Interpolating Cubic Splines

Knott, Gary D.

doi:10.1007/978-1-4612-1320-8

Cited by 120 publications

(84 citation statements)

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“…In the original TPS formulation [1], the bending energy function was defined in 2D. Here we generalize it to higher dimensions defined as α i (i= 1..128): For each of f r and f g , we have (N+129) equations in (N+129) linear can be uniquely determined using matrix operations.…”

Section: Thin Plate Spline Methodsmentioning

confidence: 99%

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Illumination estimation via thin-plate spline interpolation

Shi

Xiong²,

Funt

2011

J. Opt. Soc. Am. A

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Section: Thin Plate Spline Methodsmentioning

confidence: 99%

“…Interpolation is a common problem and there are many wellestablished interpolation methods [1]. The majority of these methods, such as bilinear or bi-cubic interpolation, are based on interpolation over training data sampled on a uniform grid.…”

Section: Introductionmentioning

confidence: 99%

Illumination estimation via thin-plate spline interpolation

Shi

Xiong²,

Funt

2011

J. Opt. Soc. Am. A

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“…For the curve fitting, B-spline [35][36][37][38][39][40][41] curve is used instead of polynomial curve to approximate the pixel data. Polynomial curve fails to approximate complex curve as shown in Figure 2.…”

Section: Proposed Approachmentioning

confidence: 99%

A novel method for straightening curved text-lines in stylistic documents

2014

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Stylistic text can be found on sign boards, street and organizations boards and logos, bulletin boards, announcements, advertisements, dangerous goods plates, warning notices, etc. In stylistic text images, text-lines within an image may have different orientations such as curved in shape or not be parallel to each other. As a result, extraction and subsequent recognition of individual text-lines and words in such images is a difficult task. In this paper, we propose a novel scheme for straightening of curved text-lines using the concept of dilation, flood-fill, robust thinning, and B-spline curve-based fitting. In the proposed scheme, at first, dilation is applied on individual text-lines to cover the area within a certain boundary. Next, thinning is applied to get the path of the text, approximate the path using the B-spline, find the angle between the normal at a point on the curve and the vertical line, and finally visit each point on the text and rotate by their corresponding angles. The proposed methodology is tested on variety of text images containing text-lines in Devanagari, English, and Chinese scripts which is evaluated on the basis of visual perception and the mean square error (MSE) calculation. MSE is calculated by line fitting applied on input and output images. On the basis of evaluation results obtained in our experiments, the proposed method is promising.

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“…To fill the occluded regions, we propose to interpolate between the correctly reconstructed pixels of each scan line using the cubic splines [15] interpolation model. Finally, after getting a dense disparity map from which we get a set of correspondence points, we reconstruct the 3D points of the face [10].…”

Section: Stereo Matching-based Reconstructionmentioning

confidence: 99%

A Framework for Long Distance Face Recognition Using Dense - and Sparse-Stereo Reconstruction

Rara

Elhabian

Ali

et al. 2009

Advances in Visual Computing

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Abstract. This paper introduces a framework for long-distance face recognition using both dense-and sparse-stereo reconstruction. Two methods to determine correspondences of the stereo pair are used in this paper: (a) dense global stereo-matching using maximum-a-posteriori Markov Random Fields (MAP-MRF) algorithms and (b) Active Appearance Model (AAM) fitting of both images of the stereo pair and using the fitted AAM mesh as the sparse correspondences. Experiments are performed regarding the use of different features extracted from these vertices for face recognition. A comparison between the two approaches (a) and (b) are carried out in this paper. The cumulative rank curves (CMC), which are generated using the proposed framework, confirms the feasibility of the proposed work for long distance recognition of human faces.

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Interpolating Cubic Splines

Cited by 120 publications

References 0 publications

Illumination estimation via thin-plate spline interpolation

Illumination estimation via thin-plate spline interpolation

A novel method for straightening curved text-lines in stylistic documents

A Framework for Long Distance Face Recognition Using Dense - and Sparse-Stereo Reconstruction

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