Q. Tian, M. N. Huhns, "Algorithms for subpixel registration", Computer Vision, Graphics and Image Processing, 35, pp. 220-233, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....after the initial discrete correspondence stage. An alternative is to simply start with more discrete disparity levels. Sub pixel disparity estimates can be computed in a variety of ways, including iterative gradient descent and fitting a curve to the matching costs at discrete disparity levels [93, 71, 122, 77, 60]. This provides an easy way to increase the resolution of a stereo algorithm with little additional computation. However, to work well, the intensities being matched must vary smoothly, and the regions over which these estimates are computed must be on the same (correct) surface. Recently, some ....

....disparity (and within the search limits) this value is used as the final disparity estimate. In future work, we would like to investigate whether initial or aggregated matching scores should be used, or whether some other approach, such as Lucas Kanade, might yield higher quality estimates [122]. 5. Evaluation methodology In this section, we describe the quality metrics we use for evaluating the performance of stereo correspondence algorithms and the techniques we used for acquiring our image data sets and ground truth estimates. 5.1. Quality metrics To evaluate the performance of a ....

Q. Tian and M. N. Huhns. Algorithms for subpixel registration. CVGIP, 35:220--233, 1986.

.... view synthesis results (the scene appears to be made up of many thin shearing layers) To remedy this situation, sub pixel disparity estimates can be computed in a variety of ways, including iterative gradient descent and fitting a curve to the matching costs at discrete disparity levels [76, 48, 40]. This provides an easy way to increase the resolution of a stereo algorithm with little additional computation. However, to work well, the intensities being matched must vary smoothly, and the regions over which these estimates are computed must be on the same (correct) surface. Recently, some ....

Q. Tian and M. N. Huhns. Algorithms for subpixel registra- tion. CVGIP, 35:220-233, 1986.

....vector fields to those corresponding to translational motion where v = v 1 v 2 ] is a constant. Periodically, there have been fairly comprehensive survey papers describing and comparing the performance of THIS WORK WAS SUPPORTED IN PART BY THE NSF GRANT CCR 9984246. many algorithms [1] 2] [3]. Unfortunately, the benchmarks comparing the performance of such algorithms tend to vary widely and fail to address the problem in a proper statistical framework. This type of performance characterization leaves open the important question of how close the algorithms in question are to being ....

....tapers off as the bandwidth increases beyond about a quarter of the full bandwidth for all of the images examined. Figure 2 shows the performance, in terms of the square root of the trace of the MSE matrix, tr(MSE) is a type of RMSE measure) for a variety of approximate ML estimators [3][6] 7] 8] 9] The pair of images is generated by synthetically shifting the tree image of [1] The results are obtained using Monte Carlo simulations at various signal to noise ratios (SNR) As expected, above a certain SNR the performance of all the estimators flattens out while the unbiased CRLB ....

Q. Tian and M. Huhns, "Algorithms for subpixel registration, " Computer Vision, Graphics, and Image Processing, vol. 35, pp. 220--233, 1986.

....image translation between a pair of images. Because this problem is of such fundamental importance, many registration algorithms have been developed over the years. In fact, there have been fairly comprehensive survey papers describing and comparing the performance of such algorithms [1] 2] [3]. Unfortunately, the benchmarks comparing the performance of such algorithms tend to vary as widely as the techniques themselves, and the typical performance measures fail to address the problem in a proper statistical framework. These performance measures have ranged from geometric error criteria ....

....n v 2 ) Even in such high SNR (low noise) situations, however, the objective functions (10) and (11) can be evaluated for only integer values of v 1 and v 2 , constraining the estimates to that of integer multiples of pixel motion. While some progress has been made to address this issue [4] 14] [3], the proposed algorithms often are based on overly simplified approximations that are known to produce biased estimates [15] For many applications in image processing, accurate subpixel image registration is needed. To register images to subpixel accuracy, the image function f(x, y) effectively ....

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Q. Tian and M. Huhns, "Algorithms for subpixel registration," Computer Vision, Graphics, and Image Processing, vol. 35, pp. 220--233, 1986.

....can handle can be very large even for small values of s. 2.1. 5 Subpixel Matching After the grid to grid matches are obtained from the hierarchical search, displacements with subpixel accuracy can be easily computed for the finest resolution level of the pyramid using a differential method [18, 21]. Subpixel accuracy is necessary to eliminate the quantization error introduced when the images are digitized. If a feature P t (u; v) has offset (ffix; ffiy) relative to P t Gamma1 (u; v) assume they were tracked and registered so that the translation (ffix; ffiy) is very small) i.e. ....

Q. Tian and M.N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986. 43

....technique. Many applications like change detection, passive navigation, feature location measurements in remote sensing, image sequence analysis, and nondestructive evaluation require registration results with an error less than one pixel, also called super resolution 9 and subpixel accuracy [Tian86]. However, subpixel registration greatly introduces additional computation power and memory space requirement. Original Subpixel Accuracy = 0.5 Subpixel Accuracy = 0.25 Subpixel Accuracy = 0.125 Figure 1.3 Images with different subpixel resolution Consider the registration of a 32x32 image with ....

....generations, pop size = population size, N A = Not Applicable) 2.2.4 Subpixel Image Registration In general, it is acceptable to achieve a registration result with an error of 1 pixel. In remote sensing, a distance of one pixel for a Landsat image corresponds to about 80 meters distance on Earth [Tian86]. This means that the pixel level registration provides a 40 meter resolution. To achieve a 4 meter resolution, one must register the images with an accuracy of 0.1 pixel. Many other instruments has even coarser resolution. For example, TRMM data have 4 Kilometer resolution. Registration results ....

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Qi Tian and M. N. Huhns, "Algorithms for subpixel registration," CVGIP, Vol. 35, pp. 220-223, 1986.

....to make it linear: arg min s 1 ,s 2 ,t # # s 1 s 2 s 2 s 1 # x i t y j # 2 . 6.8) 1 This restriction also happens with the correlation methods. To have better accuracy, it is necessary to interpolate the images, or equivalently the correlation surface, see Tian and Huhns [87]. Light version: some figures are not present 6.4. COMPLEXITY 155 Noting S = s 1 s 2 ) T and taking into account the equality # s 1 s 2 s 2 s 1 # x i = A (i) S where A (i) # x i y i y i x i # , we can rewrite Equation (6.8) into arg min S,t # #A (i) S t y j ....

....do not sample the continuous image smoothed by the lens at Nyquist rate. Most, if not all, the images we deal with, are not sampled in the conditions of Shannon reconstruction theorem. If this were the case, the registration by correlation would not only reach subpixel accuracy, as reported in [87], but would have a theoretical infinite accuracy. This would be the definitive method. But in real cases, the images are not sampled according to Nyquist rate, so their interpolation by cardinal sines does not correspond to the original continuous domain image, so the accuracy of the registration ....

Q. Tian and M.N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics and Image Processing, 35(2):220--233, August 1986.

....In actual applications, if an automatic document feeder is utilized for scanning the page in duplex mode, the relative alignment between the images on the two sides can be obtained from the feeder s geometry and the detected paper edges. Alternately, techniques from image registration [13] [14] may be adapted for aligning the images. For the images in Figs. 5 and 6, the (scaled) reflectance of white paper unprinted on either side was computed by averaging the scanned values over a 400 pixel by 400 pixel square in the top corner of the image side scan. This average value was 250.56 (for ....

Q. Tian and M. N. Huhns, "Algorithms for subpixel registration," CVGIP: Graph. Models Image Process., vol. 35, no. 2, pp. 220--233, Mar. 1986.

....hours 1.7 hours 115 200, 150 150 490 frames 14.3 hours 57 minutes Table 1: Two tracking sequences from Forest Gump were re timed using both direct and fast NCC algorithms using identical features and search windows on a 100 Mhz R4000 processor. These times include a 16 2 sub pixel search [17] at the location of the best whole pixel match. The sub pixel search was computed using Eq. 2) direct convolution) in all cases. feature size search window(s) Flint fast NCC 40 2 110 2 1 min. 40 seconds 16 seconds (subpixel=1) 40 2 110 2 n a 21 seconds (subpixel=8) Table 2: ....

Qi Tian and M. N. Huhns, "Algorithms for Subpixel Registration", CVGIP 35, p. 220-233, 1986.

....2 m 7 2 f 1 2 (43) m 0 m 1 m 3 m 4 m 6 m 7 f 1 2 =0. 44) From this, we can compute the estimates f 0 2 = m 5 2 m 2 2 m 0 2 m 1 2 m 3 2 m 4 2 if m 0 2 m 1 2 #= m 3 2 m 4 2 12 An analysis of the relationship between these two approaches can be found in [TH86] 17 or f 0 2 = m 2 m 5 m 0 m 3 m 1 m 4 if m 0 m 3 #= m 1 m 4 . Similar result can be obtained for f 1 as well. If the focal length is fixed for two images, we can take the geometric mean of f 0 and f 1 as the estimated focal length f = # f 1 f 0 . When multiple estimates of f are ....

Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

....for a array detector with and without electronic noise using an analytical test function are presented in Sec. 6 [1] A survey describing various other image registration techniques has been given by Brown [2] Other algorithms for achieving subpixel registration have been given by Tian and Huhns [3] and Goshtasby, Stockman, and Page [4] A contour based approach to image registration has been developed by Li, Manjunath, and Mitra [5] A least squares image registration algorithm has been indicated by Zikan [6] In this paper the iterative solution to the integral equation (9) in Sec. 3 is ....

Q. Tian and M. N. Huhns, "Algorithms for Subpixel Registration", Computer Vision, Graphics, and Image Processing, 35, 220 - 233 (1986).

....to the nearest pixel, which is typically not su#ciently accurate for tasks such as view interpolation. Di#erent techniques have been developed for computing sub pixel estimates, such as using a finer set of disparity hypotheses or finding the the analytic minimum of the local error surface [TH86, MSK89] Unfortunately, for challenging applications such as z keying (the insertion of graphics between di#erent depth layers in video) PW94, K 96, B 96] even this is not good enough. Pixels lying near or on occlusion boundaries will typically be mixed, i.e. they will contain blends ....

.... developed concurrently with ours, traverses the disparity space from front to back [SD97] Sub pixel (fractional) disparity estimates, which are essential for applications such as view interpolation, can be computed by fitting a curve to the matching costs at the discrete disparity levels [LK81, TH86, MSK89, KO94] This provides an easy way to increase the resolution of a stereo algorithm with little additional computation. However, to work well, the intensities being matched must vary smoothly. In this paper, we present two di#erent representations for fractional disparity estimates. ....

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Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

....and geometric information extracted from the low resolution data, given the a priori information. Low resolution image frames have to entail sub pixel overlap and have to be registered at sub pixel accuracy. This will imply a preprocessing registration, using methods such as those proposed by [23][22][3] 13] 19] Tests have been carried out on both synthetic and real images. The algorithm can be applied in the area of aerial and satellite image processing. INRIA 3D Super resolution 5 2 Preliminary Assumptions We shall, henceforth, assume that our sensor is a pin hole camera located far ....

....low resolution images, each frame can be assumed to contain the recuring samples of a nonuniform sampling sequence obtained by applying a common input function to a set of linear shift invariant systems. We, obviously, need to register the recuring samples using registration algorithms such as [23][22][3] 13] 19] Let g and z denote the vectors of unknown variables, i.e. the vectors of the albedo g (x;y) and the height z (x;y) on the super resolution grid at m th of the Nyquist rate. Here, the input is a function of g and z: f(g; z) see Appendix A) Let al..so I denote the vector of all ....

Qi Tian and M. N. Huhns. Algorithms for subpixel registration. CVGIP, 35:220--223, 1986.

....others [3] 7] 8] 9] 14] 15] 16] depend on the scene registration at subpixel accuracy. The most commonly used approach for subpixel registration consists of interpolating images prior to registration. Amongst this class of algorithms we can notably mention: correlation interpolation [4] [17], intensity interpolation[17] phase correlation interpolation [13] 17] and the geometric methods [2] It is obvious that the accuracy of these methods depends highly on the quality of the interpolation algorithm. Methods that do not use interpolation for achieving subpixel accuracy, have been ....

....[15] 16] depend on the scene registration at subpixel accuracy. The most commonly used approach for subpixel registration consists of interpolating images prior to registration. Amongst this class of algorithms we can notably mention: correlation interpolation [4] 17] intensity interpolation[17], phase correlation interpolation [13] 17] and the geometric methods [2] It is obvious that the accuracy of these methods depends highly on the quality of the interpolation algorithm. Methods that do not use interpolation for achieving subpixel accuracy, have been more scarce in the ....

[Article contains additional citation context not shown here]

Qi Tian and M. N. Huhns. Algorithms for subpixel registration. CVGIP, 35:220--223, 1986.

....can handle can be very large even for small values of s. 2.1. 3 Subpixel Matching After the grid to grid matches are obtained from the hierarchical search, displacements with subpixel accuracy can be easily computed for the finest resolution level of the pyramid using a differential method [10, 14]. Subpixel accuracy is necessary to eliminate the quantization error introduced when the images are digitized. If a feature P 0 t (u; v) has offset (ffix; ffiy) relative to P 0 t Gamma1 (u; v) assume they were tracked and registered so that the translation (ffix; ffiy) is very small) i.e. ....

Q. Tian and M.N.Huhns. Algorithms for Subpixel Registration. Computer Vision, Graphics, and Image Processing, 35:220-233, 1986.

....image transformations. We test performance with several simulations and experiments. 1 Introduction IEEE Conference on Computer Vision and Pattern Recognition (CVPR94) Seattle, June 1994 Is feature tracking a solved problem The extensive studies of image correlation [4] 3] 15] 18] 7] [17] and sum of squared difference (SSD) methods [2] 1] show that all the basics are in place. With small inter frame displacements, a window can be tracked by optimizing some matching criterion with respect to translation [10] 1] and linear image deformation [6] 8] 11] possibly with adaptive ....

Qi Tian and Michael N. Huhns. Algorithms for subpixel registration. CVGIP, 35:220--233, 1986.

....error of 10 of the pixel period can be expected. Depending on the kind of image, mean square errors range from 0.4 to 4 . INTRODUCTION In 1972, Barnea and Silverman presented the SSD algorithm, a fast way to solve the problem of image registration [1] Extending it to subpixel accuracy ([2], 3] nevertheless, increased the computational cost to an amount where real time applications seemed almost impossible. In this paper we present an adapted algorithm with real time acceptable speed and even better accuracy. To introduce the reader into the matter, the first chapter reviews the ....

....can be regarded as a kind of error correction to the pixel accuracy registration. 1.2 Interpolating the original image A 13 accuracy as shown above seemed not too satisfying for reliable applications. Another much more complicated method was therefore developed by Tian Huhns [2]. They interpolated the original image, resampled it to a higher resolution, and conducted the template matching search over this new image. Suppose an accuracy of 1 to be accomplished, an original image of size N has to be interpolated and resampled to size 100N. The search now covers all ....

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Q. Tian und M. N. Huhns, "Algorithms For Subpixel Registration", Computer Vision, Graphics and Image Processing, 35, pp 220 -- 233, 1986.

....so that the Laplacian images are not affected by possible rotations of the input images. After the grid to grid matches are obtained from the hierarchical search, the displacements with subpixel accuracy are computed for the finest resolution level of the pyramid using a differential method [10]. Subpixel accuracy is necessary to eliminate the quantization error introduced when the images are digitized. 2.3 MOTION COMPENSATION The motion compensation module removes the unwanted motion from the input image sequence based on the motion estimates provided by the motion estimation process. ....

Q. Tian and M.N.Huhns. Algorithms for subpixel registration. Computer Vision, Graphics and Image Processing, 35:220--233, 1986.

....be seen in Figure 3(a) this usually leads to an inaccurate estimation. An approach which may give more accurate results can be found in the field of image registration, where the objective is to register a pair of images with subpixel accuracy. The intensity interpolation method (Tian and Huhns [21]) attempts to reconstruct one of the images as closely as possible before the displacement of the other image is calculated. If the same reconstruction technique is used before area estimation, the accuracy of the estimation may be higher as well see Figure 3(b) Depending on the image ....

Q.I. Tian and M.N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

.... Accurate estimation of displacement or location of a signal or image is important in many applications of signal and image processing such as time delay estimation [21] target tracking [36] non contact measurement [41] 2] remote sensing [4] 11] computer vision [1] image registration [8] [39], and so on. In video coding, motion estimation is proved to be very useful for reduction of temporal redundancy. Therefore, a number of motion estimation algorithms have been devised solely for video coding [30] 10] and numerous VLSI architectures have been designed for practical video ....

Q. Tian and M. N. Huhns, "Algorithms for subpixel registration", Computer Vision, Graphics and Image Processing, vol. 35, pp. 220--233, 1986.

.... methods: Image correspondence proceeds in the frequency domain, after convolving the images with suitable band pass filters like Gabor and hypergeometric filters[18] 22] These methods obtain subpixel disparity without resorting to ad hoc techniques like local interpolation of correlation values [21]. They are less susceptible to bandlimited noise and lighting di#erences between images. However, these algorithms work poorly at depth boundaries and occluded areas [18] and cannot deal with specular reflection satisfactorily. In addition, some algorithms fall into two categories, for example, ....

Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

....also an interesting area to explore. 3 Subpixel feature detection The precise detection of the position of characteristic features (edges, discs, corners, crosses) in video images is used in computer vision, for example in vision system calibration. Shortis, Clarke and Short [30] Tian and Huhns [37], Valkenburg, McIvor and Power [39] present studies of different subpixel detection methods. Bose and Amir [5] compare different fiducials (characteristic marks drawn on objects) for an application in precise registration. Efrat and Gotsman [13] Havelock [17] study the projections of fiducials ....

Q. Tian and M.N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics and Image Processing, 35:220--233, 1986.

.... methods: Image correspondence proceeds in the frequency domain, after convolving the images with suitable band pass filters like Gabor and hypergeometric filters[19] 23] These methods obtain subpixel disparity without resorting to ad hoc techniques like local interpolation of correlation values [22]. They are less susceptible to bandlimited noise and lighting differences between images. However, these algorithms work poorly at depth boundaries and occluded areas [19] and cannot deal with specular reflection satisfactorily. In addition, some algorithms fall into two categories, for example, ....

Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

....registration accuracies when placing overlay masks, mounting integrated circuit packages on PC boards etc. Since the problem arose in industrial applications, it has received some attention both by theoreticians e.g. 1] and by application oriented engineers, e.g. 2] 3] 4] 5] 6] 7] [8]. However the problem was approached mostly via a correlation or template matching type of analysis [5] 8] 9] When dealing with binary digitizations of two level images the approach to subpixel accuracy registration was based upon either centroid computations for the digitized images [2] ....

.... Since the problem arose in industrial applications, it has received some attention both by theoreticians e.g. 1] and by application oriented engineers, e.g. 2] 3] 4] 5] 6] 7] 8] However the problem was approached mostly via a correlation or template matching type of analysis [5] [8], 9] When dealing with binary digitizations of two level images the approach to subpixel accuracy registration was based upon either centroid computations for the digitized images [2] 4] 3] or the theoretically amenable problem of digitized straight edge location [1] This paper is based on ....

Gi Tian and M. N. Huhns. Algorithms for Subpixel Registration. CVGIP, 35(2):220-- 233, 1986.

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Q. Tian, M. N. Huhns, "Algorithms for subpixel registration", Computer Vision, Graphics and Image Processing, 35, pp. 220-233, 1986.

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Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

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Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

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Q. Tian and M. N. Huhns. Algorithms for Subpixel Registration. CVGIP, 35:220--233, 1986.

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Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics, and Image Processing, 35:220--233, 1986.

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Q. Tian and M. N. Huhns. Algorithms for subpixel registration. Computer Vision, Graphics and Image Processing, 35:220--233, 1986.

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Q. Tian and M.N. Huhns, "Algorithms for Subpixel Registration", Computer Vision, Graphics and Image Processing, 35, pp.220--233, 1986

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