Color and grey level object retrieval using a 3D representation of force histogram
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Image and Vision Computing 21 (2003) 483–495
www.elsevier.com/locate/imavis
Color and grey level object retrieval using a 3D representation
of force histogram
Salvatore Tabbone, Laurent Wendling*
LORIA, Campus Scientifique, BP 239, Vandoeuvre-les-Nancy Cedex 54-506, France
Received 20 July 2001; received in revised form 14 January 2003; accepted 20 January 2003
Abstract
A new method for both grey level and color object retrieval is presented in this paper. Our feature is based on previous works on force
histogram notion which is extended here to handle with photometric information. This kind of feature has low computing time and allows
keeping fundamental geometric transformations as scale, translation, symmetry and rotation. More precisely objects processed by defining a
tridimensional signature which takes into account their photometric variations and their shapes. Experimental results show the promising
aspect of our approach.
q 2003 Published by Elsevier Science B.V.
Keywords: Photometric objects; Object matching; Force histogram; Tridimensional signature
1. Introduction 2. Related woks
A new approach for the content-based retrieval problem More and more content-based image retrieval systems
is presented in this paper. Our feature is based on force have been developed in the early years [29]. Full overviews
histogram introduced by Matsakis and Wendling [18,19] concerning the indexing problem can be found in the
which allows keeping fundamental geometric transform- literature [1,11,29]. Some systems allow querying by
ations as scale factor, translation, rotation and symmetry. It keywords, assuming that each image has been manually
has been shown in previous works that such a feature is a indexed when inserted into the database. Others systems
powerful tool to define spatial relations [18,19] between often use one or more features to describe the content of
objects and also to describe robust signatures for binary images in order to provide an automatic content-based
objects [19,35]. In this paper we show that such a notion can retrieval process. We give here a succinct description of
be extended to retrieve both grey level and color objects by some content-based approaches close to our research field.
including photometric variations in the force histogram. Generally a similarity measure based on features is used to
First, a brief overview of content-based retrieval approaches help the user to find specific images in the database.
is given in Section 2. Then, the definition of a force Typically, the indexing scheme makes use of color, texture,
histogram and its main properties are recalled in Section 3. edge and shape information.
The calculation of F3D-signatures on grey level and color
Some approaches focus on interest points [2,4,22,28] to
objects is presented in Section 4. The measure of similarity
compute different local characteristics of each image.
between two F3D-signatures is given in Section 5. Finally,
Others use texture information [6,16,17,27]. Typically,
some experimental studies using image databases and a
Gabor filters [34] or Haar wavelet transform coefficients
discussion about the advantages and the limits of our
[15] are well suited to compute these kinds of features. Early
approach are provided in Section 6.
systems were based on color histograms [12,24,30,33] or on
* Corresponding author. shape information [3,20,32]. Several content-based image
E-mail address: wendling@loria.fr (L. Wendling); tabbone@loria.fr retrieval systems merge different ways (that is encapsulation
(S. Tabbone). of features) to describe images [14,23,25,26,31]. These
0262-8856/03/$ - see front matter q 2003 Published by Elsevier Science B.V.
doi:10.1016/S0262-8856(03)00016-7484 S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495
Fig. 1. Definition of a F-signature.
systems give generally better results than the ones using histogram obtained in this way can be noisy and strongly
only one attribute. dependent on the angle threshold step of the histogram. To
In this paper we address the issue of indexing images overcome this problem, the use of straight lines following a set
based on visual content. We focus on approaches that use of directions u is considered, and the method handles with
low-level features. A new approach dealing with grey level segments, in order to decrease the processing time (see Fig. 1).
and color objects is proposed in this paper. Our feature is The extracted forces are calculated between segments—i.e.
based on the force histogram notion which is extended here the attraction force of one segment with respect to another
to handle with photometric information. Such a feature is segment is computed. Let I1 and I2 be two segments carried by
isotropic and requires low time complexity. It describes a the same straight line, let lI1 l and lI2 l be their respective
3D-signature keeping nice geometric properties as scale, lengths, and let DuI1 I2 be the distance between I1 and I2 : The
rotation and translation. attraction force from I1 to I2 is given by:
ðlI2 l ðlI1 lþDuI1 I2 þlI2 l
fr ðlI1 l; DuI1 I2 ; lI2 lÞ ¼ wr ðu 2 vÞdv du ð2Þ
3. Signature of binary object 0 DuI þlI2 l
1 I2
3.1. Description of the method For example, the calculation of f0 corresponds to lI1 l £ lI2 l
when I precedes J and to lI1 l2 =2; when I1 and I2 are
In this section, the scheme for computing the F-signature superimposed; the calculation of f2 when I1 precedes I2 ; is
of a binary graphical object, which is a particular histogram of given by
forces [18,19,35] is recalled. A histogram of forces can be ðDuI1 I2 þ lI1 lÞðDuI1 I2 þ lI2 lÞ
assumed to be the calculation of all the forces exerted between ln :
DuI1 I2 ðDuI1 I2 þ lI1 l þ ðDuI1 I2 þ lI2 lÞÞ
the pixels of a same object. Let wr be the map from R into Rþ,
null on R2 and continuous on Rpþ, such that: Let A be an object of the plane which is entirely described by a
;d [ Rpþ ; wr ðdÞ ¼ 1=d r
ð1Þ pencil of parallel straight lines of angle u from the orthogonal
frame of the image. Let Duh be a line; the set of segments of A
Let a1 and a2 be two points of R , and d be the distance between
2
beared by this straight line corresponds to Au ðhÞ ¼S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495 485
Fig. 3. F3D-signatures of previous butterflies.
All the pencils of lines Dhu of the plane which entirely describe † Translation. The information of the object is processed
A are then considered: independently of its location in the frame of the image.
Let Tu~ be a translation of vector u~ :
ðþ1
F AA l R ! Rþ ; u 7! Fðu; Au ðvÞ; Au ðvÞÞdv ð4Þ F AA ðuÞ ¼ F Tu~ ðAÞTu~ ðAÞ ðuÞ ð5Þ
21
In the discrete case, the calculation of F AA ðuÞ provides an † Symmetry. The forces exerted on an object are the same
evaluation of the forces exerted by the object on itself in following two opposite directions:
the direction u: The calculation of F AA following the set of
angles ui ðui [ ½2p; þpÞ defines the FAA 2D signature of the F AA ðuÞ ¼ F AA ðp 2 uÞ ð6Þ
object A:
† Scale factor. Only the shape of the F-signatures is
3.2. Geometric properties
considered. If a scale factor is applied to an object, its
histogram will be stretched. In such a case, the forces are
The aim of our study is to classify similar objects
multiplied by a value that depends or r and on the scale
independently of their location, their orientation and their
factor:
size. So it is important to have a feature able to take into
account fundamental geometric properties as translation, fr ðklIl; kDuIJ ; klJlÞ ¼ k22r fr ðlIl; DuIJ ; lJlÞ ð7Þ
rotation and scale factor. By definition, in the continuous
case, the properties of F allow us to find easily such † Rotation. When a rotation is applied to an object, the
geometric transformations [18,19]: histogram is shifted, as the approach is isotropic. Let u be
Fig. 4. Visualization of geometric properties.486 S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495
Fig. 5. Transformation of a color image into a matrix composed of F3D-signatures.
Fig. 6. F3D-signatures of butterflies.S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495 487
Fig. 7. Nine nearest images of pap28_1 contained in the database.
Fig. 8. Nine nearest images of pap14_1 contained in the database.
Fig. 9. Similarity ratio between the signatures of pap10_1 and another insect.488 S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495
Fig. 10. Comparison with other approaches—butterfly database—.
a direction and r be a rotation of angle u0 applied to an
object A; we have:
0 0
F AA ðuÞ ¼ F rðA;u ÞrðA;u Þ ðu þ u0 Þ ð8Þ
These properties are also valid in the discrete case, with
weak error variations, due to both histogram and sampling
steps.
4. F3D-signature
4.1. Handling with photometric objects
4.1.1. Usefulness Fig. 11. Measure of quality for the eight main clusters of butterfly.
It is possible to integrate the photometric variations shapes but in different areas of intensities. For example, the
during the definition of a F2D-signature. In this case the
butterflies presented Fig. 2 have close signatures.
grey level difference between two consecutive cuts should
A new dimension has been added to improve the
be processed. Actually two kinds of schemes may be used to
classification and to better take into account the variations
handle the level cuts ai using force histogram [18]. The first
directly derives from the generic double sum scheme
defined by Dubois and Jaulent [8] and has a high processing
time. We have then used the simple sum scheme, proposed
by Khrisnapuram et al. [13] which decreases the computing
time from quadratic to linear, that is:
X
#g
ai
A ai
F AA ¼ mi F A ð9Þ
i¼1
with #g the number of grey levels, mi the difference between
ai ai
two consecutive grey level cuts ðai 2 ai21 Þ and F A A the
signature of the binary object obtained from the level cut ai :
Generally, a bidimensional signature is accurate because
it takes care of the variations of grey levels in the image.
Nevertheless, as only the shape of the histogram is studied,
it is difficult to discriminate two objects having similar Fig. 12. Measure of quality for all the database.S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495 489
Fig. 13. F-signatures of four objects (view 08).
of photometry following the set grey level cuts. The processing due to the computation of force histograms
signatures of the previous butterfly samples are then better between planes.
differentiated by adding a third dimension to the signature As in Refs. [9,33] the new plane r; computed from R was
(see Fig. 3). defined as follows:
R
rðR; G; BÞ ¼
4.1.2. Definitions RþGþB
It is easy to show that a F3D-signature verifies the
The same processing is carried out for the other configur-
fundamental geometric properties described in Section
ations gðR; G; BÞ and bðR; G; BÞ: Then the F3D-signatures of
3.2. Let A be a photometric object and let {li }i¼1;n be a
each normalized plane were computed to define the new
strictly increasing series of grey levels ðl1 , l2 , · · · , gg
diagonal of the matrix (see Fig. 5): Frr 3D ; F3D and F3D :
bb
ln Þ including in A: Let FAA li be the force histogram In order to take into account the link between the couple of
calculated on binary objects from a binarization of planes ðRGÞ; ðRBÞ and ðBRÞ; a classical transformation [10]
threshold li (if Aðx; yÞ . li then Aðx; yÞ ¼ 1 else was used. The link between the two planes R and G became:
Aðx; yÞ ¼ 0). The set of included regions Aln # Aln21 #
· · · # Al1 may be interpreted as another representation of ðR 2 GÞ2
lRG ¼
A: So, a F3D-signature is defined by an ordered set of ðR 2 GÞ2 þ ðR 2 BÞ2 þ ðG 2 BÞ2
bidimensional signatures (checking separately the proper-
The three news planes (lRG ; lRB and lBG ) describe the link of
ties given in Section 3.2): FAA3D ¼490 S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495
Fig. 15. Fourteen nearest images of view 0 of object 53.
Fig. 5 shows an example of color object and its associated (cf. Section 3.2) can be obtained using the histogram of
F3D-matrix. forces. Each F3D-signatures is normalized by its volume to
take into account the scale factor between objects of a
4.3. Object retrieval same cluster.
Let A and B be two objects, F AA BB
3D and F3D be their
4.3.1. Distance between signatures associated normalized signature and p be the number of
A representation of the object in the same unitary frame directions processed. We set F AA AA
3D ¼S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495 491
Fig. 17. Example of F3D-signatures for progressive views of a same object.
4.1). A criteria of similarity S is maximized following all time to achieve consists results. We can remark that the
the histogram shifts to obtain an approximation of the calculation of FS is a generalization of S:
rotation factor:
( Xp ) 4.3.2. Complexity of the method
u¼0 m ðu; xÞ
AB
S ¼ max X ð10Þ The timepffifficomplexity
ffi for computing a histogram of forces
p
u¼0 M ðu; xÞ
AB
x[½0;p is in Oðpm mÞ; where m is the number of pixels of the image
P and p the number of digitalization steps of the histogram
with: mAB ðu;PxÞ ¼ ni¼1 minðF AA BB
li ðuÞ; Fli ðu þ xÞ%pÞÞ and
AA BB
[18]. This bound is reached for very highly textured images.
M ðu; xÞ ¼ i¼1 maxðF
AB n l ðuÞ; F
i
l ðu þ xÞ%pÞÞ:
i In our approach, the complexity is in OðpmÞ when using
The value of S is not sensitive to object scaling because constant force histograms (r ¼ 0 in Eq. (1)), and also in
the matched signatures are normalized. Moreover circular most cases when using other force histograms ðr – 0Þ:
shifts are applied to F AA
3D and S is obtained by maximizing For efficiency reasons, Bresenham’s algorithm [5] is used
the classical Tanimoto index (min over max). Then S is not in our implementation, as it is a fast method which
sensitive to object rotation either. minimizes error in drawing lines on integer grid points. It
The same scheme is applied to process color objects. approximates line segments defined by rational coefficients
Based on color information, normalization is split into two using only integral points. Bresenham’s algorithm is applied
cases: the diagonal and the other cells of the matrix in order only to one line, to store the horizontal and vertical shifts
to separate the characteristic signatures of the plane and representing a line scanning the image following the
between the planes interaction. The final score FS is given direction u: These shifts are used to define the pencil of
by: lines allowing to scan the whole image (with this approach
8 Xp X3 X3 9 and for a given orientation u; any pixel is only processed by
1 < mAij Bij
ð u ; xÞ =
u¼0 i¼1 j¼1 one line). The p directions are then processed to define the
FS ¼ max Xp X3 X3 ð11Þ
2 x[½0;p : M Aij Bij ðu; xÞ ; F-signature.
u¼0 i¼1 j¼1
The complexity, using grey or color images, is generally
where i; j are the coordinates of the signature in the matrix. OðnpmÞ (with n the number of grey levels considered). To
The shifts are performed for all the signatures in the same decrease the processing time no binarization was performed
Fig. 18. Comparison with other approaches—coil database—.492 S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495
the results provided are right and both the scale and the
rotation factors are taken into account by our approach.
The robustness of our approach to a specific occultation
is shown in another example presented in Fig. 8: pap14_4
and pap14_5 represents a folded butterfly belonging to the
same cluster. Moreover the less classified butterflies in Figs.
7 and 8 are dissimilar in term of photometry but are similar
in shapes (from pap19_1 to pap15_3 in Fig. 7 and from
pap16_1 to pap68_1 in Fig. 8).
Fig. 9 shows the signatures of a butterfly and another
insect. The score obtained guarantees that the matched
object is really far.
We have also used the experimental studies proposed by
Derrode [7] to make a comparative study. Fig. 10 presents
the nearest butterflies of pap15_2 using, respectively, Hue
Fig. 19. Measure of quality r—coil-100, pgm—. (a) One view, (b) two invariants (HI), Fourier-Mellin invariants (FMI) and F3D-
views, (c) four views per object.
signatures matching (F3D). A value near 0 corresponds to a
but an accumulator table has been used to manage with grey good retrieval for HI and FMI and near 1 for our approach.
levels. Then all the processings have been carried out in p We can note the presence of the butterfly pap15_6
scans of the image. recognized by only our method which is more robust to the
deformation.
A classical measure of match quality [10] was applied to
all the database to have an idea of the behavior of our
5. Experimental results approach:
!
1 XC X Ck k
5.1. Grey levels objects N 2 r Qi
r ¼ ð12Þ
N k¼1 i¼1 N 2 1
5.1.1. Butterfly database with C the number of clusters and Ck the number of samples
We have used a database provided by Derrode et al. [7]. in cluster k: N is the number of images contained in the
k
It consists of around a hundred of images of butterflies database and the rank r Qi denotes the position of the match
describing several clusters following different scales and (that is set to 1 for a correct match and to N in the worst
orientations. Fig. 6 presents four types of butterflies with case) of the query image Qki (of cluster k) in an ordered list
their associated F3D-signatures. of N match values.
Fig. 7 gives the nine nearest images of butterfly pap28_1 Figs. 11 and 12 present, in term of percentage (Y-axis),
and the scores reached. We can see that for each image the application of such a criteria over all the database of
Fig. 20. Nine nearest images of view 0 of object 51.S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495 493
Fig. 23. Similar objects.
was computed (curve X in Fig. 14) and the total number
of views of the same object found among the 71 possible
choices (curve Y in Fig. 14). Fig. 14 shows the results
Fig. 21. Robustness to view-changes. obtained for each object using one view per object. An
increasing sort was applied to the curve X to achieve a
butterflies with increasing sizes of signatures (X-axis: grey better visualization of the results.
levels £ directions). The behavior of the eight main clusters The minimum reach by the curve X is 4 and the
are shown in Fig. 11 and the mean rate over all the database maximum is 71. The high score obtained and the closeness
is given Fig. 12. The results provided show the robustness of of the two curves attest of the robustness of our approach to
our approach. We can remark that a signature having a size the change of view-points.
8 £ 8 is enough for such an application. Fig. 15 presents the 14 nearest views of an object well
recognized ðX ¼ 33Þ and the similarity ratio reached.
The first number corresponds to the identifier of the object
5.1.2. Coil-100 database
(here 53) and the second to the rotation angle in degree (here
The robustness of our approach to a change of views, 0 for the first view). The different views show that the
has been tested using the well-known coil-100 database invariance by symmetry is considered by our approach.
[21]. Such database contains 100 objects of varying Fig. 16 shows a case of low identification towards the
shapes following 72 views of 58 apart. We consider in change of view-points. Only a series of four images has been
this section grey level representations of these views. identified. Nevertheless the object 12 is in the same area of
Fig. 13 shows a view of four objects and the associated grey levels and has a close shape.
F3D-signatures. Fig. 17 presents the signatures of the views of the same
The signature of a view of each object of the database 3D objects with weak rotations (with steps of 58). Shapes of
has been matched to the 7199 remaining views. The these signatures are close because the associated views are
nearest views of a particular view of each object were close. Obviously, when the rotation applied is important, the
computed. As an object is represented following 72 signatures are different because the differences between the
views, the 71 nearest views, in term of similarity, were shapes of the objects increase.
kept. For each object the number or views rightly As previously, we have compared our method to both
classified without any view of another objects inserted Fourier-Mellin and Hue invariants. The results provide in
Fig. 18 shows that our method is more robust to the change
of view-points and has a better behavior using photometric
data.
Such a result is also underlined by the computation of
the predefined measured of quality r with Ck ¼ 72 and
N ¼ 7200 (see Eq. (12)). Three curves are proposed
(Fig. 19): an object describes by only one view (a), an
object is assumed to two opposite views—0 and p—and
the maximum of the two final similarities reached is
considered (b), from four views—following the cardinal
directions—(c).
5.2. Color images
In this section, the coil-100 database was used again to
Fig. 22. Measures of quality r (coil-100, color). (a) One view, (b) two determine if the color brings an improvement during the
views, (c) four views per object. identification step. We have also used to database of around494 S. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495
Fig. 24. Nearest image to a query photo (upper-left corner).
Fig. 25. Other example from another query photo (upper-left corner).
2500 broad images to study the behavior of our approach in F3D-signatures, following successive variations is currently
a real case. under consideration to improve the classification.
Fig. 23 shows two views of objects having similar shapes
and having low disparities in photometry. The use of color
5.2.1. Color objects information is obviously more discriminant than the one of
Coil-100 database has been used to test if the matching of grey levels. Such a result shows that the shape in the
F3D-signatures of color objects brings an advance com- signature predominates when the photometric variations
pared to grey level objects. So the object previously between two images are low.
presented in Fig. 16 having a low identification score was
studied again. The new result are given in Fig. 20 (X ¼ 11 5.2.2. Color photos
and Y ¼ 23). The similarity ratios are greater than those We have also tested our method with a database
presented in Fig. 16. composed of around 2500 broad images. Figs. 24 and 25
The rates of robustness to the change of view-points are present two results reached using our approach. The images
also improved (Fig. 21). The curves X and Y are nearer and achieved were close in term of photometry and shapes.
the number of classified views is greater. For example the 71 Other results have shown that our method provides
views of 27 objects have been full recognized. That is interesting results n several series of broad images.
also attested by the computation of r on the color database
(Fig. 22 with X-axis: planes £ grey levels £ directions),
using one view (a), two views (b) and four views (c). 6. Conclusion
It is obvious that full recognized objects have similar
shape following any view. Such a result is weak, without We have shown in this paper that an F3D-signature
learning steps, using objects having various shapes follow- allows to reach a fast and robust retrieval using both color
ing their tridimensional views. For example the views of the and grey level objects. Preliminary tests were performed
width and the length of a car are different. The learning of on color photos. Currently, we search to extend ourS. Tabbone, L. Wendling / Image and Vision Computing 21 (2003) 483–495 495
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