Subpixel Alignment of MRI Data Under Cartesian and Log-Polar Sampling

Balcı, Murat Erhan; Alnasser, Mais; Foroosh, Hassan

doi:10.1109/icpr.2006.1088

Cited by 10 publications

(12 citation statements)

References 7 publications

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“…By multiplying the complexities and the probabilities in table (I) and summing them up, the average performance of the worst case for evaluating d N −k inew is found to be O(log(L)). By following a similar analysis and examining (22), one can find that the complexity for evaluating A N −k inew is O(log(L)) as well. Also, by examining (25) one can find that complexity for evaluating d N −k inew after a non-integer shift is O(log(L + 2 h )), where h is the number of levels added to achieve the shift.…”

Section: Complexity Analysismentioning

confidence: 98%

“…In this section we explain in further detail the complexity of evaluating d N −k inew using equation (13), A N −k inew using equation (22) and d N −k inew using equation (25). By examining (13), it is easy to verify that the complexity of evaluating d N −k inew can be expressed by the difference of the bounds of the two sums in the equation, that is O(i 3 − i 1 ).…”

Section: Complexity Analysismentioning

confidence: 99%

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Phase-Shifting for Nonseparable 2-D Haar Wavelets

Alnasser

Foroosh

2008

IEEE Trans. on Image Process.

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In this paper, we present a novel and efficient solution to phase-shifting 2-D nonseparable Haar wavelet coefficients. While other methods either modify existing wavelets or introduce new ones to handle the lack of shift-invariance, we derive the explicit relationships between the coefficients of the shifted signal and those of the unshifted one. We then establish their computational complexity, and compare and demonstrate the superior performance of the proposed approach against classical interpolation tools in terms of accumulation of errors under successive shifting.

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Section: Complexity Analysismentioning

confidence: 98%

Section: Complexity Analysismentioning

confidence: 99%

Phase-Shifting for Nonseparable 2-D Haar Wavelets

Alnasser

Foroosh

2008

IEEE Trans. on Image Process.

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“…In the scope of this paper, we assume that the registration between images are known a priori or has been estimated. Translational shifts can be estimated using one of the methods by [13], [15]- [17], [38], [41], [42], [77], [101]. Even though the equations derived in Section III are for subpixel shifts, we apply the proposed SRIR method to the intersection area of any given shift, which may include an integer part, as well.…”

Section: B Proposed Methodsmentioning

confidence: 99%

Super-Resolution of Wavelet-Encoded Images

Aydin,

Foroosh

2017

Preprint

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Multiview super-resolution image reconstruction (SRIR) is often cast as a resampling problem by merging non-redundant data from multiple low-resolution (LR) images on a finer high-resolution (HR) grid, while inverting the effect of the camera point spread function (PSF). One main problem with multiview methods is that resampling from nonuniform samples (provided by LR images) and the inversion of the PSF are highly nonlinear and ill-posed problems. Non-linearity and ill-posedness are typically overcome by linearization and regularization, often through an iterative optimization process, which essentially trade off the very same information (i.e. high frequency) that we want to recover. We propose a novel point of view for multiview SRIR: Unlike existing multiview methods that reconstruct the entire spectrum of the HR image from the multiple given LR images, we derive explicit expressions that show how the high-frequency spectra of the unknown HR image are related to the spectra of the LR images. Therefore, by taking any of the LR images as the reference to represent the low-frequency spectra of the HR image, one can reconstruct the super-resolution image by focusing only on the reconstruction of the high-frequency spectra. This is very much like single-image methods, which extrapolate the spectrum of one image, except that we rely on information provided by all other views, rather than by prior constraints as in single-image methods (which may not be an accurate source of information). This is made possible by deriving explicit closed-form expressions that define how the local high frequency information that we aim to recover for the reference high resolution image is related to the local low frequency information in the sequence of views. The locality of these expressions due to modeling using wavelets reduces the problem to an exact and linear set of equations that are well-posed and solved algebraically without requiring regularization or interpolation. Results and comparisons with recently published state-of-the-art methods show the superiority of the proposed solution.

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“…The problem is often exacerbated by issues such as image quality, noise, and drastic appearance changes caused by viewpoint variations. Although, preprocessing steps such as image enhancement [32]- [34], [46], [69], [93], [107]- [109], [111]- [117], [120], [121], [123], and registration [6], [18], [19], [21], [23]- [26], [29], [30], [56]- [61], [63], [64], [110], [118], [119] may help in tackling some of the challenges, viewpoint variations remain by and large challenging.…”

Section: Introductionmentioning

confidence: 99%

View-invariant object recognition using homography constraints

Lotfian

Foroosh

2017

2017 IEEE International Conference on Image Processing (ICIP)

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Change in viewpoint is one of the major factors for variation in object appearance across different images. Thus, view-invariant object recognition is a challenging and important image understanding task. In this paper, we propose a method that can match objects in images taken under different viewpoints. Unlike most methods in the literature, no restriction on camera orientations or internal camera parameters are imposed and no prior knowledge of 3D structure of the object is required. We prove that when two cameras take pictures of the same object from two different viewing angels, the relationship between every quadruple of points reduces to the special case of homography with two equal eigenvalues. Based on this property, we formulate the problem as an error function that indicates how likely two sets of 2D points are projections of the same set of 3D points under two different cameras. Comprehensive set of experiments were conducted to prove the robustness of the method to noise, and evaluate its performance on real-world applications, such as face and object recognition.

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Subpixel Alignment of MRI Data Under Cartesian and Log-Polar Sampling

Abstract: Magnetic resonance imaging (MRI) allows numerous Fourier domain sampling schemes such as Cartesian and non-Cartesian trajectories (e.g. Polar, circular, and spherical

Cited by 10 publications

References 7 publications

Phase-Shifting for Nonseparable 2-D Haar Wavelets

Phase-Shifting for Nonseparable 2-D Haar Wavelets

Super-Resolution of Wavelet-Encoded Images

View-invariant object recognition using homography constraints

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