A Descriptor based on Intensity Binning for Image Matching

B. Balasanjeevi and C. Chandra Sekhar

Indian Institute of Technology, Madras, India

Keywords:

Image Descriptor, Computer Vision, Image Matching.

Abstract:

This paper proposes a method for extracting image descriptors using intensity binning. It is based on the fact

that, when the intensities of the interest regions are quantized, the pixels retain their bin labels under common

image deformations, up to a certain degree of perturbation. Consequently, the spatial conﬁguration and the

shape of the connected regions of pixels belonging to each bin become resilient to noise, which, as a whole,

capture the topography of the intensity map pertaining to that region. We examine the effect of classical

image deformations on this representation and seek to ﬁnd a compact yet robust representation which remains

unperturbed in the presence of noise and image deformations. We use Oxford dataset in our experiments and

the results show that the proposed descriptor gives a better performance than the existing methods for matching

two images under common image deformations.

1 INTRODUCTION

Local features have gained widespread attention re-

cently, due to their robustness to image deformations,

image occlusion and changes in viewpoint. A local

feature encodes the intrinsic pattern that captures the

essence of a region of interest, independent of other

such regions. It does not necessarily correspond to

any meaningful part of the scene and hence can be se-

lected, although not exclusively, based on the under-

lying image properties such as intensity, texture and

color. Local features have been used successfully for

image matching (Tuytelaars and Van Gool, 2004), ob-

ject recognition (Viola and Jones, 2004; Leibe et al.,

2008; Fergus et al., 2003; Lowe, 2004; Nister and

Stewenius, 2006; Zhang et al., 2007; Berg et al.,

2005), texture recognition (Zhang et al., 2007), im-

age retrieval (Mikolajczyk and Schmid, 2001), build-

ing panoramas (Brown and Lowe, 2003) and social

media (Snavely et al., 2008; Kennedy and Naaman,

2008; Agarwal et al., 2009).

The process of constructing local features involves

two stages. The ﬁrst step (localization) consists of de-

tection of Interest Regions (IR) which possess high

information content while being robust to the image

deformations like blur, illumination changes, scaling,

rotation and afﬁne transformations. Various methods

for detecting interest regions were reviewed in (Tuyte-

laars and Mikolajczyk, 2008), of which Hessian-

Afﬁne detector (Mikolajczyk and Schmid, 2005) was

shown to perform better than other methods.

The next step involves building a descriptor for

each interest region obtained from the previous step,

such that the representation is compact, discrimina-

tive, generalized and robust to image deformations

and noise.

There is a rich set of existing methods for extract-

ing descriptors which are presented in Section 2. The

proposed method is discussed in Section 3 and the re-

sults are presented in Section 4.

2 METHODS FOR EXTRACTION

OF DESCRIPTORS

Many techniques have been developed for describing

the interest regions. One of earliest known works is

steerable ﬁlters (Freeman and Adelson, 1991) which

steer derivatives in a particular direction making them

invariant to rotation. Johnson et al. (Johnson and

Hebert, 1997) introduced a representation called spin

image. Baumberg (Baumberg, 2000) proposed a de-

scriptor which uses a multi-scale Harris feature de-

tector (Harris and Stephens, 1988), with a set of in-

variants robust to local linear transformations form-

ing the descriptor. Berg, et al. (Berg et al., 2005)

proposed a deformable shape matching framework,

which incorporates geometric blur descriptor (Berg

and Malik, 2001) as well as the geometric distortion

between pairs of corresponding points. Lowe (Lowe,

2004) proposed a Scale Invariant Feature Transform

Balasanjeevi B. and Chandra Sekhar C..

A Descriptor based on Intensity Binning for Image Matching.

DOI: 10.5220/0004827700960103

In Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods (ICPRAM-2014), pages 96-103

ISBN: 978-989-758-018-5

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

(SIFT), which combines a scale invariant region de-

tector and a descriptor based on the gradient distribu-

tion in the detected regions. Ke and Suthankar (Ke

and Sukthankar, 2004) developed the PCA-SIFT de-

scriptor, which represents local appearance by prin-

cipal components of the normalized gradient ﬁeld,

which is more compact than the standard SIFT repre-

sentation. Mikolajczyk and Schmid (Mikolajczyk and

Schmid, 2005) proposed GLOH (Gradient Location

and Orientation Histogram), in which they modiﬁed

SIFT by using a circular gradient location orientation

grid, as well as the quantization parameters of the his-

tograms. Heikkil et al. (Heikkil et al., 2009) proposed

CS-LBP (Center Symmetric-Local Binary Patterns), a

variant of LBP, which is more compact than LBP and

is computationally less expensivethan LBP and SIFT.

Lazebnik (Lazebnik et al., 2005) extracted a sparse

set of afﬁne regions and then constructed descriptors

based on spin images and SIFT descriptor. Bay, et

al. (Bay et al., 2008) proposed an efﬁcient imple-

mentation of SIFT by applying the integral image to

compute image derivatives. Chen, et al. (Chen et al.,

2010) proposed a descriptor inspired by Weber’s law,

which constitutes two components: one based on rel-

ative pixel differences and other on the orientation of

the pixel, which were used to construct the descrip-

tor. Cheng, et al. (Cheng et al., 2008) introduced a

local image descriptor robust to general image defor-

mations by using multiple support regions of differ-

ent sizes centered on the interest point. Winder and

Brown (Brown et al., 2011) proposed a framework for

combining various descriptors and learned an optimal

parameter setting to maximize the matching perfor-

mance. Many of the aforementioned descriptors were

evaluated in (Mikolajczyk et al., 2005) and that SIFT

and GLOH were found to perform better when com-

pared to other descriptors under common image de-

formations. In this paper, we will be using these two

descriptors along with CS-LBP for benchmarking the

performance of the proposed descriptor.

3 THE PROPOSED METHOD

3.1 Motivation

An image descriptor should mirror the topography of

the underlying intensity map such that the representa-

tion is distinctive, compact and most importantly ro-

bust to common image deformations.

To construct a descriptor which satisﬁes these

properties, we ﬁrst analyze how the intensity map

is affected by deformations such as blur, contrast

changes, and similarity and afﬁne transformations.

Instead of considering the raw pixel intensities, we

quantize the intensity map and analyze the effect of

each deformation on the bin labels of the pixels as

follows:

1. Consider an image pair in which one of the im-

ages is perturbed with one of the aforementioned

deformations.

2. Extract the IRs from the image pair and ﬁnd the

corresponding regionsusing the method discussed

below (Section 3.1.1).

3. Quantize the intensities of the corresponding re-

gion pairs between the images and compute the

proportion of the pixels which retain the bin label.

3.1.1 Identifying the Corresponding Regions

The IRs are extracted from each image using the

Hessian-Afﬁne detector, which outputs elliptical re-

gions. Given an IR (r

) in one image, its correspond-

ing IR (CR) in the other image is obtained by pro-

jecting the region under a homography H relating the

images, and ﬁnding the IR in the second image with

the highest overlap. Let R

(i)

represent the set of IRs

in image i. For any region r

∈ R

(1)

, let r

′

represent

its projection under H . Then the corresponding re-

gion of r

is given as,

CR(r

∈ R

(1)

) = {r

∗

∈ R

(2)

|∀r

∈ R

(2)

overlap(r

′

) ≤ overlap(r

′

∗

))}

(1)

The overlap between two elliptical regions r

and

is computed based on the method proposed in

(Mikolajczyk and Schmid, 2005). The minimal rect-

angular region bounding the ellipse pair is sampled

and the amount of overlap is computed as the ratio of

the number of points belonging to both the regions to

that belonging to either of the regions. That is,

overlap(r

) =

∩ r

∪ r

(2)

Here, the numerator denotes the area of the intersec-

tion and the denominatordenotes the area of the union

of the elliptical regions.

3.1.2 Observations

The evaluation of the above method was done on Ox-

ford data set

, which contains image sets for bench-

marking the descriptors under a variety of image de-

formations. Each set consists of 6 images, with the

Oxford data set is available at http://www.robots.

ox.ac.uk/∼vgg/research/afﬁne.

ADescriptorbasedonIntensityBinningforImageMatching

reference as image 1, and the images 2 to 6 being the

increasingly perturbed versions of the reference im-

age.

Figure 1 shows the quantized regions of a pair of

corresponding IRs obtained using the procedure men-

tioned above under blur. It is evident from the ﬁgure

that quantizing the intensity maps makes the IRs strik-

ingly similar.

(a)

(b)

Figure 1: The quantized intensity maps of a pair of corre-

sponding regions using (a) 2 bins (b) 3 bins.

Figure 2 shows the percentage of pixels across all

IRs which retain their bin labels when the intensity

range of each IR is quantized into n bins, where n is

varied from 2 to 10, under a variety of image defor-

mations. As is evident from the ﬁgure, this quantity

decreases with increasing perturbation and also with

increasing number of bins, due to the fact that the

noise resilience of a pixel’s bin label varies inversely

with the width of the bin. That is, a slight perturba-

tion is sufﬁcient to effect a change in the bin label as

the number of bins increases. It should be noted that,

almost all of the pixels (90%) retain their bin labels

when n = 2. Thus, we can claim that,

The bin label of a pixel is more or less invariant

under classical image deformations, up to a certain

degree of perturbation.

Now, if the bin labels of pixels remain unchanged,

then the connected regions of the pixels belonging to

a bin will retain their shapes and spatial conﬁguration.

That is,

If we consider a pair of corresponding regions, the

shapes and the spatial conﬁgurationsof the connected

regions of pixels belonging to the same bins will be

similar.

3.2 Constructing the Descriptor

Thus, based on this observation, we can assert that the

quantized map captures the topography of the inten-

sity map of an IR. But such a representation cannot

(a) Blur

(b) Scaling and rotation

Figure 2: Evaluation of the effect of different image defor-

mations on the bin labels for different types of distortions

(a) blur (b) scaling and rotation (c) illumination changes.

be used as such due to its high dimensionality. To

obtain a compact representation, we compute second

order central moments which capture the shape and

spatial conﬁgurations of the connected regions, since

the center of mass and the spread of the region are

captured more succinctly. Also, such a construction

has an additional advantage of being a generalized de-

scription of the intensity map, making it more resilient

to image perturbations.

The descriptors are constructed as follows. Given

an image, the IRs are ﬁrst extracted using Hessian-

Afﬁne detector and each IR is quantized using one

of the three methods discussed in Section 3.5, using

n bins. We call such a quantized map as an n-map.

To represent an n-map, we compute the second order

central moment, i.e., we ﬁt an ellipse, to every con-

nected region of pixels belonging to each bin.

ICPRAM2014-InternationalConferenceonPatternRecognitionApplicationsandMethods

Algorithm 1: Compute Descriptors.

1: procedure D = COMPUTEDESC(r,n) ⊲ interest

region r with n bins

2: B ← Bin(r,n) ⊲ Quantize r using n bins

3: D ← [ ] ⊲ Initialize descriptor

4: for bin=1 .. . n do

5: K

bin

← [ ] ⊲ Initialize K

bin

6: n

bin

← #connected regions in current bin

7: for reg=1 .. . n

bin

8: E

reg

← FitEllipse(B,bin,reg)

9: K

bin

← [K

bin

reg

] ⊲ Append ellipse

10: end for

11: D ← [D K

bin

] ⊲ Append K

bin

12: end for

13: end procedure

The steps involved in constructing the descriptor

are shown in Algorithm 1. The function FitEllipse ﬁts

an ellipse to a connected region of pixels, by comput-

ing its second order central moment. An ellipse E is

represented by the 5-tuple, (u, v,a,b, c) satisfying the

equation a(x− u)

+ 2b(x− u)(y− v)+c(y− v)

= 1.

Figure 3 shows the ﬁtted ellipses for the 2-maps of a

pair of corresponding regions.

(a)

(b)

Figure 3: (a) and (b) show the ellipses ﬁtted for the con-

nected regions of each bin of the 2-maps of a corresponding

regions pair. The green ellipses belong to bin 1 and the red

ones to bin 2.

The descriptor obtained using this method is a

variable length encoding of an IR, consisting of a

set of ellipses. The descriptor is of the form D :=

,...,K

} where n denotes the number of bins

used for quantization; K

:{E

}

j=1

denotes the set of

ellipses ﬁtted for each connected region of pixels be-

longing to the i

bin; E

being the ellipse ﬁtted to the

connected region.

3.3 A Better Representation of the

Regions

The descriptor presented in Algorithm 1 ﬁts a single

ellipse to a connected region. But, if the region is not

elliptical, say, if the region is in the form of a ring,

the ellipse thus ﬁtted does not accurately capture the

shape of a region, making the descriptor less discrim-

inative and impair the performance. To circumvent

this drawback, we ﬁt multiple ellipses to a connected

region of pixels so that the ellipses ﬁt the region more

”tightly”. That is, we try to minimize the number

of pixels which lie outside the ﬁtted ellipses and the

empty area of the ﬁtted ellipses. This is equivalent

to the geometric set covering problem, which can be

stated as,

Given a grid, a set of points which are required

to be covered and a set of forbidden points, we need

to reduce the number of ellipses which cover all the

required points and none of the forbidden points.

To this end, we deﬁne the error of the ﬁt ε as

ε =

ell

cov

(3)

where N

cov

represents the number of points in the re-

gion that are covered by the ellipses and A

ell

repre-

sents the total area of the ellipses. That is, for the

error of the ﬁt ε to be low, we should maximize the

proportion of the covered points and minimize the to-

tal area of the ﬁtted ellipses.

We begin by ﬁtting a single ellipse (k = 1) to a

connected region. If the error of the ﬁt (ε) is above a

threshold δ, we increment the number of ellipses (k)

and use k-means clustering algorithm to cluster the

points into k clusters. Then, an ellipse is ﬁt to each

cluster of points and the error ε is recomputed. This

procedure is repeated till the value of ε falls below δ.

The steps are shown in Algorithm 2. It should be

noted that, as the number of ellipses, k, is increased,

ell

will decrease and N

cov

will increase.

Here, C

denotes the i

cluster, FitEllipse(C) ﬁts

an ellipse to the points belonging to cluster C , Area-

Covered(C ,E) computes the number of points in clus-

ter C that lie inside or on the ellipse E and Area(E)

computes the area of the ellipse E.

Figure 4 shows the conﬁgurations of ellipses ob-

tained for various values of k on a S-shaped region.

As can be seen, with increasing k, the ﬁtted ellipses

ADescriptorbasedonIntensityBinningforImageMatching

(a) k=1, ε = 0.35 (b) k=2, ε = 0.28

Figure 4: (a)-(c) Visual representation of Algorithm 2,

where k is the number of ellipses to be ﬁt and ε is the er-

ror of the ﬁt.

Algorithm 2: Set Cover using k-means.

1: procedure COVER(P ) ⊲ P is the given point set

2: δ = 0.1 ⊲ threshold

3: k = 0 ⊲ k:Number of clusters

4: ε = 1 ⊲ ε:Fitting error

5: N = |P | ⊲ N: no. of points in P

6: while ε >= δ do

7: k+ = 1 ⊲ Increment number of clusters

8: C = kmeans(P ,k);

9: N

cov

= 0 ⊲ N

cov

:#pixels covered

10: A

ell

= 0 ⊲ A

ell

:area of ﬁtted ellipses

11: for i = 1 → k do

12: E

= FitEllipse(C

)

13: N

cov

= N

cov

+ AreaCovered(C

)

14: A

ell

= A

ell

+ Area(E

)

15: end for

16: ε =

ell

cov

17: end while

18: end procedure

represent the region more accurately, which progres-

sively decreases the error of the ﬁt (ε).

3.4 Comparing Descriptors

Given two descriptors, the similarity score is com-

puted by accumulating the extent of overlap of the el-

lipses of the correspondingbins. The overlap between

two ellipses is computed using the method discussed

in Section 3.1.1.

Algorithm 3 describes the steps involved in com-

paring two descriptors. Here D

(.)

i, j

refers to the el-

lipse ﬁtted to the j

connected region belonging to

the i

bin; GetOverlap(E

) computes the amount

of overlap between the ellipses E

and E

Before computing the similarity of a pair of de-

scriptors, the ellipses comprising a descriptor are ro-

tated along the characteristic orientation of the IR of

the descriptor, which is obtained by ﬁnding the dom-

inant orientations in the Histogram of Gradients con-

structed for the IR (Lowe, 2004). To achieve scale in-

variance, the ellipses are mapped to a circular region

of unit radius.

Algorithm 3: Comparing Descriptors.

1: procedure ov = COMPARE(D

(1)

(2)

)

2: n ← numOfBins(D

(1)

)

3: ov ← 0 ⊲ overlap

4: for bin=1 ... n do

5: for reg

=1 ... |K

(1)

bin

| do

6: E

← D

(1)

bin,reg

7: for reg

=1 ... |K

(2)

bin

| do

8: E

← D

(2)

bin,reg

9: ov ← ov + GetOverlap(E

)

10: end for

11: end for

12: end for

13: end procedure

3.5 Splitting the Intensity Range

The binning of pixel intensities can be done using

three methods, viz., hard binning, rank based binning

and soft binning.

Hard binning: If n represents the number of bins

used for quantization and the intensity range of the

interest region is from a to b, then the size of each bin

b−a

Rank method: Let N be the number of pixels in

the connected region. The intensities of the neigh-

borhood pixels are ﬁrst sorted and the intensity of ev-

ery (N/n)

element in the sorted list deﬁnes the bin

boundary.

Soft binning: In the aforementioned binning meth-

ods, the intensity of a pixel takes an integral value

and can belong to only one bin. We relax this con-

straint and allow the pixel to belong to more than one

bin. The membership of the pixel to a particular bin

is weighed by the distance from the center of the bin.

It should be noted that a pixel can belong to at most

two bins. The weight W for a pixel p is calculated as:

W(p) = 1−

− I

(4)

Here I

is the intensity of the pixel p, I

denotes the

center of bin and S

denotes the bin width. The weight

ICPRAM2014-InternationalConferenceonPatternRecognitionApplicationsandMethods

100

ranges from 0 to 1, with 0 specifying that the pixel

does not belong to that bin and 1 indicating that the

pixel intensity lies exactly at the bin center in which

case it belongs to only that bin.

For example, say, the intensity range of a region is

101-500 and we need a 4-way split. The centers of the

bins will be 150, 250, 350 and 450. A pixel with in-

tensity 200, bordering on the boundary between bins

1 and 2, will belong to both the bins 1 and 2, with the

weights being 0.5 and 0.5 respectively. A pixel with

value 350 will belong to bin 3 with the weight of 1. A

pixel with value 175 will belong to bins 1 and 2 and

the weights will be 0.75 and 0.25 respectively. This is

illustrated in Figure 5.

Figure 5: Illustration of the weight assignment to pixels us-

ing soft binning.

4 RESULTS

The descriptors are evaluated on Oxford data set

which is used to evaluate the performance of descrip-

tors when a scene undergoesphotometric and geomet-

ric deformations. The results are presented with re-

call versus 1-precision, as used in (Mikolajczyk and

Schmid, 2005). The protocol for evaluating the de-

scriptors is as follows. Let D

(i)

denote the descriptors

belonging to image i.

1. Given an image pair, we extract the IRs using

Hessian-Afﬁne detector from both images and

compute the descriptor for each IR.

2. Potential matches: For a descriptor d

in D

(1)

, the

descriptor d

∈ D

(2)

is a potential match if their

similarity is greater than a threshold σ. The sim-

ilarity measure is the standard Euclidean distance

in case of SIFT, GLOH and CS-LBP.

3. Ground Truth: A descriptor d

∈ D

(2)

is said to

correspond to d

∈ D

(1)

if the overlap of IR of

with that of d

more than 50% (as outlined in

Section 3.1.1).

4. Correct matches: The overlap of the IR corre-

sponding to d

∈ D

(1)

with those of the potential

matches in D

(2)

is computed, using the method

outlined in Section 3.1.1 and the match is said to

be correct if the overlap is greater than 50%. It

should be noted that the correct matches for a de-

scriptor d

∈ D

(1)

are those descriptors d

∈ D

(2)

that are present in both the set of correspondences

and the set of potential matches.

5. Now the recall is given as the ratio of the num-

ber of correct matches to the total number of cor-

respondences and precision is given as the pro-

portion of correct matches among the potential

matches. For each value of σ, we compute (1-

precision) and recall, which are then used to gen-

erate the curves.

In our experiments, we compare the performance

of our descriptor with that of SIFT, GLOH

and CS-

LBP. The number of bins is ﬁxed at 8 while construct-

ing the descriptors using all the three binning meth-

ods. The region covering algorithm (Cover) outlined

in Algorithm 2, was used with rank and hard binning

methods; the threshold δ for the ellipse ﬁtting was set

at 0.1 and the maximum number of iterations for k-

means was set at 20. Figure 6 shows the performance

of the descriptors for various image deformations. It

should be noted that the region covering method was

used with rank and hard binning methods since the

connected regions belonging to the different bins can

be clearly demarcated with these binning methods.

The time taken for constructing the descriptor ranged

from 4.1s for 2 bins to 4.5s for 8 bins, where SIFT

and GLOH took 1.2s.

(a) Scaling+Rotation

Figure 6: Performance of the descriptors in the presence

of geometric deformation. Number of bins for our method

is ﬁxed at 8 while constructing descriptors using all three

binning methods.

Figure 6 shows the performance of the descriptors

in case of geometric deformations, i.e., scaling and

rotation changes. The hard binning method performs

Binaries for SIFT and GLOH were obtained

from http://www.robots.ox.ac.uk/∼vgg/research/afﬁne/

descriptors.html #binaries

ADescriptorbasedonIntensityBinningforImageMatching

101

better than the rank based binning, since the inten-

sities of the IRs are not distorted under these defor-

mations. In this case, all the three binning methods

perform better than the existing state of the art meth-

ods.

Figure 7: Performance of the descriptors in the presence of

blur. Number of bins for our method is ﬁxed at 8 while

constructing descriptors using all three binning methods.

Figure 7 shows the performance in case of blur.

The intensity maps of the corresponding IRs are con-

siderably more distorted when compared to geomet-

ric deformations. As is evident from the ﬁgure, rank

based binning works better than the other binning

methods. This can be attributed to the fact that the or-

der of the pixel intensities is not affected to a great de-

gree under these deformationsand thus the bin bound-

aries and the bin labels are less distorted when com-

pared to the other binning methods.

Figure 8: Performance of the descriptors in the presence

of nonlinear illumination changes. Number of bins for our

method is ﬁxed at 8 while constructing descriptors using all

three binning methods.

Figure 8 shows the effect of nonlinear illumination

changes on the performance of the descriptors. In the

presence of illumination changes, CS-LBP is more ro-

bust than all of the descriptors, but then in this case,

the performance of our descriptor is at par.

In conclusion, the rank based binning method with

region covering performs better than its naive coun-

terpart and the other binning methods. It was found

that the accuracy of the proposed descriptor increases

as the number of bins (n) is increased from 2 bins

and saturates when the value is 8. This is because

the descriptor is a coarse representation of the under-

lying intensity map when n is 2 and the representa-

tion becomes ﬁner with increasing n. But increasing

n beyond 8 was detrimental to the performance, be-

cause the width of the individual bins decreases with

increasing n and a slight distortion of the intensities

changes the bin labels of the pixels and deforms the n

map.

It is interesting to note that, in Figure 2, the pro-

portion of the pixels retaining the bin label is high

when the n is low. But, such n-maps are over general-

ized representations of the underlying IR and impair

the discriminative ability of the descriptor.

5 SUMMARY AND

CONCLUSIONS

In this paper, we have proposed a novel method for

constructing image descriptors, using intensity bin-

ning, which involvesquantization of the intensity map

of the interest regions and ﬁtting ellipses to each con-

nected region of the bins obtained. We also pro-

posed a better representation of such binned intensity

maps using k-means. These approaches were evalu-

ated on images with commonly occurring image de-

formations. The experiments show that the proposed

descriptor is robust to photometric and geometric de-

formations and outperforms the current state of the

art methods. As we had shown, the optimal num-

ber of bins for quantization was chosen empirically.

A more principled way would be to choose the num-

ber of bins by closer inspection of topography of the

regions obtained across multiple quantization levels,

which would be a promising direction for improving

the proposed method.

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