The variational approach to shape from shading

Horn, Berthold K. P.; Brooks, Michael J.

doi:10.1016/0734-189x(85)90010-6

Cited by 111 publications

(200 citation statements)

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“…Another contribution comes from the robust weighting of the averaged surface normals over the immediate neighbourhood. This is an interesting finding, as Horn [6] reported the empirical need for such a weighted averaging process in his early work on SFS. Finally, there is a contribution from the second-derivatives of the surfacenormal.…”

Section: Re-descending Derivativementioning

confidence: 66%

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Needle map recovery using robust regularizers

Worthington

Hancock

1999

Image and Vision Computing

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This article describes how robust error-kernels can be used as smoothness priors in recovering shape-from-shading (SFS). Conventionally, the smoothness error is added to the data-closeness (or brightness-error) as a quadratic regularizer. This leads to over-smoothing of the recovered needle-map or surface, and the loss of important detail provided by surface discontinuities. To solve this problem, we investigate the use of robust regularizers to reduce the smoothening by treating rapid changes in surface orientation as outliers in the calculation of the smoothness error. In particular, we study an existing continuous approximation to the Tukey bi-weight as a robust regularizer, and introduce a novel regularizer of the form log cosh h, which approximates the Huber estimator. The latter regularizer has a sigmoidal derivative and offers a compromise between premature outlier rejection and smoothening. Experiments on synthetic and real-world data reveal that this robust regularizer enhances needle-map recovery, without sacrificing robustness to noise or becoming over-sensitive to numerical instabilities. ᭧

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Section: Re-descending Derivativementioning

confidence: 66%

“…The classical approach to SFS is couched as an energy minimisation process using the apparatus of variational calculus [3,6]. Here the aim is to iteratively recover a needle-map representing local surface orientation by minimising an error-functional.…”

Section: Introductionmentioning

confidence: 99%

Needle map recovery using robust regularizers

Worthington

Hancock

1999

Image and Vision Computing

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“…The classic approaches to shape from shading developed by Ikeuchi and Horn [21], and by Horn and Brooks [15], hinge on the compliance with the image irradiance equation and local surface smoothness. Zheng and Chellappa [55] proposed a gradient consistency constraint that penalises differences between the image intensity gradient and the surface gradient for the recovered surface.…”

Section: Introductionmentioning

confidence: 99%

“…Zheng and Chellappa [55] proposed a gradient consistency constraint that penalises differences between the image intensity gradient and the surface gradient for the recovered surface. Moreover, although shape-from-shading [15] usually relies on the assumption of Lambertian reflectance [25], photometric correction or specularity subtraction may be applied as a preprocessing step to improve the results obtained. For instance Brelstaff and Blake [6] used a simple thresholding strategy to identify specularities on moving curved objects.…”

Section: Introductionmentioning

confidence: 99%

An optimisation approach to the recovery of reflection parameters from a single hyperspectral image

Rahman

Robles-Kelly

2013

Computer Vision and Image Understanding

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In this paper, we present a method to recover the parameters governing the reflection of light from a surface making use of a single hyperspectral image. To do this, we view the image radiance as a combination of specular and diffuse reflection components and present a cost functional which can be used for purposes of iterative least squares optimisation. This optimisation process is quite general in nature and can be applied to a number of reflectance models widely used in the computer vision and graphics communities. We elaborate on the use of these models in our optimisation process and provide a variant of the Beckmann-Kirchhoff model which incorporates the Fresnel reflection term. We show results on synthetic images and illustrate how the recovered photometric parameters can be employed for skin recognition in real world imagery, where our estimated albedo yields a classification rate of 95.09 ± 4.26% as compared to an alternative, whose classification rate is of 90.94 ± 6.12%. We also show quantitative results on the estimation of the index of refraction, where our method delivers an average per-pixel angular error of 0.15 degrees. This is a considerable improvement with respect to an alternative, which yields an error of 9.9 degrees.

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“…In the past, the first two kinds of analyses, the shape recovery and the reflectance recovery, have been intensively studied using the shape from shading method [7,8,9,16] as well as through reflectance analysis research [1,12,13,15,18] . In contrast, there has been little progress on the subject of recovering illumination from the knowledge of the shape and the reflectance of an object surface.…”

Section: Introductionmentioning

confidence: 99%