the processed mesh better reflects the sharp features of the
original model. Experiments shown that the distortion introduced by the
SwingWrapper remeshing-based compressor can be reduced down to a fifth
by executing Edge-Sharpener after decompression, with no additional
information.
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Feature Line Extraction
Given an object
digitized as sequences of scan lines, we propose an approach to the
extraction of feature lines and object segmentation based on a
multi-resolution representation and analysis of the scan data. First,
the scan lines are represented using a multi-resolution model which
provides a flexible and useful reorganization of the data for
simplification purposes and especially for the classification of points
according to their level of detail, or scale. Then, scan lines are
analyzed from a geometrical point of view in order to decompose each
profile into basic patterns which identify 2D features of the profile.
Merging the scale and geometric classification, 3D feature lines of the
digitized object are reconstructed tracking patterns of similar shape
across profiles. Finally, a segmentation is achieved which gives a
form-feature oriented view of the digitized data. The proposed approach
provides a computationally light solution to the simplification of
large models and to the segmentation of object digitized as sequences
of scan lines, but it can be applied to a wider range of digitized data.
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FreeForm Modelling
Free-form modelling is
investigated with respect to some CAD application fields, from the
traditional mechanical engineering one to the aesthetic design. In
particular, the research focuses on the extension of the
feature-concept to the free-form domain, where the freedom of the
possible defined shapes and alternatives makes hard to define a proper
classification and the insertion of a feature consists in a deformation
of the surface. Whereas in the mechanical domain few numerical
parameters are sufficient to instantiate a specific feature element; in
free-form modelling parameters must be higher geometric level entities
(e.g. curves) in order to allow for the feature shape specification. A
taxonomy of free-form features in the aesthetic design has been
proposed and prototypes are under development. The feature-based
approach is a high semantic level methodology which is independent of
the underlying geometry. Together with an application to the de-facto
standard representation by NURBS, the subdivision surface technique is
also explored as an alternative. When NURBS surfaces are adopted to
represent the geometry, the deformation process defined by the feature
curvilinear parameters has been obtained through a mechanical model
based on the Density Force Method. In case of subdivision surface, an
algorithm to perform generalised sweep operations (Sweep-like
Features), lead by a profile section propagating along a directrix, has
been implemented.
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