Patent Application: US-77524010-A

Abstract:
a computer implemented method for point matching comprising providing a pair of images captured , selecting first and second sets of interest points from the images ; constructing a control network of super points for each set of interest points ; assigning a position , with respect to the closest network control point of each control network , to other interest points on the images ; locating conjugate points for each other interest point of each set based on its assigned position ; and adding the conjugate points to the control network .

Description:
in one embodiment of the invention , an algorithm first detects and extracts super points , which have the greatest interest strength ( i . e . those points which represent the most prominent features ). a control network can then be constructed based on these super points . this control network , like a sketch , can then control the entire image , and ambiguities in the homogeneous areas can be avoided . next , every point in the image is assigned a unique position and angle relative to the closest super point in the control network . finally , for interest point matching , those points with the smallest position and angle differences are the correspondences . the correspondences are then added to the control network to construct a bigger and stronger control network . the process is continued until no more correspondences are found . the algorithm proposed in this paper includes three parts : 1 ) super point detection ; 2 ) super point matching ; and 3 ) interest point matching . the harris detector , a well - known interest point detection algorithm , can be used in to detect and extract the super points and interest points . the harris algorithm determines whether or not a point is a corner based on the harris matrix a at the point p ( x , y ). where the angle brackets denote averaging ( summation over the image patch around the point p ( x , y )). the interest strength is determined based on the magnitudes of the eigenvalues ( λ 1 and λ 2 ) of a . because the exact computation of the eigenvalues is computationally expensive , the following function m c was suggested by harris and stephens [ 1988 ] as the interest strength : the value of κ has to be determined empirically , and in the literature values in the range 0 . 04 to 0 . 06 have been reported as feasible [ schmid et al ., 2000 ]. if mc & gt ; 0 , it is a corner , otherwise , it is not a corner . obviously , the corner should be the point with the local maximum value of mc . by calculating the interest strength mc over whole image , an image which shows the interest strength can be obtained . fig1 shows two original images and their corresponding interest strength shown below each image . the brightness is directly proportional to the interest strength . two thresholds ta and tb can be set with ta & gt ; tb for the interest point detection and super point detection . the point with an interest strength greater than the threshold tb and also representing the local maximum , can be extracted as an interest point . if the interest strength of such point is greater than the threshold ta and its interest strength is a local maximum , then a super point is detected . fig2 shows extracted super points and their corresponding interest points . there are 99 super points in super point set 1 and 737 interest points in interest point set 1 . there are 111 super points in super point set 2 and 707 interest points in interest point set 2 . like most other interest point matching processes , super point matching is an exhaustive search process , so the number of super points should be limited to an acceptable range . the goal of the super point matching is to find a root from each super point set and identify the first group of correspondences ( tie points ). as shown in fig3 , the super point matching consists of three steps : 1 ) control network construction ; 2 ) assignment of relative positions and angles ; and ( 3 ) correspondence searching . in step 1 , a super point from each super point set is selected as a root , and a control network is constructed . one control network is constructed for each super point set . fig4 shows a control network constructed with super points . p and p ′ are roots , and the others are leaves . a and a ′ are start points . sixteen tie points ( correspondences ) are obtained after super point matching . “ x ” denotes an outlier . ( 1 ) a leaf from control network 1 is selected randomly as the starting point . the distance between the starting point and the root is denoted as s . ( 2 ) the corresponding starting point in control network 2 is determined according to the distance between the root and the leaf . the leaf point of control network 2 with the closest distance to s is selected as the corresponding starting point in control network 2 . ( 3 ) after the two starting points for both control networks have been determined , the relative positions ( distance between root and leaf ) and angles ( clockwise from the starting point ) are assigned to every point in both control networks . fig5 is a diagram showing relative position ( r ) and angle ( θ ) assignment ( image 1 ), and a correspondence search ( image 2 ). after the root and start points are determined , every point ( e . g . c ) can be assigned a relative position ( r ) and angle ( θ ) ( image 1 ). the closest candidate in the searching area is the correspondence ( image 2 ). correspondence searching commences in step 3 . after each point in both control networks has been assigned a relative position and angle , a corresponding point in control network 2 may be found for every leaf point in control network 1 according to their positions and angles based on the following function : where , m and n denote the number of leaves in control network 1 and control network 2 respectively ; pi and p ′ i are relative distances between root and leaf in the two control networks ; and θ pi and θ p ′ i are relative angles between starting point and leaf in the two control networks . the closest points with the smallest position differences and smallest angle differences , where both differences are less than their corresponding thresholds , will be selected as tie points ( correspondences ). otherwise , if a point does not have a correspondence , it is an outlier , as shown in fig4 . every super point can be either the root or the starting point . after super point matching , a number of correspondences are obtained . when the maximum possible number of correspondences is obtained , the corresponding root and starting points will be the final root and starting points of the super point control network . only image shift and image rotation are considered when interest points are matched by determining the root and the starting point . this is acceptable because for high resolution satellite images with narrow fields of view , affine transformations can accurately simulate the geometric distortion between two images [ habib and ai - ruzouq , 2005 ]. the process of super point matching is an iterative and exhaustive search process . every point can be either a root or a starting point . for example , in fig8 there are 20 super points in super point set 1 and 21 super points in super point set 2 . therefore , there are c 20 1 c 21 1 combinations for root selection , c 19 1 c 20 1 combinations for starting point selection , and c 18 1 c 19 1 combinations for the correspondence search . so there will be c 20 1 c 21 1 c 19 1 c 20 1 c 18 1 c 19 1 = 54583200 combinations in total . therefore , in order to avoid combination explosion and reduce the matching time , the number of super points should be limited to an acceptable range . after super point matching , a control network which consists of all the extracted correspondences is obtained . fig6 is an image showing the result of super point matching - control networks with 41 correspondences . after the super point matching , two control networks corresponding to the two interest point sets are obtained . under the control of the super point network , interest point matching becomes simple . fig7 shows a flowchart of the interest point matching process , which includes four steps . first , through a process of k - means clustering , every interest point can be grouped with the closest node of the control network . for example , as shown in fig8 , the interest points 17 , 18 , 19 , and 20 in the circle are grouped with the closest control network point “ 10 ”. then , taking node “ 10 ” as the root , together with all the interest points grouped with it ( 17 , 18 , 19 , 20 ) and node 10 &# 39 ; s father node p , a sub - control network is constructed . the father node p will be the starting point in the sub - control network . interest point matching is performed between two sub - control networks whose roots are correspondences ( tie points ). next , every point in this sub - control network is assigned a position and angle with respect to node “ 10 ” and the starting point “ p ”. in this way , every interest point is assigned a relative position and angle with respect to its closest control network point . finally , interest point matching is performed between the two sub - control networks whose root nodes are correspondences . correspondences are defined as those interest points with the minimum difference in position and angle . the new correspondences are added to the control network to construct a bigger network . this is an iterative process that continues until no new correspondence is added to the control network . the final control network is the result of interest point matching . in the process of interest point matching , it is crucial to set a suitable threshold for the position and angle differences . in remote sensing and photogrammetry , the images always contain complicated local distortions because of the long baselines ( long distance between images ) and ground relief variations . in such a situation , the effective ground distance for different sensors will vary with changes in ground relief , incidence angle and sensor position . for example , in fig9 , a distance s on the ground with a slope is acquired by two sensors s 1 and s 2 with incidence angles θ 1 and θ 2 respectively . the distance difference caused by ground relief variation in such a case can be defined as follows : where ds is the distance difference caused by the ground relief variation ; θ 1 , θ 2 are the incidence angles of sensor s 1 and sensor s 2 respectively ; β is the slope of the ground ; and s is the ground distance . obviously , the distance difference can vary with ground slope and incidence angle . as shown in the graphs in fig1 , the distance difference changes with the incidence angle and ground slope ( assuming that the forward incidence angle θ 1 equals the backward incidence angle θ 1 ). the distance difference is proportional to the ground slope and the incidence angle . for an image pair , the incidence angles are constants , so the ground slope is the only variable . in an image , the slope varies with the ground relief variation . therefore , the only way to limit the distance difference between two images is to limit the ground distance . a small ground distance will lead to a small distance difference and vice - versa . that is why in the interest point matching algorithm , all interest points should be grouped with their closest control network points . it is important to determine the best way to select the threshold for the distance difference and angle difference . obviously , a large threshold will increase the number of false matches , so in order to reduce false matches , the threshold should preferably be set as small as possible , but when the distance difference between two images is large , a small threshold may mean that correspondences are over - looked and more iterations may be needed to find matches . another concern may be that a small threshold may lead to false matches and exclude the correct correspondence . this is possible , but because the interest point is a local maximum , there is only a small probability that in the small search area there is another local maximum and the correct one is farther away from the search area . the threshold can therefore be set by considering the radius of the local maximum . for example , if the local maximum is contained in a 5 by 5 pixel window , a threshold of 2 pixels or less can be considered as a safe threshold . as shown in fig1 , a stereo pair of level 1 a ikonos images was acquired on jun . 25 , 2004 , over penang , malaysia . the incidence angles are 30 ° and 3 . 5 ° respectively . a rectangular area ( 400 by 400 pixels ) was selected as the test area . fig1 shows two pairs of images . the pair ( a ) and ( a ′) were taken directly from the original images without rotation . a second pair ( b ) and ( b ′) is comprised of ( b ) which was taken from the original left image and ( b ′) which was taken from the right image which has been rotated 45 °. in this test area , there is large area of grass which was used to test the algorithm &# 39 ; s capability of reducing ambiguity and avoiding false matching in a smooth area . fig1 shows the results of interest point matching corresponding to the image pairs from fig1 ( a ), ( a ′) and fig1 ( b ), ( b ′) respectively . the pair ( a ) and ( a ′) shows 410 correspondences and the pair ( b ) and ( b ′) shows 264 correspondences . as shown in fig1 , a stereo pair of ikonos images which was acquired on feb . 22 , 2003 , in hobart , australia . the incidence angles are forward 75 ° and backward 69 ° respectively ( fraser and hanley , 2005 ). a rectangular area ( 400 by 400 pixels ) was selected as the test area . fig1 shows two pairs of images : ( c ) and ( c ′) are a test image pair ( 400 by 400 pixels ) taken directly from the original images without rotation , while ( d ) and ( d ′) is another test image pair ( 400 by 400 pixels ) where ( d ) was taken directly from the original left image and ( d ′) was taken from the right image which has been rotated 315 °. this is an urban area with a large area of grass where the algorithm &# 39 ; s capability of reducing ambiguity and avoiding false matching in smooth areas could be tested . fig1 shows the results of interest point matching corresponding to the image pairs from fig1 ( c ), ( c ′) and fig1 ( d ), ( d ′) respectively . the image pair ( c ) and ( c ′) show 641 correspondences and the image pair ( d ) and ( d ′) show 561 correspondences . fig1 shows test area 3 , which was also taken from the stereo image pair in penang . because the above two test areas are relatively flat and somewhat small , a larger test area from a mountainous area was selected as test area 3 in order to test the algorithm under a different set of conditions . a rectangular area ( 2000 by 2000 pixels ) was selected as test area 3 . fig1 shows image pair ( e ) and ( e ′), taken directly from the original images . this is a mixed area of mountain and urban land cover . in this test area , there is large area of forest which was used to test the algorithm &# 39 ; s capability of reducing ambiguity and avoiding false matching in a smooth area . the mountainous area was used to test the algorithm &# 39 ; s capability of processing large distortions . fig1 shows the results of interest point matching corresponding to the image pair from fig1 ( e ) and ( e ′). there are 5674 correspondences in total . in order to test the proposed algorithm , five test areas shown in fig2 , which are located in the densest forestry region of fredericton , new brunswick , canada , are chosen to challenge the capability of dealing with the ambiguity problem in the homogeneous area . six scenes of quickbird images cover the test field . all test image pairs are selected in the overlapping area . the corresponding results of interest point matching are illustrated in fig2 to 25 respectively . in fig2 , 813 correspondences are obtained in test area 4 . in fig2 , 929 correspondences are obtained in test area 5 . in fig2 , 759 correspondences are obtained in test area 6 . in fig2 , 857 correspondences are obtained in test area 7 . in fig2 , 875 correspondences are obtained in test area 8 . all the experiments illustrated satisfactory results without any false matches . even in the smooth areas ( e . g . a large area of grassland ), this algorithm avoided false matches efficiently . in addition , because each interest point is assigned a unique position and angle with regard to its closest control point , its correspondence is searched only within the corresponding sub - control network , thus the process of interest point matching is very fast . by using an ibm ( processor 1 . 70 ghz , 1 . 69 ghz , 768 mb of ram ), each experiment took only a few seconds . fig2 and 27 together form an image pair taken with a convention digital camera . a method of interest point matching according to the present invention was applied to the images . correspondences found using methods according to the invention are shown in fig2 and 29 . methods of the invention can be used to match images for example for mosaicing images and for overlaying of images for change detection analysis . the success of the algorithm embodied in this invention depends on the control network . on one hand , the control network incorporates the spatial information and easily overcomes the problem of ambiguity in the homogeneous area . on the other hand , if the first group of correspondences from the super point matching is wrong , then all the other correspondences extracted based on this control network later on will also be false . this may be the main concern for this algorithm . however , for every different image , the control network of super points is almost always unique , except that there is not any prominent texture in the image and the whole image is homogeneous or filled with man - made texture . therefore , this algorithm does not work in the complete homogeneous area , such as the area covered by snow , water , or sand . fortunately , a complete homogeneous image is extremely rare . the method described above may be embodied in sequences of machine - executable instructions which , when executed by a machine , cause the machine to perform the actions of the method . the machine that executes the instructions may be a general - purpose or special - purpose processor . by way of example , the machine - executable instructions may be stored on a number of machine - readable media , such as cd - roms or other types of optical disks , floppy diskettes , roms , rams , eproms , eeproms , magnetic or optical cards , flash memory , or other types of machine - readable media that are suitable for storing electronic instructions . the methods disclosed herein could also be performed by a combination of both hardware and software . while illustrative and presently preferred embodiments of the invention have been described in detail herein , it is to be understood that the inventive concepts may be otherwise variously embodied and employed , and that the appended claims are intended to be construed to include such variations , except as limited by the prior art . auer , matin , peter regitnig , and gerhard a . holzapfel . 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