Bézier and Splines in Image Processing and Machine Vision by Sambhunath Biswas

By Sambhunath Biswas

Digital picture processing and computing device imaginative and prescient have grown significantly over the past few a long time. Of a few of the options, built thus far splines play a favorable and critical position in lots of of them. robust mathematical concept and straightforwardness of implementations is without doubt one of the keys in their good fortune in lots of study matters.

This publication bargains with quite a few photograph processing and laptop imaginative and prescient difficulties successfully with splines and includes:

• the importance of Bernstein Polynomial in splines

• effectiveness of Hilbert test for electronic images

• targeted insurance of Beta-splines, that are really new, for attainable destiny purposes

• discrete smoothing splines and their power in software

• snakes and energetic contour versions and their uses

• the importance of worldwide optimum contours and surfaces

Finally the publication covers wavelet splines that are effective and potent in several snapshot purposes.

Dr Biswas is a procedure analyst on the Indian Statistical Institute, Calcutta the place he teaches computer imaginative and prescient in M Tech (Computer Science). His learn pursuits comprise snapshot processing, desktop imaginative and prescient, special effects, trend popularity, neural networks and wavelet image-data analysis.

Professor Lovell is a examine chief in nationwide ICT Australia and examine Director of the clever Real-Time Imaging and Sensing examine team on the collage of Queensland. His study pursuits are at the moment focussed on optimum picture segmentation, real-time video research and face popularity.

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Extra resources for Bézier and Splines in Image Processing and Machine Vision

Example text

The graylevels in F01 (x, y) lie in the interval 42 2 Image Segmentation [0, s] and in F02 (x, y), it is limited to (s, L − 1]. From the standpoint of object/background thresholding, F01 (x, y) can be viewed as the object while F02 (x, y) is the background, without loss of generality. To check the feasibility of global approximation of the subimages so obtained, we approximate, first of all, F01 (x, y) by a polynomial of order p ≤ q (q is a predefined upper limit on the order of polynomials) satisfying a criterion C.

8 Concluding Remarks 31 A reconstructed image normally deviates from its original version if the reconstruction is not perfect. Therefore, to observe the deviation of the image quality, one can compute different objective measures. One such is to provide the error in area and shape compactness between the original and reconstructed images. Kulpa [96] provided a good way to compute the area and perimeter. Since the key pixels are always on the contour and the reconstructed arcs between them are restricted by the respective B´ezier characteristic triangles, the maximum error for an arc is the area of its pair of B´ezier characteristic triangles.

15. Butterfly input. 17(b) and (c), respectively. Positions of key pixels in both the input and output remain unaltered. 4 shows the effectiveness of the cleaning operations on the generated points for the butterfly image. 16(b) shows such an intermediate state for Method 1 before its final reconstructed output. Here, d denotes a pixel to be deleted and X corresponds to the position where a pixel is to be inserted to keep connectivity. 7 Approximation Capability and Effectiveness 3 I 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 2 2 2 3 3 3 2 2 2 2 2 3 3 2 2 3 2 2 2 2 2 2 2 2 2 2 3 29 2 2 2 2 2 I I 2 2 2 2 2 2 2 2 2 3 3 3 3 3 2 2 2 I 2 2 3 2 2 3 2 2 2 2 2 2 I 2 2 2 3 2 2 3 3 3 2 2 2 2 3 2 2 2 I 3 2 2 3 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 I 2 2 2 2 2 d 2 (a) 3 I 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 2 2 d 2 2 d 3 x d d x 3 2 2 2 2 3 3 2 3 2 2 2 3 2 2 2 2 2 2 2 2 d d 2 3 3 2 2 2 x 2 2 2 I I 2 2 2 2 2 d d 2 2 2 x d 3 x d 3 x d 2 2 2 3 d d I 3 x d 2 d 2 3 2 3 3 3 d 3 d 3 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 I 2 2 2 2 2 2 3 3 2 d 2 I 3 2 2 d I 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 (b) 3 I 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2 3 3 2 3 3 2 2 2 3 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 I I 2 2 2 2 2 2 2 2 2 2 3 3 2 3 3 2 3 2 2 2 3 2 I 2 2 2 2 2 3 2 2 2 2 2 I 2 2 2 2 2 3 2 2 3 3 3 2 2 2 2 2 2 2 2 3 3 I 3 2 2 2 I 2 2 3 2 2 2 2 2 (c) Fig.

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