Image sampling, reconstruction, and the effect of sample-scene phasing

Park, Stephen K.; Schowengerdt, Robert A.

doi:10.1364/ao.21.003142

Cited by 64 publications

(45 citation statements)

References 12 publications

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“…This applies to dimensions and to interpolating as well as noninterpolating basis functions [21]- [23]. In the restricting conditions where , for bandlimited functions and when the basis function is interpolating, this error kernel reduces to the kernel proposed in [24].…”

Section: A Error Kernelmentioning

confidence: 99%

Interpolation revisited [medical images application]

Thévenaz

Blu

Unser

2000

IEEE Trans. Med. Imaging

721

126

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Abstract-Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order can be expressed as the convolution of a B-spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. We discuss implementation and performance issues, and we provide experimental evidence to support our claims.Index Terms-Approximation constant, approximation order, B-splines, Fourier error kernel, maximal order and minimal support (Moms), piecewise-polynomials.

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Section: A Error Kernelmentioning

confidence: 99%

Interpolation revisited [medical images application]

Thévenaz

Blu

Unser

2000

IEEE Trans. Med. Imaging

721

126

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“…Park and Schowengerdt conducted a study on the impact of a sensor's PSF on the scan imaging of an object's edge, which was characterized by both the system and random errors [19]. In the research on the impact of a sensor's PSF on object proportion extraction, the mean error of the proportion estimation has been well discussed [9,12], but those works lacked an analysis of the variance of the object proportion estimation.…”

Section: Discussionmentioning

confidence: 99%

Simulation of the Impact of a Sensor’s PSF on Mixed Pixel Decomposition: 1. Nonuniformity Effect

Liu

Hou

2016

Remote Sensing

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Abstract:The nonuniformity of the spatial response to surface radiation is a fundamental characteristic of all airborne and spaceborne sensors that inevitably introduces uncertainty into the estimation of object proportions by the spectral unmixing of mixed pixels. Simulated data of the surface radiation distribution and a TM (thematic mapper) response matrix were developed and utilized to imitate the generation of mixed pixels and the extraction of the object proportion via a Monte Carlo simulation, and then, the nonuniformity effect of a sensor's PSF (point spread function) was explored. The following conclusions were drawn: (1) given a nonuniform spatial response of a sensor to a surface scene with a constant object proportion and various object distribution patterns, the mixed pixel DN (digital number) of a remotely-sensed image becomes a random variable, which causes a PSF nonuniform effect on the object proportion extraction; (2) for the estimated object proportion, the corresponding true object proportion appears with a random variation; its upper and lower bounds take on an asymmetrical spindle shape; and models of these bound curves at any probability level were established; (3) there exists a negative linear relationship between the bias of the spectral unmixing and the estimated proportion; the bias is zero at an estimated proportion of 50%, and when the estimated proportions are approximately 100% and 0%, the object proportion is overestimated by 0.78% and underestimated by 0.78%, respectively; (4) the relationship between the standard deviation of the spectral unmixing and the estimated proportion follows a symmetrical polynomial function opening downward; the standard deviation reaches a maximum of 4.4% at the estimated proportion of 50%, and when the estimated proportion is approximately 100% or 0%, the standard deviation is a minimum, 1.05%. The above findings contribute to a comprehensive understanding of the PSF nonuniformity effect, have the potential to compensate for the bias of proportion estimation and present its confidence interval at any probability level.

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“…Our approach could also be used for super-resolution [16,3,5,4], but here we use individual not multiple images, and we aim to predict what the original camera would return if shifted, not an enhanced image. An illuminating 1D analytic study complementary to our 2D empirical one is [15]. For a unified "information optimizing" approach to sampling and reconstruction, see [7].…”

Section: Introductionmentioning

confidence: 99%

Empirical filter estimation for subpixel interpolation and matching

Triggs

Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001

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We study the low-level problem of predicting pixel intensities after subpixel image translations. This is a basic subroutine for image warping and super-resolution, and it has a critical influence on the accuracy of subpixel matching by image correlation. Rather than using traditional frequency-space filtering theory or ad hoc interpolators such as splines, we take an empirical approach, finding optimal subpixel interpolation filters by direct numerical optimization over a large set of training examples. The training set is generated by subsampling larger images at different translations, using subsamplers that mimic the spatial response functions of real pixels. We argue that this gives realistic results, and design filters of various different parametric forms under traditional and robust prediction error metrics. We systematically study the performance of the resulting filters, paying particular attention to the influence of the underlying image sampling regime and the effects of aliasing ("jaggies"). We summarize the results and give practical advice for obtaining subpixel accuracy.

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Image sampling, reconstruction, and the effect of sample-scene phasing

Cited by 64 publications

References 12 publications

Interpolation revisited [medical images application]

Interpolation revisited [medical images application]

Simulation of the Impact of a Sensor’s PSF on Mixed Pixel Decomposition: 1. Nonuniformity Effect

Empirical filter estimation for subpixel interpolation and matching

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