Many Object recognition techniques perform some flavour of point pattern matching between a model and a scene. Such points are usually selected through a feature detection algorithm that is robust to a class of image transformations and a suitable descriptor is computed over them in order to get a reliable matching. Moreover, some approaches take an additional step by casting the correspondence problem into a matching between graphs defined over feature points. The motivation is that the relational model would add more discriminative power, however the overall effectiveness strongly depends on the ability to build a graph that is stable with respect to both changes in the object appearance and spatial distribution of interest points. In fact, widely used graph-based representations, have shown to suffer some limitations, especially with respect to changes in the Euclidean organization of the feature points. In this paper we introduce a technique to build relational structures over corner points that does not depend on the spatial distribution of the features

Albarelli, A.

Bergamasco, F.

Rossi, L.

Torsello, A.

Vascon, S.

English

Many Object recognition techniques perform some flavour of point pattern matching between a model and a scene. Such points are usually selected through a feature detection algorithm that is robust to a class of image transformations and a suitable descriptor is computed over them in order to get a reliable matching. Moreover, some approaches take an additional step by casting the correspondence problem into a matching between graphs defined over feature points. The motivation is that the relational model would add more discriminative power, however the overall effectiveness strongly depends on the ability to build a graph that is stable with respect to both changes in the object appearance and spatial distribution of interest points. In fact, widely used graph-based representations, have shown to suffer some limitations, especially with respect to changes in the Euclidean organization of the feature points. In this paper we introduce a technique to build relational structures over corner points that does not depend on the spatial distribution of the features. © 2012 ICPR Org Committee

ALBARELLI, Andrea

BERGAMASCO, Filippo

ROSSI, LUCA

TORSELLO, Andrea

S. Vascon

Archivio istituzionale della ricerca - Università degli Studi di Venezia Ca' Foscari

A Stable Graph-Based Representation for Object Recognitionthrough High-Order MatchingA. Albarelli, F. Bergamasco, L. Rossi, S. Vascon and A. TorselloUniversita` Ca’ Foscari Veneziawww.dais.unive.itAbstractMany Object recognition techniques perform someflavour of point pattern matching between a model anda scene. Such points are usually selected through a fea-ture detection algorithm that is robust to a class of im-age transformations and a suitable descriptor is com-puted over them in order to get a reliable matching.Moreover, some approaches take an additional step bycasting the correspondence problem into a matchingbetween graphs defined over feature points. The mo-tivation is that the relational model would add morediscriminative power, however the overall effectivenessstrongly depends on the ability to build a graph that isstable with respect to both changes in the object appear-ance and spatial distribution of interest points. In fact,widely used graph-based representations, have shownto suffer some limitations, especially with respect tochanges in the Euclidean organization of the featurepoints. In this paper we introduce a technique to buildrelational structures over corner points that does notdepend on the spatial distribution of the features.1. IntroductionObject recognition can be performed through manydifferent approaches, ranging from the spatial analysisof color distribution [5] to contour matching [13]. Inthis paper we focus on techniques that work by match-ing sets of feature points that have been extracted fromboth a model image and a scene. For this kind of ap-proach to succeed, the interest points should be repeat-able, that means that the sets of features extracted un-der moderately different conditions of pose and lightingshould exhibit a reasonable overlap. To this end, Harrisoperator [7], Maximally Stable Extreme Regions [12]or Differences of Gaussians [11] are widely used inliterature. Moreover, a robust and distinctive descrip-tor, such as SIFT [10] or SURF [8] must be computedfor each interest point in order to ensure an accurateFigure 1. Matching two stable graphscorrespondence. While techniques that rely only onthe descriptor for point-wise matching can be very ef-fective [9] and efficient [14], the adoption of spatialconstraints has proven to enhance the overall reliabil-ity of the correspondences. Such constraints can beexpressed, for instance, as a precise class of transfor-mations to which the points matched must adhere [2]or as a set of relations between features that must bepreserved through the injection that connects model todata points [16]. The latter class of constraints caststhe search for a correspondence to a graph-matchingproblem, that can be solved (heuristically) with gen-eral or specialized techniques [4]. However, it is notalways straightforward to choose a proper relationalmodel for the data points. Delaunay triangulation [3]and k-nearest-neighbour graphs (where each point isconnected to the k nearest points) are popular choicessince they are simple to compute and exhibit a meaning-ful planar organization. Unfortunately, with these ap-proaches the connectivity is usually settled by the rela-tive position of the points in the Euclidean space, whichhappens to be a property that is not resilient to changesin pose and occlusions.In the following section we introduce a relationalstructure that does not depend on the position of thepoints and that can be built directly on Harris cor-ners without requiring the expensive computation of afeature descriptor. Additionally, we propose a game-theoretic matching schema that allows to find corre-spondences that respect the topology of the graph andthat are also coherent with respect to geometrical con-straints (see Fig. 1).Figure 2. Building a stable graph2. Stable Graph CreationThe vertices of the proposed graph, defined as the setV = {v1, v2...vn}, are exactly the n image pixels thatexhibit the stronger response with respect to the Harrisoperator [7], after non-maximal suppression and abovea given threshold. For each vertex v, a simple descriptoris computed as:δ(v) = (e′, e′′, λ′, λ′′) (1)where e′,e′′ and λ′,λ′′ are respectively the normalizedeigenvectors and the eigenvalues of the covariance ma-trix of the square image patch centered on the vertex vwith a given side wc. The main idea behind the pro-posed representation is that the connectivity betweentwo vertices should depend only on the descriptors in-volved, rather than on the positions of the vertices. Tothis end we define the edge set as E as:E = {(v1, v2) ∈ V × V |e′1 · e′2 < αd} (2)this means that an edge insists between two vertices ifand only if the respective main eigenvectors are orthog-onal enough. From an image processing point of viewthis makes sense, in fact this rule avoids to connect localclusters of points that share the same edge and, by con-trast, connects vertices that represent parts of the objectswell apart. In the following section we will make clearhow these conditions help in obtaining reliable matches.In Fig. 2 the graph building process is shown. The ver-tices are shown in the first half of the image along withthe direction of the corresponding eigenvectors. In thesecond part of the same figure the stable graph builtupon those vertices is displayed. Specifically, a valueof αd of 0.04 (that corresponds to about 88.5 degrees)was used. Visually, the graph seems to be very dense,however this is due to the fact that the very nature ofthe proposed approach tends to build edges spanningfrom one side of the object to the other. Indeed, theaverage degree of the graph shown is slightly below 4.By changing respectively the Harris response thresholdand the value of αd, graphs with a different numberof vertices and with different edge densities can be ob-tained. Of course, the usual trade-off between the num-ber of features and their distinctiveness applies. Fig. 3displays a comparison between the structures producedover the same vertex set extracted from two slightly dif-ferent images, respectively by the Delaunay triangula-tion, the knn-graph and our method. While topologicalchanges are apparent with the first two techniques, it isnot easy to tell how much of the non-planar structureis preserved by the stable graph. However, this will beassessed in the following as the three graph-based rep-resentations will be used for object recognition.3. Game-Theoretic MatchingThe Matching between graphs is performed usingthe game-theoretic framework presented in [1] and [2].According to this technique it is possible to cast the cor-respondence problem in an optimization process that isguaranteed to converge under payoff-monotonic evolu-tionary dynamics [15]. Two steps are needed to exploitsuch framework: the preparation of a set of matchingcandidates that will be selected through the evolution-ary process and the definition of a payoff function be-tween pairs of candidates to drive the evolution towardthe selection of a globally coherent set of matches.3.1 Candidate SelectionDifferently from [2], where correspondences aresearched between well characterized features, we aredealing with rather poor descriptors (see Eq. 1). Sincewe trust the graph to be repeatable, we propose to creatematching candidates between edges rather than vertices,thus each high-order putative match is defined by thequadruple ((va, vb), (v1, v2)) where (va, vb) is an edgein the model and (v1, v1) is an edge in the data. For eachedge in the model a maximum of k candidates are pro-duced. Those candidates are selected by choosing thosethat exhibit a better alignment of the principal eigenvec-tors and similar eigenvalues between the correspondingvertices (see Fig. 4-1).Figure 3. Comparison between graphsFigure 4. The proposed pipeline for stable graph matching (see text for details).3.2 Payoff DefinitionThe payoff between two candidates expresses thecompatibility between them. A high payoff lets twocandidate to thrive together, while a payoff of value 0prevents the evolutionary process to select both the can-didates in the final population. Since we want the matchto be one-to-one, we set the payoff to 0 if two candidatesshare the same model or data edge. Additionally, wealso want to enforce topological constraints, thus we setthe payoff to 0 if the incidence relation between sourceand data edges is not consistent. This is the case, forinstance, if the model edges in two candidates share avertex, but the corresponding edges in the data do not.If both one-to-one and topological constraints are satis-fied, the payoff is computed as a function that accountsfor the relative direction and length of the edges:pi(((va, vb), (v1, v2)),((vc, vd), (v3, v4)))=1σ√2pie−v(((va,vb),(v1,v2)),((vc,vd),(v3,v4)) )22σ2(3)where σ is a term that regulates the selectivity of thematch and v is a function that measures the compati-bility between the scaling transforms induced by the 6distances among the involved vertices (see Fig. 4-2):v(((va, vb), (v1, v2)),((vc, vd), (v3, v4)))= mini=1..6,j=1..6logRiRj(4)with the 6 distance ratios being:R1 =‖va−vb‖‖v1−v2‖ R2 =‖vc−vd‖‖v3−v4‖ R3 =‖va−vc‖‖v1−v3‖R4 =‖vb−vd‖‖v2−v4‖ R5 =‖va−vd‖‖v1−v4‖ R6 =‖vb−vc‖‖v2−v3‖(5)Since we compare ratios the approach is scale indepen-dent. The log in Eq. 4 makes the measure symmetricand of 0 average, the min takes the worst value, theGaussian of Eq. 3 maximizes the payoff when all theratios are preserved. The computation of an examplepayoff matrix is shown in Fig. 4-3. The payoff be-tween b1, b4 or a1, b1 is 0 because of the one-to-oneconstraint, while the payoff between a1, b4 or c2, b4 is0 because of the topology constraint (for instance a andb share a vertex while 1 and 4 do not). Among the non-zero values, we can observe that the compatibility be-tween a1, c2, c2, d3 and a1, d3 is high because all theratios are preserved fairly well (note that the actuallycomputable ratios over c2, d3 are only 3 because of thedegeneration induced by the shared vertex). By con-trast, the payoff between the remaining pairs of candi-dates is low as some ratios are poorly maintained. Infact, after a few iterations of the evolutionary game (seeFig. 4-4), candidates b1 and b4 become extinct, whilea1,c2 and d3 have been selected as the correct matches.4. Experimental EvaluationIn this section we analyze the object recognition per-formance obtained using the described pipeline with theproposed stable graph, the Delaunay triangulation andthe knn-graph. We also added in the comparison theoriginal SIFT-based affine game-theoretic matcher [2](AGT). The dataset has been produced using 10 ob-jects from the ALOI dataset [6]. For each object a setof different points of view was selected and randomaffine transformations were applied. Additionally, halfof the resulting images were cluttered by applying ran-dom square patches extracted from other images in theset. One at a time, each object in the dataset was usedas a query and the results were sorted according to theaverage payoff of the surviving population (which is ex-pected to be higher when the match is good). In thefirst half of Fig. 5 the result sets obtained by the com-pared methods for the same query are shown. In theupper-right corner of the same figure we display a sin-gle example that shows the match preservation of ourFigure 5. Experimental evaluation of the proposed method (see text for description).method even when severe clutter is applied. Finally,we also plotted a precision/recall graph in order to sup-ply a quantitative overview. While the stable graph of-fers the best relational representation for the proposedhigh-order matching, it can be observed that the originalAGT performs sightly better for high recall rates. How-ever, to be fair, it should be stressed that AGT adopts therobust SIFT descriptor, which requires several secondsto be computed over the tested images. Conversely, thevery simple computation of the Harris response can beperformed up to two orders of magnitude faster.5. ConclusionsWe introduced a novel graph-based representationthat is built by connecting feature points in the spaceof their descriptor rather than in the Euclidean space.Despite the low distinctiveness of the characterization,good recognition results have been obtained adoptingan edge-based high-order matching technique that en-forces the topology of the proposed representation.References[1] A. Albarelli, S. R. Bulo`, A. Torsello, and M. Pelillo.Matching as a non-cooperative game. In ICCV: IEEEIntl. Conf. on Comp. Vis. IEEE Comp. Society, 2009.[2] A. Albarelli, E. Rodola`, and A. Torsello. Impos-ing Semi-Local geometric constraints for accurate cor-respondences selection in structure from motion: AGame-Theoretic perspective. International Journal ofComputer Vision, pages 1–18, Mar. 2011.[3] B. N. Boots. Delaunay triangles: An alternative ap-proach to point pattern analysis. In Proc. of the Ass. ofAmerican Geographers, volume 6, pages 26–29, 1974.[4] T. S. Caetano, T. Caelli, D. Schuurmans, and D. A. C.Barone. Graphical models and point pattern matching.IEEE Trans. Pattern Anal. Mach. Intell., 28(10):1646–1663, Oct. 2006.[5] S. Ekvall, D. Kragic, and F. Hoffmann. Object recogni-tion and pose estimation using color cooccurrence his-tograms and geometric modeling. Image Vision Com-put., 23(11):943–955, Oct. 2005.[6] J.-M. Geusebroek, G. J. Burghouts, and A. W. M.Smeulders. The amsterdam library of object images.Int. J. Comput. Vision, 61(1):103–112, 2005.[7] C. Harris and M. Stephens. A combined corner andedge detector. In Proc. Fourth Alvey Vision Conference,pages 147–151, 1988.[8] T. T. Herbert Bay and L. V. Gool. SURF: Speeded uprobust features. In 9th European Conference on Com-puter Vision, volume 3951, pages 404–417, 2006.[9] G. Kordelas and P. Daras. Robust sift-based featurematching using kendall’s rank correlation measure. InIEEE int. conf. on Image processing, ICIP’09, pages325–328, Piscataway, NJ, USA, 2009. IEEE Press.[10] D. Lowe. Distinctive image features from scale-invariant keypoints. In International Journal of Com-puter Vision, volume 20, pages 91–110, 2003.[11] D. Marr and E. Hildreth. Theory of edge detection.Royal Soc. of London Proc. Series, 207:187–217, 1980.[12] J. Matas, O. Chum, M. Urban, and T. Pajdla. Robustwide-baseline stereo from maximally stable extremalregions. Image and Vision Comp., 22(10):761–767,2004.[13] J. Shotton, A. Blake, and R. Cipolla. Multiscale categor-ical object recognition using contour fragments. IEEETrans. Pattern Anal. Mach. Intell., 30(7):1270–1281,July 2008.[14] S. Taylor, E. Rosten, and T. Drummond. Robust featurematching in 2.3s. In CVPR: IEEE Computer SocietyConf. on Comput.Vis. and Pat. Rec., pages 15–22, 2009.[15] J. Weibull. Evolutionary Game Theory. MIT, 1995.[16] K.-J. Yoon and M.-G. Shin. Reducing ambiguity in ob-ject recognition using relational information. In Asianconf. on Computer vision, ACCV’10, pages 293–306,Berlin, Heidelberg, 2011. Springer-Verlag.

A Stable Graph-Based Representation for Object Recognition through High-Order Matching

Aston Publications Explorer

A stable graph-based representation for object recognition through high-order matching

A. Albarelli

F. Bergamasco

L. Rossi

A. Torsello

Archivio Ricerca Ca'Foscari

A Stable Graph-Based Representation for Object Recognition
through High-Order Matching
A. Albarelli, F. Bergamasco, L. Rossi, S. Vascon and A. Torsello
Universita` Ca’ Foscari Venezia
www.dais.unive.it
Abstract
Many Object recognition techniques perform some
flavour of point pattern matching between a model and
a scene. Such points are usually selected through a fea-
ture detection algorithm that is robust to a class of im-
age transformations and a suitable descriptor is com-
puted over them in order to get a reliable matching.
Moreover, some approaches take an additional step by
casting the correspondence problem into a matching
between graphs defined over feature points. The mo-
tivation is that the relational model would add more
discriminative power, however the overall effectiveness
strongly depends on the ability to build a graph that is
stable with respect to both changes in the object appear-
ance and spatial distribution of interest points. In fact,
widely used graph-based representations, have shown
to suffer some limitations, especially with respect to
changes in the Euclidean organization of the feature
points. In this paper we introduce a technique to build
relational structures over corner points that does not
depend on the spatial distribution of the features.
1. Introduction
Object recognition can be performed through many
different approaches, ranging from the spatial analysis
of color distribution [5] to contour matching [13]. In
this paper we focus on techniques that work by match-
ing sets of feature points that have been extracted from
both a model image and a scene. For this kind of ap-
proach to succeed, the interest points should be repeat-
able, that means that the sets of features extracted un-
der moderately different conditions of pose and lighting
should exhibit a reasonable overlap. To this end, Harris
operator [7], Maximally Stable Extreme Regions [12]
or Differences of Gaussians [11] are widely used in
literature. Moreover, a robust and distinctive descrip-
tor, such as SIFT [10] or SURF [8] must be computed
for each interest point in order to ensure an accurate
Figure 1. Matching two stable graphs
correspondence. While techniques that rely only on
the descriptor for point-wise matching can be very ef-
fective [9] and efficient [14], the adoption of spatial
constraints has proven to enhance the overall reliabil-
ity of the correspondences. Such constraints can be
expressed, for instance, as a precise class of transfor-
mations to which the points matched must adhere [2]
or as a set of relations between features that must be
preserved through the injection that connects model to
data points [16]. The latter class of constraints casts
the search for a correspondence to a graph-matching
problem, that can be solved (heuristically) with gen-
eral or specialized techniques [4]. However, it is not
always straightforward to choose a proper relational
model for the data points. Delaunay triangulation [3]
and k-nearest-neighbour graphs (where each point is
connected to the k nearest points) are popular choices
since they are simple to compute and exhibit a meaning-
ful planar organization. Unfortunately, with these ap-
proaches the connectivity is usually settled by the rela-
tive position of the points in the Euclidean space, which
happens to be a property that is not resilient to changes
in pose and occlusions.
In the following section we introduce a relational
structure that does not depend on the position of the
points and that can be built directly on Harris cor-
ners without requiring the expensive computation of a
feature descriptor. Additionally, we propose a game-
theoretic matching schema that allows to find corre-
spondences that respect the topology of the graph and
that are also coherent with respect to geometrical con-
straints (see Fig. 1).
Figure 2. Building a stable graph
2. Stable Graph Creation
The vertices of the proposed graph, defined as the set
V = {v1, v2...vn}, are exactly the n image pixels that
exhibit the stronger response with respect to the Harris
operator [7], after non-maximal suppression and above
a given threshold. For each vertex v, a simple descriptor
is computed as:
δ(v) = (e′, e′′, λ′, λ′′) (1)
where e′,e′′ and λ′,λ′′ are respectively the normalized
eigenvectors and the eigenvalues of the covariance ma-
trix of the square image patch centered on the vertex v
with a given side wc. The main idea behind the pro-
posed representation is that the connectivity between
two vertices should depend only on the descriptors in-
volved, rather than on the positions of the vertices. To
this end we define the edge set as E as:
E = {(v1, v2) ∈ V × V |e′1 · e′2 < αd} (2)
this means that an edge insists between two vertices if
and only if the respective main eigenvectors are orthog-
onal enough. From an image processing point of view
this makes sense, in fact this rule avoids to connect local
clusters of points that share the same edge and, by con-
trast, connects vertices that represent parts of the objects
well apart. In the following section we will make clear
how these conditions help in obtaining reliable matches.
In Fig. 2 the graph building process is shown. The ver-
tices are shown in the first half of the image along with
the direction of the corresponding eigenvectors. In the
second part of the same figure the stable graph built
upon those vertices is displayed. Specifically, a value
of αd of 0.04 (that corresponds to about 88.5 degrees)
was used. Visually, the graph seems to be very dense,
however this is due to the fact that the very nature of
the proposed approach tends to build edges spanning
from one side of the object to the other. Indeed, the
average degree of the graph shown is slightly below 4.
By changing respectively the Harris response threshold
and the value of αd, graphs with a different number
of vertices and with different edge densities can be ob-
tained. Of course, the usual trade-off between the num-
ber of features and their distinctiveness applies. Fig. 3
displays a comparison between the structures produced
over the same vertex set extracted from two slightly dif-
ferent images, respectively by the Delaunay triangula-
tion, the knn-graph and our method. While topological
changes are apparent with the first two techniques, it is
not easy to tell how much of the non-planar structure
is preserved by the stable graph. However, this will be
assessed in the following as the three graph-based rep-
resentations will be used for object recognition.
3. Game-Theoretic Matching
The Matching between graphs is performed using
the game-theoretic framework presented in [1] and [2].
According to this technique it is possible to cast the cor-
respondence problem in an optimization process that is
guaranteed to converge under payoff-monotonic evolu-
tionary dynamics [15]. Two steps are needed to exploit
such framework: the preparation of a set of matching
candidates that will be selected through the evolution-
ary process and the definition of a payoff function be-
tween pairs of candidates to drive the evolution toward
the selection of a globally coherent set of matches.
3.1 Candidate Selection
Differently from [2], where correspondences are
searched between well characterized features, we are
dealing with rather poor descriptors (see Eq. 1). Since
we trust the graph to be repeatable, we propose to create
matching candidates between edges rather than vertices,
thus each high-order putative match is defined by the
quadruple ((va, vb), (v1, v2)) where (va, vb) is an edge
in the model and (v1, v1) is an edge in the data. For each
edge in the model a maximum of k candidates are pro-
duced. Those candidates are selected by choosing those
that exhibit a better alignment of the principal eigenvec-
tors and similar eigenvalues between the corresponding
vertices (see Fig. 4-1).
Figure 3. Comparison between graphs
Figure 4. The proposed pipeline for stable graph matching (see text for details).
3.2 Payoff Definition
The payoff between two candidates expresses the
compatibility between them. A high payoff lets two
candidate to thrive together, while a payoff of value 0
prevents the evolutionary process to select both the can-
didates in the final population. Since we want the match
to be one-to-one, we set the payoff to 0 if two candidates
share the same model or data edge. Additionally, we
also want to enforce topological constraints, thus we set
the payoff to 0 if the incidence relation between source
and data edges is not consistent. This is the case, for
instance, if the model edges in two candidates share a
vertex, but the corresponding edges in the data do not.
If both one-to-one and topological constraints are satis-
fied, the payoff is computed as a function that accounts
for the relative direction and length of the edges:
pi
(
((va, vb), (v1, v2)),
((vc, vd), (v3, v4))
)
=
1
σ
√
2pi
e−
v(((va,vb),(v1,v2)),((vc,vd),(v3,v4)) )
2
2σ2
(3)
where σ is a term that regulates the selectivity of the
match and v is a function that measures the compati-
bility between the scaling transforms induced by the 6
distances among the involved vertices (see Fig. 4-2):
v
(
((va, vb), (v1, v2)),
((vc, vd), (v3, v4))
)
= min
i=1..6,j=1..6
log
Ri
Rj
(4)
with the 6 distance ratios being:
R1 =
‖va−vb‖
‖v1−v2‖ R2 =
‖vc−vd‖
‖v3−v4‖ R3 =
‖va−vc‖
‖v1−v3‖
R4 =
‖vb−vd‖
‖v2−v4‖ R5 =
‖va−vd‖
‖v1−v4‖ R6 =
‖vb−vc‖
‖v2−v3‖
(5)
Since we compare ratios the approach is scale indepen-
dent. The log in Eq. 4 makes the measure symmetric
and of 0 average, the min takes the worst value, the
Gaussian of Eq. 3 maximizes the payoff when all the
ratios are preserved. The computation of an example
payoff matrix is shown in Fig. 4-3. The payoff be-
tween b1, b4 or a1, b1 is 0 because of the one-to-one
constraint, while the payoff between a1, b4 or c2, b4 is
0 because of the topology constraint (for instance a and
b share a vertex while 1 and 4 do not). Among the non-
zero values, we can observe that the compatibility be-
tween a1, c2, c2, d3 and a1, d3 is high because all the
ratios are preserved fairly well (note that the actually
computable ratios over c2, d3 are only 3 because of the
degeneration induced by the shared vertex). By con-
trast, the payoff between the remaining pairs of candi-
dates is low as some ratios are poorly maintained. In
fact, after a few iterations of the evolutionary game (see
Fig. 4-4), candidates b1 and b4 become extinct, while
a1,c2 and d3 have been selected as the correct matches.
4. Experimental Evaluation
In this section we analyze the object recognition per-
formance obtained using the described pipeline with the
proposed stable graph, the Delaunay triangulation and
the knn-graph. We also added in the comparison the
original SIFT-based affine game-theoretic matcher [2]
(AGT). The dataset has been produced using 10 ob-
jects from the ALOI dataset [6]. For each object a set
of different points of view was selected and random
affine transformations were applied. Additionally, half
of the resulting images were cluttered by applying ran-
dom square patches extracted from other images in the
set. One at a time, each object in the dataset was used
as a query and the results were sorted according to the
average payoff of the surviving population (which is ex-
pected to be higher when the match is good). In the
first half of Fig. 5 the result sets obtained by the com-
pared methods for the same query are shown. In the
upper-right corner of the same figure we display a sin-
gle example that shows the match preservation of our
Figure 5. Experimental evaluation of the proposed method (see text for description).
method even when severe clutter is applied. Finally,
we also plotted a precision/recall graph in order to sup-
ply a quantitative overview. While the stable graph of-
fers the best relational representation for the proposed
high-order matching, it can be observed that the original
AGT performs sightly better for high recall rates. How-
ever, to be fair, it should be stressed that AGT adopts the
robust SIFT descriptor, which requires several seconds
to be computed over the tested images. Conversely, the
very simple computation of the Harris response can be
performed up to two orders of magnitude faster.
5. Conclusions
We introduced a novel graph-based representation
that is built by connecting feature points in the space
of their descriptor rather than in the Euclidean space.
Despite the low distinctiveness of the characterization,
good recognition results have been obtained adopting
an edge-based high-order matching technique that en-
forces the topology of the proposed representation.
References
[1] A. Albarelli, S. R. Bulo`, A. Torsello, and M. Pelillo.
Matching as a non-cooperative game. In ICCV: IEEE
Intl. Conf. on Comp. Vis. IEEE Comp. Society, 2009.
[2] A. Albarelli, E. Rodola`, and A. Torsello. Impos-
ing Semi-Local geometric constraints for accurate cor-
respondences selection in structure from motion: A
Game-Theoretic perspective. International Journal of
Computer Vision, pages 1–18, Mar. 2011.
[3] B. N. Boots. Delaunay triangles: An alternative ap-
proach to point pattern analysis. In Proc. of the Ass. of
American Geographers, volume 6, pages 26–29, 1974.
[4] T. S. Caetano, T. Caelli, D. Schuurmans, and D. A. C.
Barone. Graphical models and point pattern matching.
IEEE Trans. Pattern Anal. Mach. Intell., 28(10):1646–
1663, Oct. 2006.
[5] S. Ekvall, D. Kragic, and F. Hoffmann. Object recogni-
tion and pose estimation using color cooccurrence his-
tograms and geometric modeling. Image Vision Com-
put., 23(11):943–955, Oct. 2005.
[6] J.-M. Geusebroek, G. J. Burghouts, and A. W. M.
Smeulders. The amsterdam library of object images.
Int. J. Comput. Vision, 61(1):103–112, 2005.
[7] C. Harris and M. Stephens. A combined corner and
edge detector. In Proc. Fourth Alvey Vision Conference,
pages 147–151, 1988.
[8] T. T. Herbert Bay and L. V. Gool. SURF: Speeded up
robust features. In 9th European Conference on Com-
puter Vision, volume 3951, pages 404–417, 2006.
[9] G. Kordelas and P. Daras. Robust sift-based feature
matching using kendall’s rank correlation measure. In
IEEE int. conf. on Image processing, ICIP’09, pages
325–328, Piscataway, NJ, USA, 2009. IEEE Press.
[10] D. Lowe. Distinctive image features from scale-
invariant keypoints. In International Journal of Com-
puter Vision, volume 20, pages 91–110, 2003.
[11] D. Marr and E. Hildreth. Theory of edge detection.
Royal Soc. of London Proc. Series, 207:187–217, 1980.
[12] J. Matas, O. Chum, M. Urban, and T. Pajdla. Robust
wide-baseline stereo from maximally stable extremal
regions. Image and Vision Comp., 22(10):761–767,
2004.
[13] J. Shotton, A. Blake, and R. Cipolla. Multiscale categor-
ical object recognition using contour fragments. IEEE
Trans. Pattern Anal. Mach. Intell., 30(7):1270–1281,
July 2008.
[14] S. Taylor, E. Rosten, and T. Drummond. Robust feature
matching in 2.3s. In CVPR: IEEE Computer Society
Conf. on Comput.Vis. and Pat. Rec., pages 15–22, 2009.
[15] J. Weibull. Evolutionary Game Theory. MIT, 1995.
[16] K.-J. Yoon and M.-G. Shin. Reducing ambiguity in ob-
ject recognition using relational information. In Asian
conf. on Computer vision, ACCV’10, pages 293–306,
Berlin, Heidelberg, 2011. Springer-Verlag.


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A stable graph-based representation for object recognition through high-order matching

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