Second Generation Curvelet Transforms Vs Wavelet transforms and Canny Edge Detector for Edge Detection from WorldView-2 data

Abstract

Edge detection is an important assignment in image processing, as it is used as a primary tool for pattern recognition, image segmentation and scene analysis. Simply put, an edge detector is a high-pass filter that can be applied for extracting the edge points within an image. Edge detection in the spatial domain is accomplished through convolution with a set of directional derivative masks in this domain. On one hand, the popular edge detection spatial operators such as; Roberts, Sobel, Prewitt, and Laplacian are all defined on a 3 by 3 pattern grid, which is efficient and easy to apply. On the other hand, working in the frequency domain has many advantages, starting from introducing an alternative description to the spatial representation and providing more efficient and faster computational schemes with less sensitivity to noise through high filtering, de-noising and compression algorithms. Fourier transforms, wavelet and curvelet transform are among the most widely used frequency-domain edge detection from satellite images. However, the Fourier transform is global and poorly adapted to local singularities. Some of these draw backs are solved by the wavelet transforms especially for singularities detection and computation. In this paper, the relatively new multi-resolution technique, curvelet transform, is assessed and introduced to overcome the wavelet transform limitation in directionality and scaling. In this research paper, the assessment of second generation curvelet transforms as an edge detection tool will be introduced and compared to traditional edge detectors such as wavelet transform and Canny Edge detector. Second generation curvelet transform provides optimally sparse representations of objects, which display smoothness except for discontinuity along the curve with bounded curvature. Preliminary results show the power of curvelet transform over the wavelet transform through the detection of nonvertical oriented edges, with detailed detection of curves and circular boundaries, such as non straight roads and shores. Conclusions and recommendations are given with respect to the suitability; accuracy and efficiency of the curvelet transform method compared to the other traditional methods

Multimodal biometric cryptosystem based on fusion of wavelet and curvelet features in robust security application

“…Edge detection is important in image processing, wavelet decomposes image into a set of functions which are formed by translating and dilating mother wavelet. Curvelet transform provides better edge representation than wavelets as it needs less coefficients (Elhabiby et al, 2012).…”

Fog Removal by Multiple Polynomial Regression Model through Curvelets

“…With the help of synthetic depth map the values of the coefficients α0, α1 and α2 are found out. Finally a hazy image is generated by using the equation (1) and equation (2). Once the values of these parameters are known then the scene radiance can be found out by using the equation given below:…”

“…The model is linear as it is linear in the parameters α0, α1 and α2. This model describes a three dimensional space in D, b 2 …”

“…-(sc(dp(x))) (2) where x = (x, y) is a 2D vector, H(x) is a 3D RGB vector of the color at a pixel(pixel of the hazy image), C(x) is a 3D RGB vector of the color of the light reflected by the scene point at x(pixel of a fog/haze free image). C is known as the scene radiance, t is a map called transmission or transparency of the fog/haze.…”

“…Curvelets represent edges better than wavelets. [2] In the early researches the defogging used the conventional approach of histogram processing to remove the haze [3]. In polarization based methods two images of the same scene are taken into consideration [4,5] .The images taken are with different degrees of polarization.…”