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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014 5643 Image Matching Using SIFT Features and Relaxation Labeling Technique—A Constraint Initializing Method for Dense Stereo Matching Jyoti Joglekar, Shirish S. Gedam, and B. Krishna Mohan Abstract—A probabilistic neural-network-based feature- matching algorithm for a stereo image pair is presented in this paper, which will be useful as a constraint initializing method for further dense matching technique. In this approach, scale-invariant feature transform (SIFT) features are used to detect interest points in a stereo image pair. The descriptor which is associated with each keypoint is based on the histogram of the gradient magnitude and direction of gradients. These descriptors are the preliminary input for the matching algorithm. Using disparity range computed by visual inspection, the search area can be restricted for a given stereo image pair. Reduced search area improves the computation speed. Initial probabilities of matches are assigned to the keypoints which are considered as probable matches from the selected search area by Bayesian reasoning. The probabilities of all such matches are improved iteratively using relaxation labeling technique. Neighboring probable matches are exploited to improve the probability of best match using consistency measures. Confidence measures considering the neighborhood, unicity, and symmetry are some validation techniques which are built into the technique presented here for finding accurate matches. The algorithm is found to be effective in matching SIFT features detected in a stereo image pair with greater accuracy, and these accurate correspondences can be used in finding the fundamental matrix which encodes the epipolar geometry between the given stereo image pair. This fundamental matrix can then be used as a constraint for finding inliers that are used in matching methods for deriving dense disparity map. Index Terms—Feature, image matching, probabilistic relax- ation, stereo vision, validation. I. I NTRODUCTION W E UNDERSTAND that our surroundings are 3-D. How- ever, traditional imaging systems produce images in two dimensions; hence, understanding and reconstruction of the 3-D geometry of an object from its image or images are of prime importance. In the field of computer vision applications, stereo image analysis is an important part of such 3-D surface reconstruction [1]. It is known that, in a stereo pair of digital images, there is a pixel-to-pixel correspondence in the overlapping region of a Manuscript received March 10, 2013; revised September 12, 2013; accepted October 5, 2013. The authors are with the Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India (e-mail: jyotij@ iitb.ac.in; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2013.2291685 pair. The relative shift between the positions of a keypoint in a stereo image pair is the disparity which depicts the 3-D position of that point in the real world [2]. Accurately identifying and matching of these keypoints are very important to estimate the depth information. Thus, the accuracy of the reconstruction of a scene from its image mainly depends upon the accuracy with which these conjugate points are identified and matched. There are varieties of constraints that can be used to guide the correspondence problem depending upon the properties of the imaging systems and the images [3]. Correspondence points are the projections on the image planes of a single point that is present in a 3-D scene [4], [5]. Hence, establishing point-to-point correspondence at the maximum possible points in the 3-D scene is a key problem in stereo computation. The most prominent difference between various matching algorithms is the distinction between different matching primi- tives used by the matching algorithms. The primitives are of different types: windows composed of gray values or features of interest points or edges extracted in each image of a stereo image pair or topological relation between features. These gray values, features, and relations between features are determined and matched by two distinct ways: area-based matching and feature-based matching. Feature-based matching determines the correspondence be- tween image features, and it does not require very precise initial estimates unlike area-based matching. Semantic features with a given spatial geometry or known physical properties or features based on intensity variations are the primary inputs that are used for matching. Feature-based matching provides a set of accurate matching points. However, feature-based matching cannot pro- vide sufficient information for dense matching, and it should be augmented by area-based matching for generating a dense disparity map needed for more accurate 3-D reconstruction. Whereas the output of the feature-matching algorithm can pro- vide an accurate set of ground control points in case of remotely sensed images, the output of our proposed feature-based match- ing algorithm is used as a constraint initializer for the next step of dense matching. We propose a probabilistic relaxation ap- proach for solving the scale-invariant feature transform (SIFT) [6] feature-based matching problem. The organization of this paper is as follows. Section II covers the literature review and the comparison of related work with the proposed algorithm. Section III presents the methodology used in detecting interest points. Section IV discusses the probabilistic neural network 0196-2892 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014 5643

Image Matching Using SIFT Features and RelaxationLabeling Technique—A Constraint Initializing

Method for Dense Stereo MatchingJyoti Joglekar, Shirish S. Gedam, and B. Krishna Mohan

Abstract—A probabilistic neural-network-based feature-matching algorithm for a stereo image pair is presented inthis paper, which will be useful as a constraint initializingmethod for further dense matching technique. In this approach,scale-invariant feature transform (SIFT) features are used todetect interest points in a stereo image pair. The descriptor whichis associated with each keypoint is based on the histogram of thegradient magnitude and direction of gradients. These descriptorsare the preliminary input for the matching algorithm. Usingdisparity range computed by visual inspection, the search areacan be restricted for a given stereo image pair. Reduced searcharea improves the computation speed. Initial probabilities ofmatches are assigned to the keypoints which are considered asprobable matches from the selected search area by Bayesianreasoning. The probabilities of all such matches are improvediteratively using relaxation labeling technique. Neighboringprobable matches are exploited to improve the probability ofbest match using consistency measures. Confidence measuresconsidering the neighborhood, unicity, and symmetry are somevalidation techniques which are built into the technique presentedhere for finding accurate matches. The algorithm is found to beeffective in matching SIFT features detected in a stereo imagepair with greater accuracy, and these accurate correspondencescan be used in finding the fundamental matrix which encodesthe epipolar geometry between the given stereo image pair. Thisfundamental matrix can then be used as a constraint for findinginliers that are used in matching methods for deriving densedisparity map.

Index Terms—Feature, image matching, probabilistic relax-ation, stereo vision, validation.

I. INTRODUCTION

W E UNDERSTAND that our surroundings are 3-D. How-ever, traditional imaging systems produce images in

two dimensions; hence, understanding and reconstruction ofthe 3-D geometry of an object from its image or images are ofprime importance. In the field of computer vision applications,stereo image analysis is an important part of such 3-D surfacereconstruction [1].

It is known that, in a stereo pair of digital images, there isa pixel-to-pixel correspondence in the overlapping region of a

Manuscript received March 10, 2013; revised September 12, 2013; acceptedOctober 5, 2013.

The authors are with the Centre of Studies in Resources Engineering, IndianInstitute of Technology Bombay, Mumbai 400076, India (e-mail: [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2013.2291685

pair. The relative shift between the positions of a keypoint in astereo image pair is the disparity which depicts the 3-D positionof that point in the real world [2]. Accurately identifying andmatching of these keypoints are very important to estimate thedepth information. Thus, the accuracy of the reconstructionof a scene from its image mainly depends upon the accuracywith which these conjugate points are identified and matched.There are varieties of constraints that can be used to guide thecorrespondence problem depending upon the properties of theimaging systems and the images [3].

Correspondence points are the projections on the imageplanes of a single point that is present in a 3-D scene [4],[5]. Hence, establishing point-to-point correspondence at themaximum possible points in the 3-D scene is a key problemin stereo computation.

The most prominent difference between various matchingalgorithms is the distinction between different matching primi-tives used by the matching algorithms.

The primitives are of different types: windows composed ofgray values or features of interest points or edges extractedin each image of a stereo image pair or topological relationbetween features. These gray values, features, and relationsbetween features are determined and matched by two distinctways: area-based matching and feature-based matching.

Feature-based matching determines the correspondence be-tween image features, and it does not require very precise initialestimates unlike area-based matching. Semantic features with agiven spatial geometry or known physical properties or featuresbased on intensity variations are the primary inputs that are usedfor matching. Feature-based matching provides a set of accuratematching points. However, feature-based matching cannot pro-vide sufficient information for dense matching, and it shouldbe augmented by area-based matching for generating a densedisparity map needed for more accurate 3-D reconstruction.Whereas the output of the feature-matching algorithm can pro-vide an accurate set of ground control points in case of remotelysensed images, the output of our proposed feature-based match-ing algorithm is used as a constraint initializer for the next stepof dense matching. We propose a probabilistic relaxation ap-proach for solving the scale-invariant feature transform (SIFT)[6] feature-based matching problem. The organization of thispaper is as follows. Section II covers the literature review andthe comparison of related work with the proposed algorithm.Section III presents the methodology used in detecting interestpoints. Section IV discusses the probabilistic neural network

0196-2892 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

5644 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014

used for the matching model. Section V includes results anddiscussion. Section VI offers conclusion drawn from the workpresented in this paper.

II. LITERATURE REVIEW AND THE PROPOSED ALGORITHM

The relaxation processes for stereo correspondence aremainly of two types: optimization based and probabilisticbased. In the optimization-based process, an energy func-tion minimization is done, which is formulated by certainconstraints. Probabilistic processes assign initial probabilitiesbased on similarity in feature values. These probabilities areupdated iteratively depending on matching of neighboringfeatures and other application constraints. The probabilisticrelaxation labeling is used in [7]–[18]. The optimization-basedapproach is used in [19]–[22].

The early work on which our ideas are based is that ofRosenfeld et al. [7], Pajares et al. [8], and Christmas et al. [9].Recent advances in probabilistic relaxation theory are incorpo-rated in these papers. The main contribution of our paper is theuse of SIFT features as the source for finding interest points [6]instead of using edge segments for the stereovision matchingproblem as in [8]. The advantage of SIFT features is that theyare stable and invariant to transformations, while edge segmentsare unstable, which can result in mismatches. Our methodenforces consistency considering the position of neighboringfeatures. As SIFT features are scale and affine invariant, thereis an increased possibility of detecting the same features in bothimages of a stereo pair. The similarity constraint is imposedwhile assigning initial probability to the matches. In our pro-posed matching method, the correspondences are pruned withvalidation techniques such as unicity, symmetry, and confidencemeasure considering the neighborhood. The unicity techniqueensures that a single strongest match is selected as a matchfrom right probable matches. Symmetry is achieved by runningthe matching algorithm, considering first the left image fromthe stereo image pair as the reference image and then the rightimage as reference image and selecting the set of matcheswhich are common from left to right and right to left. Theconfidence measure is developed using the neighborhood of theinterest point considered for matching as well as the probablematches using their positional information. This confidencemeasure is used in finding likelihood estimate to improve thematching probability of probable matches by the relaxationlabeling technique. The output of this matching process isused in finding the fundamental matrix which encodes theepipolar geometry between the images of the stereo pair usingthe RANSAC algorithm. The fundamental matrix is useful infinding inliers. This set of inliers can provide a very good setof ground control points in case of remotely sensed satelliteimages. Furthermore, when an area-based algorithm is run forfinding a dense correspondence for the same stereo image pair,the fundamental matrix derived from the proposed methodcan be used for validation to check the epipolar geometrybetween the left and right views of the stereo image pair tofind the inliers. Thus, these constraint methods embedded inthis proposed feature-matching algorithm provide a good guidefor the dense correspondence problem.

The output of feature matching for identifying correspon-dence is useful for coarse automatic registration. For an ac-curate feature matching, the detected features must be uniqueand invariant to different affine transformations. However,in practice, features acquired in stereo image pair vary tosome extent due to variations caused by noise, illuminationchange, and view point change; as a result, these features loseuniqueness and discriminating capability. The feature detectionscheme must be capable of handling small variations in featuresto maintain the maximum discriminating capability betweenfeatures.

Feature-matching algorithms suffer from a number of limi-tations, like low discriminating capability of representation andlack of uniqueness in the representation of the same feature.The following is a brief survey of related work. Bitangent curvematching [23] uses first-order derivatives which are sensitiveto noise. Three-tuple matching [24] also calculates the first-order derivatives which are sensitive to noise and require asmooth surface of the objects. Geometric histogram matching[25] makes use of 3-D Hough transform [26] that makes therepresentation computationally complex and expensive. If asignificant texture is present on the surface of the object, theRoth’s technique [27] is consistent in feature point extraction.There are various area-based matching algorithms surveyedby Scharstein et al. [28] which yield a dense disparity map.However, these techniques cannot be compared with feature-matching techniques as the area-matching techniques are ap-proximate dense matching methods, while feature-matchingtechniques use high-level features for accurate matching. SIFTfeatures are used by some feature-matching algorithms, andthe match for keypoint is found by identifying its nearestneighbor in the database of keypoints. The metrics used forkeypoint vector matching and finding nearest neighbor areEuclidian distance [6], variance normalized correlation (VNC)[29], and sum of square difference (SSD) [30]. The approximatenearest neighbor approach, which is the best-bin-first (BBF)algorithm, uses Euclidian distance for finding the closest neigh-bor with high probability [31]. The priority search order wasfirst examined by Arya and Mount [32]. Further computationalproperties are provided in Arya et al. [33]. With these metrics,the proportion of good matches is 50%–60%. The accuracyof good matches as well as the number of good matchescan be improved by our proposed novel approach for featurematching.

In the proposed approach, a Bayesian rule is used in assign-ing the initial matching probabilities as in [9]. However, in thework of Christmas et al. [9], the initial probabilities are as-signed using the unary attributes of features, like length, color,and orientation of object, while in our method, the Euclidiandistance between SIFT descriptors of the features is used toassign the initial probabilities. The advantage of this approachis that the accuracy of the initial probability estimates is moreas a binary relation is used. The descriptor is computed usingunary attributes of the interest points. Furthermore, our methoduses another binary relation involving positions of neighborsto update the probabilities of matches using the arithmeticrule of relaxation labeling. The advantage is fast convergenceof the algorithm. By pruning initial matches having initial

JOGLEKAR et al.: IMAGE MATCHING USING SIFT FEATURES AND RELAXATION LABELING TECHNIQUE 5645

probabilities greater than some threshold, a limited number ofneighbors are selected, which contribute to consistency, therebyreducing computational complexity.

Initially, the interest points are detected, and a descriptoris assigned to each interest point using the SIFT algorithm[6]. A probabilistic relaxation labeling approach is used tomatch these interest points. A comparison of this method withvarious other approaches such as the BBF, VNC, and SSDmethods is carried out, and the results are presented. BBF usesthe Euclidian distance between the feature vectors in findingfeature correspondence. The VNC method uses normalizedcorrelation in matching the feature vectors.

III. FEATURE POINT EXTRACTION AND DESCRIPTORS

Those parts of the image that have special properties andhave some structural significance are usually referred to asimage features. The regions having visually identifiable texturesare also among such features. Some of the other examples areedges, corners, and image gradients. Many computer vision ap-plications have the feature extraction process as an intermediatestep for locating particular elements on an image.

For our matching model in Section IV, the first step is to findthe interest points in the stereo image pair. While extractingkeypoints, some of the important factors to be considered areinvariance, detectability, interpretability, and accuracy. Manyapplications in the area of photogrammetry and computer vi-sion use the extracted features as primary input for furtherprocessing and analysis. The invariance property of the interestpoints detected is very important as the same features shouldbe detected under different transformations (geometric andradiometric) in a pair of stereo images so that they will be usefulfor the matching process [34].

Two-dimensional locations in the images are found by aninterest point detector. Here, the SIFT-based feature detector,as mentioned previously, is used to find keypoints in the im-age pair. After analyzing the region around the location ofthe keypoint, a descriptor is assigned to every keypoint, asthe region characterizes the keypoint under consideration withrespect to its neighboring pixels, like intensity variation, changein gradient, histogram of magnitude, gradient, and direction.

A very brief description of the SIFT operator is presentedhere for the sake of completeness. The SIFT descriptor usesa difference of Gaussian detector [6] and is used to findkeypoints. A descriptor which is a vector of dimension 128is assigned to each keypoint by the SIFT algorithm. Thedescriptor is normalized by dividing the descriptor vector byits magnitude so that the descriptor becomes illumination in-variant. A histogram of gradient location and orientation isused as a descriptor. It is demonstrated with various measuresthat the SIFT descriptors outperform other descriptors [35].An extended version of the SIFT descriptor is presented in[36]. It is known as gradient location and orientation histogram(GLOH). As the number of directions chosen to representthe histogram in GLOH is more than that in SIFT, the sizeof the descriptor is larger in GLOH. Here, the size can bereduced using principal component analysis, but in that case,

the computational complexity is more. Hence, in the presentalgorithm, the SIFT descriptor is used.

For every keypoint of the stereo image pair, a SIFT descriptoris computed and normalized. The descriptor computed usingthe gradient magnitude and orientation at each sample point isweighted by a Gaussian weighing function with σ equal to onehalf of the width of the descriptor window to assign a weight tothe magnitude of each sample point [6].

IV. MATCHING MODEL

After feature computation for the keypoint, the next stepis to match these keypoints. Ideally, we want to match eachkeypoint in the left image, which is considered as the referenceimage with a keypoint in the right image. In reality, in a stereoimage pair, generally, the overlap is 60%–80%, and we can findvalid matches for only some of the interest points in the leftimage. The algorithm is proposed for maximizing the numberof matches and improving the accuracy of matches.

A primary input to the matching algorithm is a set of interestpoints and their descriptors, computed using the SIFT algorithmas discussed in Section III. A stereo image pair is used inselecting interest points in both images (left and right) with theSIFT algorithm. For every interest point from both images, adescriptor is computed. Around every interest point, a pixel areaof size 16 × 16 is considered. For each sample size of 4 × 4,gradient magnitude and orientation are assigned. A histogramof gradient orientation showing eight bins gives a descriptor toevery sample size of 4 × 4. For a 16 × 16 sample size aroundthe interest point, a descriptor vector of dimension 4× 4× 8 isobtained. Thus, the descriptor vector is of size 128.

A. Notations

We represent the feature points from the left image as a setof N points

B = {b1, b2, b3, . . . , bN}.

We wish to match these features from the left image of astereo pair with the features of the right image. Let the numberof features detected in the right image be M , introduced ascategories:

C = {c1, c2, c3, . . . ., cM}.

We wish to match bi with cj as shown in Fig. 1. Suppose nneighbors of bi are selected and represented by set Bin, whereBin ∈ B

Bin = {bi1, bi2, bi3, . . . , bin}.

Let a category set Cm ∈ C be the interest points selectedfrom the right image for finding a match for bi

Cm = {c1, c2, c3, . . . , cm}.

The Euclidian distance between the descriptors of bi and cjis computed:

εi(c) = {εi(c1), εi(c2), εi(c3), . . . , εi(cm)} .

5646 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014

Fig. 1. bi is the keypoint in the selected area from the left image, and cj isthe keypoint in the selected area from the right image. bi and cj together makea category pair.

Four more binary relations are computed. The Euclidiandistance and angle between the relative positions of neighborsof bi are computed:

εd(bi) = {εd(bi1), εd(bi2), εd(bi3), . . . , εd(bin)}∠(Bin) = {∠(bi1),∠(bi2),∠(bi3), . . .∠(bin)} .

The Euclidian distance and angle between the relative posi-tions of the selected categories cj are computed as

εd(cij) =i=1,2,...mj=1,2,...m

⎡⎢⎢⎢⎢⎢⎢⎣

εd(c11) · · · εd(c1m)...

......

......

...εd(cm1) · · · εd(cmm)

⎤⎥⎥⎥⎥⎥⎥⎦

∠(cij) =i=1,2,...mj=1,2,...m

⎡⎢⎢⎢⎢⎢⎢⎣

∠(c11) · · · ∠(c1m)...

......

......

...∠(cm1) · · · ∠(cmm)

⎤⎥⎥⎥⎥⎥⎥⎦.

B. Matching Model

The next step is to decide the approximate maximum dis-parity range for each keypoint. The range is decided by visualinspection of the stereo image pair. The disparity is presentat the left and right images as the stereo images are capturedfrom different viewpoints and orientations. An area is selectedaround every keypoint node considering possible maximumdisparity range. All of the interest points are found in theselected area around the interest point in the right image. Thisprocedure of selecting the area around the interest point andthen considering all of the interest points lying inside the areaas probable matches, assigning initial probability, and changingthe probability of the probable matches using the relaxationlabeling technique is repeated iteratively for each left interestpoint under consideration and its probable matches in the rightimage.

Similarly for all interest points of the left image, a fixedwindow size is selected around each left interest point underconsideration, and all interest points lying inside the windoware chosen as neighbors for that left interest point. Theseneighboring interest points from the left image are used inimproving the matching probability by consistency property. Asshown in Fig. 1, the left interest point node bi forms a pair with

each interest point node cj from the area chosen in the rightimage (based on approximate maximum disparity range). Eachpair is called a category pair.

The initial weights are now assigned for every interest pointcj in the selected area of the right image. The initial weight ofeach interest point in the selected area is inversely proportionalto the Euclidian distance between the corresponding descriptorsof the category pair. If the Euclidian distance is more, itindicates that the descriptors of the two points are mismatched.Hence, less initial weight is given to that interest point. Forevery category cj , the weight is calculated as

wi(cj) =1

εi(cj) + 1, cj �= c̄. (1)

If the Euclidian distance between descriptors is more, thenthe weight for the category is less and vice versa. To handle theproblem of zero Euclidian distance, the denominator is adjustedas (εi(cj) + 1). Hence, a disparity category which associateshighly similar pair of interest points is given a large weightvalue, and the category with maximum Euclidian distance willbe assigned the lowest weight. The importance of the Euclid-ian distance between the SIFT descriptor for assigning initialweights on which the initial matching probability of a keypointdepends can be varied using a scaling factor k ranging from 0.5to 1.5. Thus, the convergence speed can be adjusted.wi(cj) is the weight of the category, and it is in the interval

[0, 1]. For every category set c, c̄ is the undefined category.The undefined category is introduced as there is a possibilityof no match for an interest point of the left image in the rightimage. As the stereo image pair overlap is generally 60%–80%,some interest points from the left image may not have a matchat all. If an interest point bi(x, y) from the left image does notcorrespond to any interest point in the selected area of the rightimage, then the weight for that category is undefined. Let theweight in this case be wi(c̄) for c̄.

The weights cannot be considered as the initial probabilityfor matching because the weights are not adding up to one aswi(c̄) is undefined. Hence, weights are not used as probabilityestimates. This interest point matching problem is consideredas a classification problem, where the left keypoint is assignedto one of the categories from the selected area as differentclasses. Hence, bi is mapped to one of the categories cj . Letthe maximum initial weight assigned to one of the categoriesbe maxWi(c). We are assigning initial probability to the unde-fined category as per the following:

poi (c̄) = 1−maxcj �=c̄

(wi(cj)) . (2)

By applying the Bayesian rule, the initial probabilities of thecategories are computed as follows:

poi (cj) = pi(c|j)× (1− poi (c̄)) , cj �= c̄ (3)

where

pi(c|j) conditional probability that bi has category cj asmatching category, given that bi is matchable;

JOGLEKAR et al.: IMAGE MATCHING USING SIFT FEATURES AND RELAXATION LABELING TECHNIQUE 5647

(1− poi (c̄)) prior probability that bi is matchable. The condi-tional probability is computed as

pi(c|j) =wi(cj)

L∑cj=1

cj �=c̄

wi(cj)

. (4)

Initial probabilities are assigned to every category of theselection area from the right image using (2)–(4). These prob-abilities which depend only on the similarity of the descriptorsof candidate matching points can be improved using the con-sistency property. The probability updating rule should havethe following property: The new probability pk+1

i (cj) shouldtend to increase when neighbors with highly probable categoryconsistent with cj are found nearby the keypoint under consid-eration. For the left interest point, the neighbors are selected,and their positions are decided by the Euclidian distance andangle. The category from the right selected area is consideredconsistent if the Euclidian distance and angle of the category areless than some threshold. The threshold is selected empiricallyand is changed adaptively for different regions. The categoriesare considered consistent if

|εd(bin)− εd(cjm)| < threshold

|∠(bin)− ∠(cjm)| < Th

where n is the number of neighbors of the left interest point andm is the number of neighbors of the right category which areconsidered as probable matches.

For computing the updated probability pk+1i (cj) for all cj in

the category set c, the likelihood estimation is carried out. Thedegree to which the cj of c strengthens the probability of thecategory cj should be related to estimated likelihood

qkij(c) =L∑

j,m=1

pi(cj) (5)

where |εd(bin)− εd(cjm)| < Th and

|∠(bin)− ∠(cjm)| < Th.

qkij(c) is the estimated likelihood considering the neighbor-hood of cj .L is the number of neighbors of cj in the category set in

the area selected in the right image, and n is the number ofneighbors of bi, for which the match is to be selected.

The rule used for updating category probability is

pk+1ij (c) =

pki (cj)qkij(c)

L∑j=1

pki (cj)qkij(c)

. (6)

The denominator of (6) acts as a normalizing factor. Further-more, the probability of category j is improved by the neighborsof cj as

pk+1i (cj) =

L∑l=1

alpk+1il (cj). (7)

Here, each category is updated iteratively. The values in thekth iteration are used to calculate the values in the k + 1thiteration. The weights al are associated with the contributionof different neighbors of cj . As shown in Fig. 1, there are fourneighborhood points of bi in the area selected in the left image.The weights al can be constant for all neighborhood points orvary in proportionality with the number of matching neighborsbetween the left neighborhood point and cj under considerationin the right selected area.

For updating the probabilities of the categories in the rightimage, (5)–(7) are used iteratively. The probability of one in-terest point will increase, and the probabilities of other interestpoints will go on reducing iteratively. After a few iterations,the algorithm will converge. Finally, a category from the rightselected area having the highest probability is considered asthe best match for the keypoint under consideration bi. If thehighest probability is less than some threshold, the match is notaccepted.

V. RESULTS AND DISCUSSION

This proposed feature-matching algorithm works for anyrange of disparity between a pair of stereo images and doesnot require information regarding camera orientation. Disparityin the pair of images of the same scene or object is due totranslation or rotation of the sensor. The feature correspondenceis a good guide for remotely sensed stereo images to generateground control points. The accurate correspondence is usefulfor coarse registration of the stereo image pair by finding theparameters of affine transformation between the images of thestereo pair. This coarse-registered stereo image pair is used forfurther dense matching for 3-D reconstruction.

In the presented algorithm, the probability of the valid matchis improved by considering relative positions of the neighborsusing the Euclidian distance and angle between neighbors. Asthe relative distance between neighbors is used to improvethe probability of the correct match, the accuracy to choosea correct match among the neighbors also improves. Equation(1) in the proposed algorithm computes the weights using theEuclidian distance between the left and right keypoint descrip-tors. The descriptors are computed by the binary code for SIFTprovided by Lowe and freely available at the URL.1

Four test stereo image pairs are chosen for testing the pro-posed algorithm. The first pair, TSIP1, is a high-resolutionimage with less complexity and of size 256 × 256 pixels.The second pair, TSIP2, is a satellite image taken by Indianremote sensing satellite with low spatial resolution and highcomplexity, having substantial affine distortion, change in 3-Dviewpoint, addition of noise, and change in illumination, and itis of size 235 × 370 pixels. Two more stereo image pairs con-sidered for experiments are building and church of size 480 ×640 pixels and are available at the URL.2 These stereo imagepairs also have a substantial amount of affine distortion. SIFTfeatures are chosen for all of the images of the stereo pair asdescribed in the preceding paragraphs.

1http://www.cs.ubc.ca/~lowe/keypoints/.2www.uttowa.ca/viva/projects/imagepairs/.

5648 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014

TABLE ITSIP1: TEST STEREO IMAGE PAIR 1; TSIP2: TEST STEREO IMAGE

PAIR 2; BBFA: BEST-BIN-FIRST ALGORITHM; PPRAG: PROPOSED

PROBABILISTIC RELAXATION ALGORITHM—GLOBAL THRESHOLD

The execution time of the “proposed probabilistic relaxationalgorithm” (PPRA) for the test images TSIP1 is 14 s, and forTSIP2, it is 283 s. The execution time of the proposed algorithmis more as our method uses the relaxation labeling techniqueand validation techniques for improving the accuracy of the cor-respondences. The execution time increases as the maximumdisparity range and number of keypoints to be matched areincreased. The number of accurate correspondences is more inour method as a consequence of the various built-in validationtechniques, like unicity, symmetry, and confidence measure.The number of matches and the number of inliers after findingthe epipolar geometry of the stereo image pair for differentmatching methods are given in Table I. The classical feature-matching methods SSD, VNC, and BBFA are compared withthe proposed algorithm PPRA. The results prove that the PPRAmethod gives more number of matched points than the otherthree methods. The number of matches is more, even after prun-ing the matches with unicity and confidence measure whichare the built-in validation methods of PPRA. Furthermore,symmetry validation check is used in pruning the matches.The epipolar geometry of the stereo image pairs is found byderiving the fundamental matrix using the RANSAC method.This fundamental matrix is used in finding the number of inliersand the percentage of good matches. The time complexity of theproposed algorithm is more as compared to the other methods,but the proposed method PPRA selects more good matches afterpruning the matches.

A. Comparison of PPRA With Other Methods

Comparison of our method with feature-matching methods,like SSD, VNC, and BBFA, is done, and the graphs in Fig. 2show the performance of the algorithm for the number ofmatches found and proportion of inliers after achieving epipolargeometry of the stereo image pair. The results show that theproportions of matches as well as that of inliers given bythe proposed method are much better than the other methods.Furthermore, the output of this algorithm finds the epipolargeometry between images of the stereo pair.

Fig. 3 shows TSIP1. The BBFA is used for the comparisonof the performance with PPRA. BBFA is chosen for compar-ison as it uses SIFT points for matching and the Euclidiandistance between the SIFT descriptors as a similarity measure.BBFA uses Euclidian distance and closest neighbor to that

Fig. 2. Comparison of the performances of the proposed PPRA method withother feature-matching methods, namely, SSD, VNC, and BBFA.

Fig. 3. TSIP1 with keypoints superimposed on it.

TABLE IITSIP1: TEST STEREO IMAGE PAIR 1; TSIP2: TEST STEREO IMAGE

PAIR 2; BBFA: BEST-BIN-FIRST ALGORITHM; PPRAG: PROPOSED

PROBABILISTIC RELAXATION ALGORITHM—GLOBAL THRESHOLD;PPRAL: PROPOSED PROBABILISTIC RELAXATION

ALGORITHM—LOCAL THRESHOLD

of the second closest neighbor approach. All matches wherethe distance ratio is greater than 0.7 are rejected in BBFA.The matches found with the method of BBFA are 244 for thegiven test stereo image pair shown in Fig. 3. The PPRA with

JOGLEKAR et al.: IMAGE MATCHING USING SIFT FEATURES AND RELAXATION LABELING TECHNIQUE 5649

Fig. 4. Wrong points selected as match by the BBFA method.

Fig. 5. Correct match selected for the same interest point by the proposedalgorithm. (a) Left interest point and neighbors. (b) Right probable matches.(c) Selected interest point as a match from the right image.

global threshold finds 289 matches for TSIP1. The accuracyof the correspondences of TSIP1 is checked with the groundtruth disparity map given at the URL,3 and the accuracy ofthe disparity of the matched point is 98% for TSIP1. Theminimum and maximum horizontal disparities of TSIP1 are −9and 3, respectively, and the minimum and maximum verticaldisparities of TSIP1 are −4 and 4, respectively, for the matchedkeypoints. A comparison of the number of matched points withthe method using only BBFA and with the PPRA method usingglobal and local thresholds is shown in Table II. The resultsof pruning the matches after the validation techniques are alsoshown in Table II. Fig. 4 shows the wrong point selected byBBFA. Fig. 5 shows, for the same left interest point, the correctmatch from the right image as selected by the PPRA.

3http://vision.middleburry.edu/stereo/.

Fig. 6. TSIP2. (a) Left image. (b) Right image.

Fig. 7. SIFT keypoints shown for TSIP2.

Fig. 6 shows TSIP2. Fig. 7 shows the SIFT features forTSIP2. Fig. 8 shows the performance of the matching algorithmPPRA with one selected left interest point for TSIP2, which is aremotely sensed image, taken by Indian remote sensing satelliteCartosat1 in 2007 for a typical suburban area of a city. The

5650 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014

TABLE IIIPROBABILITIES OF THE SELECTED NEIGHBORING POINTS EVOLVED FOR

FOUR ITERATIONS BY THE RELAXATION TECHNIQUE, SHOWN IN FIG. 8(d)

spatial resolution of this image is 2.5 m. In Fig. 8(b), theselected interest point is shown with red ∗, and its neighborsare shown. A fixed window size is selected around the leftkeypoint for which a match is to be found from the right image.In Fig. 8(c), neighboring interest points for the left image areshown. The search window in the right image for finding thematch is chosen based on the maximum horizontal and verticaldisparities present in the stereo image pair. The minimum andmaximum horizontal disparities of TSIP2 are −32 and 11, re-spectively, and the minimum and maximum vertical disparitiesof TSIP2 are −33 and 31, respectively, for the matched key-points. The size of the search window becomes large, and thenumber of neighbors selected will be more due to the large dis-parity range. The horizontal disparity of the image pair TSIP2is large as seen above. Hence, the number of selected neighborsis more. After pruning these neighbors with the K nearestneighbors approach, Fig. 8(d) shows the selected points whichare probable matches. Table III shows how the probabilities ofthe interest points in the selected area from the right image asshown in Fig. 8(d) evolve by the relaxation labeling techniqueusing PPRA for TSIP2. For one keypoint, the probability isincreased while reducing the probability of the other keypoints.

The time complexity of the PPRA matching algorithmincreases if the number of selected neighbors in the leftwindow and right search window is more. Sufficient numbersof neighbors are required for developing confidence measure,required for the consistency property. The execution timefor TSIP2 is more due to the large search window, and morenumber of neighbors are contributing in the relaxation labelingtechnique through the consistency property. In Fig. 8(e), theselected match from the right image for the left interest pointis shown. Fig. 9 shows the performance of PPRA for a fewmatching pairs.

The algorithm PPRA with global threshold works satisfac-torily and finds 387 matching points with higher accuracy.Furthermore, PPRA with local threshold finds 832 matchedpoints. The results after pruning the matched point pairs aftervalidation techniques, like symmetry, relative neighbor posi-tions, and unicity [29], are shown in Table I. The BBF algorithmfor the same pair finds only 105 correspondences. For theproposed algorithm, for a specific left keypoint, the set of rightkeypoint probabilities evolves, through the iterations, usingthe consistency property and relaxation labeling technique.Thus, the execution time increases as the number of neighborsincreases. The neighboring keypoints contribute in decidingthe final selection of keypoint from the right image. If the

Fig. 8. (a) Left interest point. (b) Left interest point and its neighbor.(c) Interest points from the selected area of the right image as probable matches.(d) Selected right probable matches based on initial probability. (e) Selectedmatch from the right image.

JOGLEKAR et al.: IMAGE MATCHING USING SIFT FEATURES AND RELAXATION LABELING TECHNIQUE 5651

Fig. 9. Result of the proposed matching algorithm with probabilistic approach. The joined lines show a few matching point pairs of the left and right images.

correct disparity range is known, then the time complexityof the algorithm improves as the selection of the number ofneighboring keypoints inside the search window in the rightimage will be minimized. However, even if the disparity rangeis not known accurately, the algorithm works effectively, givingthe correct and more number of valid matches as compared tothe SSD, VNC, and BBF algorithms.

The number of correct matches is counted considering alimiting candidate probability greater than 0.8. The presentedmatching algorithm is robust to 2-D rotation in image plane, asthe rotation and scale-invariant SIFT algorithm is used in se-lecting the keypoints. In case of rotation, different neighboringkeypoints are selected as the right image plane is rotated. Thenumber of keypoints selected in the right selection area willnot vary much as the disparity range does not change. In caseof scaling of the right image, if the right image is enlarged,the disparity range increases. Hence, the sample size aroundthe keypoint under consideration increases. However, it hardlyaffects the computing speed as the number of neighboring key-points found in the selected area, which contributes in evolvingthe matching probability of a keypoint, remains same.

B. Validation Techniques and PPRA

Some basic validation techniques are used in pruning thematches. Initially, validation of the matches is done by visualinspection using maximum allowable vertical and horizontaldisparity ranges. The matches outside the maximum disparityrange are discarded.

Another validation technique used is symmetry, where, first,the left image is considered as a scene and the right image as amodel and vice versa. The common matches are selected as truematches. The results after the validation techniques are shownin Table II.

In the proposed algorithm explained in Section IV, the in-terest point having the highest matching probability, which isrefined iteratively, is chosen as a unique best match. Hence,the validation technique unicity [29] is incorporated in the pro-posed algorithm. The relaxation labeling process for updatingthe matching probability also uses consistency property, whererelative neighboring positions are considered.

The problem of occlusion plays an important role instereo matching. Some basic assumptions like uniqueness andsmoothness, and triangular geometry are invalid in occludedregions. A constraint from the occlusion geometry is necessary

for significant improvement in accuracy in further dense match-ing. The left occluded regions are visible only in the left stereoimage and have no corresponding feature points in the rightimage and vice versa. The occluded regions in one stereo imagecorrespond to discontinuities of depth map in another stereoimage. However, SIFT feature points are found in the interiorpart of the object of an image and not in the boundary region,and therefore, the problem of discontinuity does not arise in theproposed SIFT-based feature-matching algorithm.

However, the location of the occluded regions can be markedby identifying the objects with fewest possible number offeature matches. The clusters of features can be identified byHough transform [26] with a consistent interpretation by usingeach feature to vote for all poses of the occluded area underconsideration that are consistent with the features. However,occluded area detection is not in the scope of this paper.

VI. CONCLUSION

Correspondences obtained in the feature-matching algorithmproposed in this paper are a useful input as ground controlpoints for remotely sensed images. These correspondences areuseful for coarse registration of stereo image pair. These coarse-registered images are further used for matching for findingdense disparity map.

The probabilistic approach explained in the proposed algo-rithm for feature point matching uses a consistency propertyto improve the candidate probabilities using the relaxationlabeling technique. Instead of keypoint-by-keypoint matching,the approach of finding neighboring keypoints and selectingthe match for the keypoint under consideration in the selectedarea of the left image, using neighboring keypoints contributingfrom the selected area of the right image, improves the accuracyof the valid match. Expensive 2-D search over the entire imageis reduced by applying interest point operator to both images,and it also greatly improves the search space. The built-invalidation techniques, like unicity, symmetry, and confidencemeasure of the proposed algorithm, improve the accuracy ofcorrespondences. The fundamental matrix derived from theoutput correspondences is useful for validation, for findinginliers in further step of dense matching.

The algorithm converges quickly within a few iterations andcan be applied to images having a wide disparity range. It isrobust over a large range of disparity. The method is robust to2-D rotation in image plane and scaling.

5652 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewersfor the valuable suggestions and constructive review comments.The authors would also like to acknowledge the efforts taken bythe IEEE TGRS editorial team for the comments.

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Jyoti Joglekar received the Master of Engineeringdegree in computer engineering from the Universityof Mumbai, Mumbai, India, in 2004. She is currentlyworking toward the Ph.D. degree in the Centre ofStudies in Resources Engineering, Indian Institute ofTechnology Bombay, Mumbai.

Her areas of research are stereo image analysis,feature-based image-matching algorithms, and area-based image-matching algorithms.

Ms. Joglekar is a Life Member of the IndianSociety of Remote Sensing.

Shirish S. Gedam received the Master of Technol-ogy degree with specialization in remote sensingand the Ph.D. degree from the Indian Institute ofTechnology (IIT) Bombay, Mumbai, India, in 1984and 1991, respectively.

He is currently an Associate Professor with theCentre of Studies in Resources Engineering, IITBombay. His areas of research include stereo andmultimodal image processing and analysis for 3-Dmapping, especially the feature extraction andmatching aspects. He is also actively working in the

area of precision processing of GPS data and GPS meteorology.Dr. Gedam is a Life Member of the Indian Society of Remote Sensing and

Indian Society of Geomatics.

B. Krishna Mohan received the Ph.D. degree inelectrical engineering from the Indian Institute ofTechnology (IIT) Bombay, Mumbai, India, in 1991.

He is currently an Associate Professor with theCentre of Studies in Resources Engineering, IITBombay. His areas of research include satelliteimage processing and analysis, machine learningalgorithms, and educational content development forremote sensing and image processing.

Dr. Mohan is a Life Member of the Indian Societyof Remote Sensing and Indian Society of Geomatics.

He was the recipient of the 2003 IETE M. N. Saha Memorial Award for BestApplication Oriented Paper in IETE Journal of Research. He received the IndianSociety of Remote Sensing’s National Geospatial Award for Excellence inDecember 2013.