Direct analytical methods for solving Poisson equations in computer vision problems

Simchony, T.; Chellappa, Rama; Shao, Min

doi:10.1109/34.55103

Cited by 224 publications

(169 citation statements)

References 12 publications

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“…We can simply use a Fourier transform on the entire image to re-integrate, a very fast method, using homogeneous Neumann boundary conditions. As well, in order to combine the Ambient and Flash gradients such that integrability is preserved, we project the combined set of edges onto an integrable convex set in the Fourier domain, before reintegrating via inverse Fourier transform [21,22]. The reintegrated ambient image for our example image is shown in Fig.…”

Section: Shadow-free Ambient Image Recoverymentioning

confidence: 99%

Removing Shadows using Flash/Noflash Image Edges

Drew

Finlayson

2006

2006 IEEE International Conference on Multimedia and Expo

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Flash/noflash pairs have been used for noise-reduction in ambient-light images. But not explicitly studied is the problem of shadows in the ambient images. While shadows are lessened in a flash image, other problems arise, and other shadows are produced. It is known that we can in fact produce a flash-only (no ambient) image by subtracting the two images, but the result is not as pleasant as the ambient image, because of several artifacts due to the flash. Here, we use the pure-flash image to detect the ambient shadows. We argue that first going to a "spectrally sharpened" color space, and then focusing on the difference in a log domain of the flash image minus the ambient image, gives a very simple feature space consisting of two components -one in an illuminant-change 3-vector direction, and one along the gray axis. This space provides excellent separation of the shadow and nonshadow areas. Inserting edges from the flash image within the ambient-shadow region into the ambient image edge map and inverting Poisson's equation fills in the shadow. In this way, we arrive at an image with the advantages of the ambient-only image -warmth, no flash effects such as disturbing illumination dropoff with distance, pixel saturation etc. -but no shadows.

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Section: Shadow-free Ambient Image Recoverymentioning

confidence: 99%

Removing Shadows using Flash/Noflash Image Edges

Drew

Finlayson

2006

2006 IEEE International Conference on Multimedia and Expo

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“…To calculate height maps, the filtered gradients were integrated using a multigrid solver 13 for the Poisson equation 14 that minimizes integration inconsistency errors [ Fig. 2(g)].…”

Section: Pse Algorithmmentioning

confidence: 99%

Photometric stereo endoscopy

et al. 2013

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Abstract. While color video endoscopy has enabled wide-field examination of the gastrointestinal tract, it often misses or incorrectly classifies lesions. Many of these missed lesions exhibit characteristic three-dimensional surface topographies. An endoscopic system that adds topographical measurements to conventional color imagery could therefore increase lesion detection and improve classification accuracy. We introduce photometric stereo endoscopy (PSE), a technique which allows high spatial frequency components of surface topography to be acquired simultaneously with conventional two-dimensional color imagery. We implement this technique in an endoscopic form factor and demonstrate that it can acquire the topography of small features with complex geometries and heterogeneous optical properties. PSE imaging of ex vivo human gastrointestinal tissue shows that surface topography measurements enable differentiation of abnormal shapes from surrounding normal tissue. Together, these results confirm that the topographical measurements can be obtained with relatively simple hardware in an endoscopic form factor, and suggest the potential of PSE to improve lesion detection and classification in gastrointestinal imaging. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…However, this technique may prove to be inefficient-without further research-for dense data problems with nonuniform weighting on the data constraints, such as the optical flow problem, since the size of the associated (dense) capacitance matrix is too large. Although this problem may be circumvented by incorporating the capacitance matrix technique as part of an iterative scheme [15], however, it was pointed out in [16] that this semidirect numerical scheme only converges when the regularization parameter is very large. In this paper, we will introduce a physically based adaptive preconditioning technique which when used in conjunction with the conjugate gradient algorithm, outperforms-in computational efficiency-previously proposed preconditioning methods for some early vision problems in literature [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Physically based adaptive preconditioning for early vision

Lai

Vemuri

1997

IEEE Trans. Pattern Anal. Machine Intell.

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Abstract-Several problems in early vision have been formulated in the past in a regularization framework. These problems, when discretized, lead to large sparse linear systems. In this paper, we present a novel physically based adaptive preconditioning technique which can be used in conjunction with a conjugate gradient algorithm to dramatically improve the speed of convergence for solving the aforementioned linear systems. A preconditioner, based on the membrane spline, or the thin plate spline, or a convex combination of the two, is termed a physically based preconditioner for obvious reasons. The adaptation of the preconditioner to an early vision problem is achieved via the explicit use of the spectral characteristics of the regularization filter in conjunction with the data. This spectral function is used to modulate the frequency characteristics of a chosen wavelet basis, and these modulated values are then used in the construction of our preconditioner. We present the preconditioner construction for three different early vision problems namely, the surface reconstruction, the shape from shading, and the optical flow computation problems. Performance of the preconditioning scheme is demonstrated via experiments on synthetic and real data sets. We note that our preconditioner outperforms other methods of preconditioning for these early vision problems, described in computer vision literature.Index Terms-Early vision, computational vision, adaptive preconditioning, wavelet transform, regularization, surface reconstruction, shape from shading, optic flow computation.

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Direct analytical methods for solving Poisson equations in computer vision problems

Cited by 224 publications

References 12 publications

Removing Shadows using Flash/Noflash Image Edges

Removing Shadows using Flash/Noflash Image Edges

Photometric stereo endoscopy

Physically based adaptive preconditioning for early vision

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