Subpixel estimation of shifts directly in the Fourier domain

Balcı, Murat Erhan; Foroosh, Hassan

doi:10.1109/tip.2006.873457

Cited by 73 publications

(50 citation statements)

References 33 publications

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“…[36,9,1] addressed the problem by phase correlation. [36] proposed a method based on linear weighting the main phase correlation peak and the difference between its two neighboring sidepeaks.…”

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How Accurate Can Block Matches Be in Stereo Vision?

Sabater¹,

Morel²,

Almansa³

2011

SIAM J. Imaging Sci.

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Abstract. This article explores the sub-pixel accuracy attainable for the disparity computed from a rectified stereo pair of images with small baseline. In this framework we consider translations as the local deformation model between patches in the images. A mathematical study shows first how discrete block-matching can be performed with arbitrary precision under Shannon-Whittaker conditions. This study leads to the specification of a block-matching algorithm which is able to refine disparities with sub-pixel accuracy. Moreover, a formula for the variance of the disparity error caused by the noise is introduced and proved. Several simulated and real experiments show a decent agreement between this theoretical error variance and the observed RMSE in stereo pairs with good SNR and low baseline. A practical consequence is that under realistic sampling and noise conditions in optical imaging, the disparity map in stereo-rectified images can be computed for the majority of pixels (but only for those pixels with meaningful matches) with a 1/20 pixel precision.Key words. Block-matching, sub-pixel accuracy, noise error estimate.1. Introduction. Stereo algorithms aim at reconstructing a 3D model from two or more images of the same scene acquired from different angles. Assuming for a sake of simplicity that the cameras are calibrated, and that the image pair has been stereo-rectified, our work will focus on the matching process. The matching of stereo images has been studied in depth for decades. We refer to [43] and [6] for a complete comparison of different methods.Generally stereo matching methods are divided in two classes, the local algorithms and the global ones. Given two images of the same scene, the local methods compare a small block of pixels surrounding each pixel in the first image to the candidate blocks on the epipolar line in the second image. The blocks are usually compared by the normalized cross correlation (NCC) or the sum of squared differences (SSD). Having a minimum of the SSD does not guarantee at all that the match is correct. In general, only a significant proportion of the image can be reliably matched (about 40 to 80%). Block-matching methods can indeed produce wrong disparities near the intensity discontinuities in the images. This "fattening effect" is a classic problem in block-matching methods. It occurs when a salient image feature (typically an edge) lies within the comparison window ϕ but away from its center. This can produce a large error near points at which the disparity ε has a jump. Several papers have attempted with some success to alleviate this problem by using adaptive shape windows [21,48,22,18], adaptive support-weight windows [53], a barycentric correction [12], or by feature matching methods [44]. If the images of the stereo pair u 1 and u 2 have little aliasing, [12] showed that the recovered disparity map obtained by minimizing a continuous quadratic distance between u 1 and u 2 has therefore two main error terms: the fattening error, and the error due to noise. There ar...

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“…[9] proposed high order statistics in order to attain subpixel accuracy when registering in noisy images with a low SNR. [1] showed that the continuous and discrete phase difference is a 2D sawtooth signal. They count the number of cycles of the phase difference and give the noninteger fraction of the last cycle as the subpixel shift.…”

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confidence: 99%

How Accurate Can Block Matches Be in Stereo Vision?

Sabater¹,

Morel²,

Almansa³

2011

SIAM J. Imaging Sci.

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“…The FTMA method is a well-established technique in image analysis used in, for example, superresolution [16][17][18]. Assuming, for simplicity, that we have two images of an object, represented by f 1 (x 1 ,y 1 ) and f 2 (x 2 ,y 2 ), where the x and y coordinates specify the object's center of mass in the given image.…”

Section: Fourier Transform Motion Analysismentioning

confidence: 99%

Motion analysis of optically trapped particles and cells using 2D Fourier analysis

et al. 2012

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Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end-and side-view imaging, the stiffness of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination of diffusion coefficients and the trapping forces.

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“…POC or phase correlation is used to estimate the shift values and the similarity between signals [6]- [10]. The continuous expression of POC was first introduced as PHAT [5], and the POC in terms of FFT was proposed by Kuglin and Hines in 1975 [6].…”

Section: Introductionmentioning

confidence: 99%

Multiple-peak model fitting function for DCT sign phase correlation with non-integer shift precision

Ito

Kiya

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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We propose two fitting functions for shift estimation using discrete cosine transform sign phase correlation (DCT-SPC) with non-integer accuracy. The DCT-SPC can be used in order to estimate the shift values and the similarity between two signals. However, the estimated shift values are limited to integer numbers. The proposed fitting functions enable the DCT-SPC to estimate the non-integer shift values using only the sign of the DCT coefficients. The multiple-peak model in the proposed fitting functions provides more accurate values than other models. Simulations are presented to demonstrate the effectiveness of the proposed fitting functions.

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Subpixel estimation of shifts directly in the Fourier domain

Cited by 73 publications

References 33 publications

How Accurate Can Block Matches Be in Stereo Vision?

How Accurate Can Block Matches Be in Stereo Vision?

Motion analysis of optically trapped particles and cells using 2D Fourier analysis

Multiple-peak model fitting function for DCT sign phase correlation with non-integer shift precision

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