Feature description based on Center-Symmetric LocalMapped Patterns

Carolina Toledo Ferraz, Osmando Pereira Jr., Adilson GonzagaDepartment of Electrical Engineering, University of São Paulo

Av. Trabalhador São Carlense, 400 - 13566-590São Carlos, SP - Brazil

caferraz8@usp.br, osmandoj@gmail.com, agonzaga@sc.usp.br

ABSTRACTLocal feature description has gained a lot of interest in manyapplications, such as texture recognition, image retrieval andface recognition. This paper presents a novel method forlocal feature description based on gray-level difference map-ping, called Center-Symmetric Local Mapped Pattern (CS-LMP). The proposed descriptor is invariant to image scale,rotation, illumination and partial viewpoint changes. Fur-thermore, this descriptor more effectively captures the nu-ances of the image pixels. The training set is composed ofrotated and scaled images, with changes in illumination andview points. The test set is composed of rotated and scaledimages. In our experiments, the descriptor is compared tothe Center-Symmetric Local Binary Pattern (CS-LBP). Theresults show that our descriptor performs favorably com-pared to the CS-LBP.

Categories and Subject DescriptorsI.5.2 [Pattern Recognition]: Design Methodology—fea-ture evaluation and selection

Keywordsregion description, image matching, region detection, featuredescription

1. INTRODUCTIONIn image processing, the local feature description plays an

important role in applications such as texture recognition,content-based image retrieval and face recognition. The ob-jective is to build a descriptor histogram vector providing arepresentation that allows efficient matching of local struc-tures between images.

A good descriptor has some important features includinginvariance to illumination, rotation and scale. Furthermore,it should be robust to errors in detection, geometric distor-tions from different points of view and photometric defor-mations caused by different lighting conditions [13].

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.SAC’14 March 24-28, 2014, Gyeongju, Korea.Copyright 2014 ACM 978-1-4503-2469-4/14/03 ...$15.00.

One of the most widely known key feature descriptors pu-blished in the literature is the Scale-Invariant Feature Trans-form (SIFT) [12]. It was introduced by Lowe in 1999 [11]. Itis characterized by a 3D histogram of gradient locations andorientations and stores the bins in a vector of 128 positions.Many variations of SIFT have been proposed, such as Prin-cipal Components Analysis SIFT (PCA-SIFT) [9], GradientLocation and Orientation Histogram (GLOH) [10], SpeededUp Robust Features (SURF) [3], Colored SIFT (CSIFT) [1],Center-Symmetric Local Binary Pattern (CS-LBP) [8] andKernel Projection Based SIFT (KPB-SIFT) [17].

PCA-SIFT applies the standard Principal ComponentsAnalysis (PCA) technique to the normalized gradient patchesextracted around local features. PCA is able to linearlyproject high-dimensional descriptors onto a low-dimensionalfeature space and reduce the high frequency noise in the de-scriptors. However, the PCA-based feature descriptors needan offline stage to train and estimate the covariance matrixused for PCA projection. Thus, the application of PCA-based features is limited. The GLOH descriptor also usesPCA to reduce the descriptor size. It is very similar toSIFT, however, it uses a Log-Polar location grid instead ofa Cartesian one. SURF approximates SIFT using the Haarwavelet response and using integral images to compute thehistograms bins. It uses a descriptor vector of 64 positions,providing a better processing speed. CSIFT tries to solvethe problem of color image descriptors, improving on SIFT,which is designed mainly for gray images. It uses the colorinvariance model to build the descriptor. CS-LBP [8] com-bines the strengths of the well-known SIFT descriptor andthe Local Binary Pattern (LBP) texture operator. In [8], itis shown that the construction of the CS-LBP descriptor issimpler than SIFT, but it generates a feature vector of 256positions, which is twice the SIFT vector size. KBP-SIFT[17] reduced the dimension of the descriptor from 128 to only36 bins by applying a kernel projection on the orientationgradient patches rather than using smoothed weighted his-tograms. The approach is tolerant to geometric distortionsand does not require a training stage; however, the perfor-mance evaluation is not superior in all cases with respect toSIFT.

In a recent work, Vieira, Chierici, Ferraz and Gonzaga[15] present a new descriptor based on fuzzy numbers thatthey called the Local Fuzzy Pattern (LFP). This methodinterprets the gray-level values of an image neighborhood asa fuzzy set and each pixel level as a fuzzy number. A mem-bership function is used to describe the membership degreeof the central pixel to a particular neighborhood. Moreover,

39http://dx.doi.org/10.1145/2554850.2554895

the LFP methodology is a generalization of previously pub-lished techniques such as the LBP, the Texture Unit [6], theFuzzy Number Edge Detector (FUNED) [4] and the Cen-sus Transform [16]. One evolution of the LFP is the LocalMapped Pattern (LMP) [5], where the authors consider thesum of the differences of each gray-level of a given neigh-borhood to the central pixel as a local pattern that can bemapped to a histogram bin using a mapping function.

In this paper, we propose a new interest region descrip-tors, denoted as the Center-Symmetric Local Mapped Pat-tern (CS-LMP). CS-LMP combines the desirable propertiesof the CS-LBP using the LMP methodology. This new de-scriptor captures the small transitions of pixels in the imagemore accurately, resulting in a greater number of correctmatches than with CS-LBP. Furthermore, they do not usePCA to decrease the size of the feature vector, but insteadquantize the histogram into a fixed number of bins.

The rest of this paper is organized as follows. In Section2, we briefly describe the methods of CS-LBP and LMP.Section 3 gives details on the proposed approach CS-LMP.The experimental evaluation and the results are presentedin Section 4. Finally, we conclude the paper in Section 5.

2. LOCAL DESCRIPTORSIn computer vision, local descriptors are based on image

features extracted from compact image regions using his-tograms to generate a feature vector.

In this section, two local descriptors are presented: theCS-LBP and the LMP.

2.1 Center-Symmetric Local Binary Pattern(CS-LBP)

The CS-LBP is a modified version of the LBP texture fea-ture and SIFT descriptor, inheriting the desirable propertiesof both texture features and gradient-based features. Thefeatures are extracted by an operator similar to the LBPand the constrution of the descriptor is similar to SIFT.This methodology has many properties such as tolerance toillumination changes, robustness on flat image areas, andcomputational simplicity [7]. In [8], the authors state thatthe LBP produces a rather long histogram and thereforeis difficult to use in the context of an image descriptor. Tosolve this problem, they modified the scheme of how to com-pare the pixels in the neighborhood. Instead of comparingeach pixel with the center one, the method compares center-symmetric pairs of pixels as illustrated in Figure 1. We cansee that for 8 neighbors, LBP produces 256 different binarypatterns (patternLBP ∈ [0, 255]), whereas for CS-LBP, thisnumber is only 16 (patternCS−LBP ∈ [0, 15])).

The interest region detectors, such as Hessian-Affine, Harris-Affine, Hessian-Laplace and Harris-Laplace [14, 13], providethe regions that are used to compute the descriptors. Aftercomputing the regions, they are mapped to a circular regionof a constant radius to obtain the scale and affine invariance.These regions are fixed at 41 × 41 pixels and the pixel val-ues are in the range [0,1]. Rotation invariance is obtainedby rotating the normalized regions in the direction of thedominant gradient orientation.

For the construction of the descriptor, the image regionsare divided into cells with a location grid, and for each cell, aCS-LBP histogram is built. The CS-LBP feature extractionfor each pixel of the region is accomplished according toEquation 1:

Figure 1: LBP and CS-LBP features for a neighbor-hood of 8 pixels

CS − LBPR,N,T (x, y) =

(N/2)−1∑i=0

s(ni − ni+(N/2))2i, (1)

where ni and ni+(N/2) correspond to the gray values ofcenter-symmetric pairs of pixels of N equally spaced pixelson a circle of radius R and

s(x) =

{1, if x > T,

0, otherwise.

To avoid boundary effects in which the descriptor abruptlychanges as a feature shifts from one cell to another, bilin-ear interpolation over the x and y dimensions is used toshare the weight of the feature between the four nearestcells. The share for a cell is determined by the bilinear in-terpolation weights [8]. Thus, the resulting descriptor is a3D histogram of the CS-LBP feature locations and values.The final descriptor is built by concatenating the feature his-tograms computed for the cells and the last normalizationto obtain the maximum unit for each bin. To eliminate theinfluence of very large descriptor elements, the bins of thehistogram are limited to 0.2 and the histogram is normalizedagain. For a 4 × 4 Cartesian grid, the final feature vectorcontains 256 positions.

2.2 Local Mapped Pattern (LMP)The LMP methodology assumes that each gray-level dis-

tribution within an image neighborhood is a local pattern.This pattern can be represented by the gray-level differencesaround the central pixel. Figure 2 shows an example of a3× 3 neighborhood and a 3D graphic of the respective localpattern.

Figure 2: Gray-level differences as a local pattern

Each pattern defined by a W × W neighborhood will bemapped to a histogram bin hb using Equation 2, where fg(i,j)is the mapping function, P (k, l) is a weighting matrix of pre-defined values for each pixel position within the neighbor-hood, and B is the number of the histogram bins. This equa-tion represents the weighted sum of each gray-level difference

40

between the neighboring pixels and the central one, mappedonto the [0,1] interval by a mapping function and roundedto B possible bins.

hb = round

(∑Wk=1

∑Wl=1(fg(i,j)P (k, l))∑W

k=1

∑Wl=1 P (k, l)

)(B − 1), (2)

Through Equation 2, it is possible to derive some pre-viously published approaches for local pattern analysis. TheLocal Binary Pattern (LBP) can be derived from Equation2 using the Heaviside step function shown in Equation 3:

fg(i,j) = H[A(k, l)− g(i, j)] (3)

where

H[A(k, l)− g(i, j)] =

{0 if [A(k, l)− g(i, j)] < 0;1 if [A(k, l)− g(i, j)] ≥ 0.

Taking into account the basic LBP with a 3× 3 neighbor-hood of pixels, the weighting matrix will be:

P (k, l) =

⎡⎣ 1 2 4

128 0 864 32 16

⎤⎦

The LBP is thus a particular case of the LMP approach.Using different mapping functions, the LMP methodology

could extract specific features from the image using localpattern processing.

For texture analysis, the LMP approach uses a smoothapproximation to the Heaviside step function by a logisticfunction, a logistic curve, or a common sigmoid curve as inEquation 4.

fg(i,j) =1

1 + e−[A(k,l)−g(i,j)]

β

, (4)

where β is the curve slope and [A(k, l)−g(i, j)] are the gray-level differences within the neighborhood centered in g(i, j).The proposed weighting matrix is:

P (k, l) =

⎡⎣ 1 1 1

1 1 11 1 1

⎤⎦

When using the sigmoid curve, the method is called LMP-s.

Sigmoid functions, whose graphs are “S-shaped” curves,appear in a great variety of contexts, such as the transferfunctions of many neural networks. Their ubiquity is no ac-cident; these curves are among the simplest nonlinear curves,striking a graceful balance between linear and nonlinear be-havior. Figure 3 shows the mapping functions fg(i,j) usedin Equation 2 for the LMP-s (sigmoid) and LBP (Heavisidestep) approaches.

3. CENTER-SYMMETRIC LOCAL MAPPEDPATTERN (CS-LMP)

The CS-LBP descriptor described in the previous sectionhas the following disadvantage: the difference between thesymmetrical pairs and the center are thresholded to 0 or 1,and do not capture the nuances that can occur in the image.

(a) Mapping function to theLMP-s method

(b) Mapping function to theLBP method

Figure 3: Gray-level differences mapped by Equa-tion 2. a) Local Mapped Pattern. b) Local BinaryPattern

Analyzing the advantage of flexibility of the LMP methodto be malleable by changing the mapping function and theweight matrix in the Equation 2, and the disadvantage ofthe CS-LBP descriptor (stiffness in using the step function),we propose a new descriptor named CS-LMP based on theCS-LBP, but using a mapping function suitable for the cal-culation of characteristics in the LMP method.

Equation 5 shows the feature extraction for each pixel ofthe interest region, defined in a neighborhood W ×W :

CS−LMPR,N,f (x, y) = round

(∑N/2−1i=0 f(i)P (i))∑N/2−1

i=0 P (i)

)b (5)

where b is the number of histogram bins minus one, P (i)is the ith element of the weight matrix P defined in theEquation 6, and f(i) is the sigmoid mapping function definedin Equation 7.

P = [p0p1p2...pN/2−1]t (6)

where

pi = 2i

f(i) =1

1 + e−[ni−ni+(N/2)]

β

(7)

where ni and ni+(N/2) correspond to the gray level values ofthe center-symmetric pairs of N equally spaced pixels on acircle of radius R and β is the sigmoid curve slope. If the co-ordinates of ni on the circle do not correspond to the imagecoordinates, the gray-value of this point is interpolated.

Figure 4 illustrates the operation of the CS-LMP aftersetting b to 15 (16 bins minus one).

We adopted the Hessian-Affine detector because it presentsbetter results for detecting interest regions in images [8].Afterwards, the regions are mapped to a circular region ofconstant radius and rotated in the direction of the dominantgradient, as described in [8] and [12]. Each region is dividedinto cells with a grid size of 4 × 4. The features are ex-tracted for each pixel of the interest region using a CS-LMPdescriptor and a histogram is built for each cell.

The parameters R, N and β were empirically established,the best results were obtained and these will be discussed inSection 4.

As it was presented in [7], a bilinear interpolation is madeover the x and y dimensions to share the weight of the fea-ture between the four nearest cells. Thus, a 3D histogram of

41

Figure 4: CS-LMP features for a neighborhood of 8pixels

the CS-LMP feature locations and values is built as shown inFigure 5. The descriptor is made by concatenating the fea-ture histograms computed for the cells, obtaining a vector of256 positions(4× 4× 16). The descriptor is then normalizedas in the CS-LBP presented in Section 2.1.

(a) Inputregion

(b) 4×4cells’ divi-sion

(c) 4×4×16=256bins of concate-nated histogram

Figure 5: CS-LMP descriptor.

4. EXPERIMENTAL EVALUATIONIn this section, we present the performance of the CS-LMP

and CS-LBP descriptors applied to the matching of imagepairs using nearest-neighbor similarity.

The image database is available on the internet 1 2. Ithas 8 sets of images with 6 different types of transforma-tions: viewpoint change, rotation change, scale, ilumination,JPEG compression and blur. The training images used inthis paper are shown in Figure 6 and the test images areshown in Figure 7.

Table 1 presents the evaluation of the parameter β in themethod CS-LMP for the image “bark”. We tested somevalues of the β parameter and we generated the recall ×precision curves, measuring its respective area under curve(AUC). For most of the test images, the best value of β wasnear 0.6 for CS-LMP.

The evaluation criteria is explained in the next subsection.

4.1 Evaluation criteriaThe performance of the CS-LMP descriptor was evaluated

and compared with CS-LBP, using an evaluation criterionbased on Heikkila et al. [7, 8]. This criterion consists of thenumber of correct and false matches for a couple of images,knowing a priori the set of true matches (i.e., the groundtruth). Heikkila et. al. [8] determine the ground truth

1http://www.robots.ox.ac.uk/ vgg/research/affine/2http://lear.inrialpes.fr/people/mikolajczyk/

(a) graf1 (b) graf4 (c) bark1 (d) bark4

(e) leu-ven1

(f) leu-ven4

(g) trees1 (h) trees4

(i) ubc1 (j) ubc4 (k) boat1 (l) boat4

(m) bike1 (n) bike4 (o) wall1 (p) wall4

Figure 6: Training Images: graf (viewpoint change),bark (scale and rotation change), trees (blur image),leuven (ilumination change), ubc (JPEG compres-sion), boat (scale and rotation change), bike (blurimage), wall (viewpoint change)

(a) resid1 (b) resid4 (c) eastpark1

(d) eastpark4

(e) eastsouth1

(f) eastsouth4

(g)zmars1

(h)zmars4

(i)zmonet1

(j)zmonet4

(k) ax-terix1

(l) ax-terix4

(m) belle-done1

(n) belle-done4

(o) bip1 (p) bip4

Figure 7: Test Images: resid, east park, eastsouth (scale and rotation), zmarks, zmonet (rota-tion change), axterix, belledone, bip (scale change)

by the overlap error of the two regions. The overlap errordetermines how a region A of image 1 overlaps region B ofimage 2. Image 2 is projected on image 1 by a homographymatrix H.

The overlap error is defined by the ratio of the intersection

42

Table 1: β evaluation example for the image “bark”

β AUC0.1 0.89930.2 0.90730.3 0.91000.4 0.91730.5 0.91730.6 0.91960.7 0.91630.8 0.8960

and the union of the regions given by Equation 8:

εS = 1− (A ∩HTBH)/(A ∪HTBH) (8)

A match is assumed to be correct if εS < 0.5.To evaluate the performance of our descriptors, we present

the results with recall × precision curves [2] and their respec-tive AUC.

Precision represents the number of correct matches overthe total number of possible matches returned (falses+corrects)and is defined by Equation 9.

precision =nc

n(9)

where n is the number of possible matches returned andthe Euclidean distance between their descriptors is below athreshold td. The number of correct matches nc includesthe matched pairs whose Euclidean distance between theirdescriptors is below a threshold td and εS < 0.5

Recall represents the ratio between the correct matchesand the total number of true matches (the ground truth)and is defined by Equation 10.

recall =nc

M, (10)

whereM is the number of elements in the set of true matches.To construct the recall × precision curve, each point is

defined by choosing n ∈ [1, N ], where N represents the totalnumber of possible matches. Analyzing this curve, a perfectdescriptor would give a precision equal to 1 for any recall.

4.2 Matching resultsThe interest region detector used to compute the descrip-

tors was the Hessian-Affine detector. As discussed in theprevious subsection, the parameters set for the CS-LMPwere β = 0.6, b = 15, R = 2, and N = 8. For the CS-LBP, we used the parameters R = 2, N = 8, and T = 0.01[7].

We generated the recall × precision curves for all imagesof the test set and calculated the AUC for each of them.However, for reasons of clarity, we present only four of themin Figure 8. Note that there is a good precision for low recallfor the four descriptors, i.e., the first region pairs returnedare correct matches; however, as the number of region pairsreturned increases, the precision decreases. We can see thatthe reduction of precision is more accentuated by CS-LBP.As the number of returned matches increases (n), CS-LMPachieves a greater number of correct matches (nc) comparedto CS-LBP.

The AUC results are shown in Table 2 for the CS-LMPand CS-LBP descriptors. Note that for all images, CS-LMPhas an AUC value greater than CS-LBP.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

recall

precision

CS−LMPCS−LBP

(a) resid

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

recall

precision

CS−LMPCS−LBP

(b) east park

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

recall

precision

CS−LMPCS−LBP

(c) east south

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

recall

precision

CS−LMPCS−LBP

(d) zmars

Figure 8: Results of the recall × precision curves forCS-LMP and CS-LBP descriptors.

Table 2: Area under curve (AUC)

Image CS-LMP CS-LBP

resid 0.9043 0.8332east park 0.8758 0.7842east south 0.9027 0.7816

zmars 0.9659 0.9499zmonet 0.9659 0.9364axterix 0.9577 0.9237

belledonne 0.7878 0.6704bip 0.8889 0.8495

Table 3 presents the values for recall, precision and the nbest returned correspondences by the two descriptors. Forexample, for the image named “resid”, taking into accountthe first 1027 possible matches returned, we have 580 correctmatches for the CS-LMP and 545 for the CS-LBP descrip-tor. The image “east south” presents the difference of 60correct matches favorable to the CS-LMP and for the image“east park”, our proposed approach outstands by 52 correctmatches over the CS-LBP.

Figure 9 presents the correct matches achieved betweenthe image pair called “resid”. It was performed to check theimages test results when applying the descriptors CS-LMPand CS-LBP.

5. CONCLUSIONSIn this paper, we proposed a novel method for feature des-

cription based on local pattern analysis. The method com-bines the LMP operator and the CS-LBP descriptor. It usesthe CS-LBP-like descriptor and replaces the step functionby the sigmoid function.

CS-LMP features has many properties that make it well-suited for this task: a relatively short histogram and tole-rance to rotation and scale change. Furthermore, it doesnot require setting many parameters. The performance ofthe CS-LMP descriptor was compared to the CS-LBP des-criptor in terms of recall × precision curves. As CS-LMP

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Table 3: Correct Matches

Image Recall Precision Correct Matches

CS-LMP resid 0.9265 0.5648 580/1027CS-LBP 0.8706 0.5307 545/1027CS-LMP east park 0.9079 0.4904 641/1307CS-LBP 0.8343 0.4507 589/1307CS-LMP east south 0.9266 0.495 745/1505CS-LBP 0.8520 0.4551 685/1505CS-LMP axterix 0.9718 0.7169 276/385CS-LBP 0.9366 0.6909 266/385CS-LMP belledonne 1.0 0.1293 15/116CS-LBP 0.8667 0.1121 13/116CS-LMP bip 0.9032 0.6538 476/728CS-LBP 0.8596 0.6223 453/728CS-LMP zmars 0.9689 0.0764 1681/22001CS-LBP 0.9568 0.0755 1660/22001CS-LMP zmonet 0.9714 0.7827 407/520CS-LBP 0.9427 0.7596 395/520

200 400 600 800 1000 1200 1400 1600

100

200

300

400

500

600

(a) CS-LMP - 356 correct matches

200 400 600 800 1000 1200 1400 1600

100

200

300

400

500

600

(b) CS-LBP - 350 correct matches

Figure 9: Matches achieved between the image paircalled “resid”. Total of 361 correspondences.

captures the gray-level nuances of the images better, therecall × precision curves show a better performance thanCS-LBP methodology. We can conclude that CS-LMP isa promising descriptor, with better performance over theCS-LBP descriptor. Among the 8 tested images, the AUCof the recall × precision curve was greater for all imagesfor CS-LMP than CS-LBP. Moreover, the number of correctcorrespondences outperformed the CS-LBP.

6. ACKNOWLEDGMENTSThe authors would like to thank the Sao Paulo Research

Foundation (FAPESP), grant #2011/18645-2, and NationalCouncil for Scientific and Technological Development (CNPQ)for their financial support of this research.

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