Chapter-VI 6.1 INTRODUCTION This chapter provides necessary background for edge detection which is a sub process of image segmentation. Image segmentation is the process of dividing the image into regions or segments which are dissimilar in certain aspects or features such as colour, texture or gray level. Edge detection is an important task in image processing and it is a type of image segmentation technique where edges are detected in an image. Edges are introduced as a set of connected points lying on the boundary between two regions. The edges represent object boundaries and therefore can be used in image segmentation to subdivide an image into its basic regions or objects. The techniques discussed in this chapter provide a general application oriented framework in which both spatial and frequency domains are analyzed to achieve proper edge detection. Fundamentally, an edge is a local concept whereas a region boundary is a more global idea due to its definition. A reasonable definition of edge requires the ability to measure gray-level transitions in a meaningful way. Edge pixels are pixels at which the intensity of an image function varies abruptly and edges are a set of connected edge pixels. Edge detectors are local image processing methods designed to detect edges. In a function, singularities can be characterized easily as discontinuities where the gradient approaches infinity. However, image data is discrete, so edges in an image are often defined as the local maxima of the gradient [Gonzalez & Woods, 2008]. 6.2 GOAL OF EDGE DETECTION Edges produce a line drawing from an image of that scene. Some important features that can be extracted from the edges of an image are lines, curves and corners. These features are used by higher level computer vision algorithms. 127 6.2.1 Causes of intensity changes in images The various factors that contribute to intensity level changes are Geometric events Object boundary (discontinuity in depth and/or surface color and texture) Surface boundary (discontinuity in surface orientation and/or surface color and texture) Non-geometric events 6.3 Specularity (direct reﬂection of light, such as a mirror) Shadows (from other objects or from the same object) Inter-reflections between objects MODELS OF EDGES There are several ways to model edges and the number of approaches used for edge detection are discussed and these edge models are classified based on their intensity profiles. (a) (b) Fig. 6.1. (a) Model of an ideal edge (b) model of a ramp edge 128 Figure 6.1. (a) shows step edge involving a transition between two intensity levels occuring ideally over the distance of 1 pixel.Step edges occur in images generated by a computer for use in areas such as solid modelling and animation.Figure 6.1. (b) shows a model of intensity of ramp profile where the slope of the ramp is inversely proportional to the degree of blurring in the edge. In practice, digital images have edges that are blurred and noisy,with the degree of blurring detemined principally by the electronic components of the imaging system [Gonzalez & Woods, 2008]. 6.4 OVERVIEW OF EDGE DETECTION Edge is a boundary between two homogeneous regions. The gray level properties of the two regions on either side of an edge are distinct and exhibit some local uniformity or homogeneity between them. Typical analysis and detection of edges can be done using derivatives with their magnitude and direction. • Magnitude of the derivative: measure of the strength/contrast of the edge • Direction of the derivative vector: edge orientation An edge is typically extracted by computing the derivative of an image intensity function. Derivatives of digital function are defined in terms of differences. There are various ways to approximate these differences: first order and second order derivative. Fig. 6.2 Image of variable intensity and their horizontal intensity profile with its first and second order derivative. 129 Figure 6.2 shows an image of variable intensity,details near the edge showing the horizontal intensity profile with its first and second order derivatives. 6.4.1 First order derivative The approximation of the first order derivative at a point dimensional function Taylor series about of one- is obtained by expanding the function and letting into and the digital difference can be drawn considering only the linear terms. The ﬁrst order derivative of the function be expressed as or as , can and it is the slope of the tangent line to the function at the point . Computing the first order derivative: Finite difference in 1D function is given by Computing the first order derivative: Finite difference in 2D function is given by When computing the first order derivative at a location , the value of the function at that point is subtracted from the next point. 6.4.2 Second order derivative The second derivative of a function is the derivative of the derivative of that function. The first derivative of the function decides whether the function is increasing or decreasing similarly second order derivative decides whether the function is increasing or decreasing. Computing the second order derivative: Finite difference of 1D function is given by (6.3) Computing the second order derivative: Finite difference of 2D function along and directions are given by 130 (6.4) (6.5) 6.4.3 Analysis of first and second order derivatives First order derivative produces thicker edges whereas second order derivative has a stronger response to fine details, thin lines, isolated points, noise and produces double edge response. In addition second order derivative provides zero crossing (transition from positive to negative and vice-versa) and is considered as a good edge detector. There are two additional properties of a second order derivatives around an edge • It produces two values for every edge in an image • Its zero crossing can be used for locating the centers of thick edges. • It is more sensitive to noise. Computation of second order derivative requires both previous and successive points of the function and is capable of detecting discontinuities such as points, lines and edges. The segmentation of an image along the discontinuities is achieved by running a mask through an image. The generalized spatial domain is given in Table 6.1. Table 6.1. Mask. W1 W2 W3 W4 W5 W6 W7 W8 W9 131 mask in The response of the mask is given by (6.6) ∑ ‘ ’ is the intensity of the pixel whose spatial location corresponds to the location of the coefficient in the mask. 6.5 TECHNIQUES OF EDGE DETECTION Edges characterize object boundaries and are therefore useful for segmentation, registration and object identification in image analysis. The two different techniques are categorized as (i) Spatial domain techniques (ii) Transform domain techniques Each of these two techniques are covered in detail in the two subsections: 6.5.1 Spatial Domain Techniques of Edge Detection This section focuses on spatial domain techniques of edge detection where the magnitude of the gradient determines the edges. Due to wealth of information associated with edges, edge detection is an important task for many applications related to computer vision and pattern recognition. The features of edge detection are: Edge strength and Edge orientation. Edge strength determines the magnitude of the edge pixel and edge orientation provides the angle of the gradient. The magnitude of the gradient is zero in uniform regions of an image and has a considerable value based on intensity level variations. The edge detectors in spatial domain are categorized into gradient based which determines edges based on first order derivate and Laplacian based which locates edges based on second order derivate. The gradient is defined as a two dimensional column vector and the magnitude of the gradient vector is referred to as gradient. The strength of the response of a derivative operator is proportional to the degree of discontinuity of an image at the point at which the operator is applied. Thus, image differentiation enhances edges and other discontinuities such as noise 132 and deemphasizes areas with slowly varying gray-level values. It is observed that the first- and second-order derivatives have the capability to encounter a noise, a point, a line, and then the edge of an object. For an image the magnitude of the gradient is given by [ ] (6.7) (6.8) [( ) ( ) ] (6.9) by approximating the squares and square root by absolute values, mag( | |. The direction of the gradient vector is given by direction of an edge at | | * +. The is perpendicular to the direction of the gradient vector at the point. The first order derivatives produce thick edges and enhance prominent details. The edges are obtained by applying appropriate filter mask for an image and is given by [ The center point ] denotes and indicates so on. The gradient operators are represented by masks gradient of an image and and , which measure in two orthogonal directions. The bidirectional gradients of an image are represented by inner products of an image and masks and 6.5.1.1 Roberts Operator This operator was one of the first and foremost edge detectors and was proposed by Roberts. As a differential operator the idea behind Roberts cross operator is to approximate the gradient of an image through discrete differentiation which is obtained by computing the sum of the squares of the differences between 133 diagonally adjacent pixels. To perform edge detection through the Roberts operator, convolution of the original image with the following two kernels is done: * + & * + 6.5.1.2 Sobel Operator At each point in an image, the result of the Sobel operator is either the corresponding gradient vector or the norm of this vector. The Sobel operator is based on convolving the image with an integer valued filter in horizontal, vertical directions and is inexpensive in terms of computations. This operator performs a 2D spatial gradient measurement on an image and so emphasizes regions of high spatial frequency that correspond to edges. Typically it is used to find the approximate absolute gradient magnitude at each point in an input gray scale image. The magnitude of the Sobel gradient operator is given by √ . [ ] [ & ] The magnitude is represented by [ ] [ By approximation ] | |+| | (6.10) (6.11) 6.5.1.3 Prewitt Operator The Prewitt operator is based on convolving the image with a small integer valued filter in horizontal and vertical directions. Thus, the gradient approximation which it produces is relatively crude, in particular for high frequency variations in the image. 134 The magnitude of the Prewitt gradient operator is given by √ [ where [ ] ] [ & [ ] ] (6.12) 6.5.1.4 Canny Operator The drawback of the above methods is that, a fixed operator cannot be used to obtain optimal result. A computational approach was developed and an optimal detector can be approximated by the first order derivative of a Gaussian [Canny, 1986]. His analysis is based on step-edges corrupted by additive Gaussian noise and the image is smoothened by Gaussian convolution. Canny has proved that the ﬁrst order derivative of the Gaussian closely approximates the operator that optimizes the product of signal-to-noise ratio and localization. This edge detection technique produces edges from two aspects – edge gradient direction and strength, with good SNR and edge localization performance [Jun Li & Sheng Ding, 2011]. Thus the algorithm is computed by and using Gaussian function (6.13) (6.14) is the derivate of with respect to : is the derivate of with respect to : The magnitude of the gradient is computed by √ which includes non-maxima suppression and hysteresis thresholding. Due to multiple responses, edge magnitude may contain wide ridges around the local 135 maxima and it removes non-maxima pixels preserving the connectivity of the contours through non-maxima suppression. It combines both the derivative and smoothing properties through Gaussian function in an optimal way to obtain good edges. Hysteresis thresholding receives non-maxima suppression output and identifies weak, strong and moderate pixels based on thresholding. The performance of the Canny algorithm relies on parameters like standard deviation for the Gaussian filter, and its threshold values. This Canny algorithm uses an optimal edge detector based on a set of criteria, which includes finding the most edges by minimizing the error rate, marking edges as closely as possible to the actual edges to maximize localization, and marking edges only once when a single edge exists for minimal response. According to Canny, the optimal filter that meets all the three above criteria above can be efficiently approximated using the first derivative of a Gaussian function. 1) The first stage involves smoothing the image by convolving with a Gaussian filter. 2) This is followed by finding the gradient of the image by feeding the smoothened image through a convolution operation with the derivative of the Gaussian in both the vertical and horizontal directions. Both the Gaussian mask and its derivative are separable, allowing the 2-D convolution operation to be simplified. 3) The non-maximal suppression stage finds the local maxima in the direction of the gradient, and suppresses all others, minimizing false edges. The local maxima are found by comparing the pixel with its neighbours along the direction of the gradient. This helps to maintain the single pixel thin edges before the final thresholding stage [Shirvakshan & Chandrasekar, 2012]. 4) Instead of using a single static threshold value for the entire image, the Canny algorithm introduced hysteresis thresholding, which has some adaptively to the local content of the image. There are two threshold levels, where . Pixel values above high and , low value are immediately classified as edges. By tracing the edge contour, neighboring pixels with gradient magnitude values less than can still be marked as edges as long as they are above . This process alleviates problems associated with edge discontinuities by identifying 136 strong edges, and preserving the relevant weak edges, in addition to maintaining some level of noise suppression. While the results are desirable, the hysteresis stage slows the overall algorithm down considerably. 6.5.1.5 Laplacian Operator The Laplacian method searches for zero crossings in the second derivative of the image to find edges. An edge has the one-dimensional shape of a ramp and calculating the derivative of an image can highlight its location [Raman Maini & Himanshu Aggarwal, 2010]. The Laplacian based edge detection for an image is based on second order derivatives and is given by (6.15) The second order derivative is more aggressive than first order derivative in enhancing sharp changes and has a stronger response to fine details. This operator enhances fine details and is unacceptably sensitive to noise; the magnitude of the Laplacian produces double edges but fails to detect edge direction. Edges are formed from pixels with derivative values that exceed a preset threshold. The strength of the response of a derivative operator is proportional to the degree of discontinuity of an image at the point at which the operator is applied. Thus, image differentiation enhances edges and other discontinuities such as noise and deemphasizes areas with slowly varying gray-level values. 6.5.1.6 Merits and Demerits of classical operators In summary, comparing the responses between first and second-order derivatives, the following conclusions are arrived at (1) First-order derivatives generally produce thicker edges in an image and have a stronger response to a graylevel step. (2) Second-order derivatives have a stronger response to fine detail, such as thin lines, isolated points and produce double response at step changes in gray level. In most applications, the second order derivative is better suited than the first order derivative for image enhancement because of the ability to enhance fine detail due to zero-crossing. The strategy is to utilize the Laplacian to highlight fine detail, and the gradient to enhance prominent edges. The performance of these partial 137 derivative operators are shown in Figure.6.3 which in turn represents the results for an image of narrowed artery nerve (defect in heart). 6.5.2 Transform domain techniques of edge detection The transform domain technique seems to be promising as there is no loss of edge information and helps in shape and contour tracking problem. The transform domain techniques of edge detection were developed to work for noisy images. Although the maxima of the modulus of the DWT are good approximation of the edges in an image, even in the absence of noise there are many false edges. Therefore a criterion must be determined to separate the real edges from the false edges. A threshold on the intensity of the modulus maxima is a good criterion and is described in following section. Streaking effect is the breaking up of an edge contour caused by the operator output fluctuating above and below threshold along the length of the contour. 6.5.2.1 Discrete Wavelet Transform approach It is difficult to extract meaningful boundaries under noisy circumstances directly from gray level image data, when the shapes are complex. But better results have been achieved by first transforming the image into frequency domain information and detecting discontinuities in intensity levels, then grouping these edges, thus obtaining more elaborate boundaries. Though the Fourier Transform (FT) was pioneer in transform domain, due to drawbacks of frequency domain representation alone, the concept of wavelet a powerful tool for spectral representation was developed for simultaneous time frequency representation. With this development, wavelet theory is suitable for local analysis, singularity and edge detection and have proved that the maxima of the wavelet transform modulus can detect the location of the irregular structures. This technique has [Mallat & Hwang, 1992] refined the wavelet edge detector, in which a scale of the wavelet that adapts to the scale of an image can be optimized and its noise level minimizes the effect of noise on edge detection. The edges of more significance are important and are kept intact by wavelet transforms and insignificant edges introduced by noise are removed. Wavelet based edge detection method can detect edges of a series of integer scales in an image. This can be useful when the image is noisy, or when edges of certain detail or texture are to be neglected. 138 The wavelet version of the edge detection is implemented by smoothening the surface with a convolution kernel and is denoted as and is dilated. This is computed with two wavelets that are partial derivatives of : To limit overhead the scale varies along the dyadic sequence for . ( ) (6.16) Let us denote for convenience ̅ and ̅ The dyadic wavelet transform of ( ) at is represented as ⟨ ̅ ⟩ The Discrete Wavelet Transform components are proportional to the smoothened by ̅ coordinates of the gradient vector of . ⃗( / . ̅ ) The modulus of the gradient is proportional to the wavelet transform modulus ( ) √| | | | (6.17) The magnitude of the wavelet transform modulus at the corresponding locations indicates the strength of the edges caused by sharp transitions. ( The angle of the gradient is given by An edge point at scale is a point, such that ) (6.18) ( ) is locally maximum and these points are called Wavelet Transform Modulus Maxima (WTMM).Thus the scale space support of these modulus maxima corresponds to multiscale edge points [Mallat, 2009]. 139 Edges of higher significance are more likely to be kept by the wavelet transform across scales. edges of lower significance are more likely to disappear when the scale increases. A wavelet filter of large scales is more effective for removing noise, but at the same time increases the uncertainty of the location of edges. Wavelet filters of small scales preserve the exact location of edges, but cannot distinguish between noise and real edges. It is required to use a larger scale wavelet at positions where the wavelet transform decreases rapidly across scales to remove the effect of noise, while using a smaller scale wavelet at positions where the wavelet transform decreases slowly across scale to preserve the precise position of the edges. Although the maxima of the modulus of the DWT are a good approximation of the edges in an image, even in the absence of noise there are many false edges as can be seen in Figure 4.2 (b). Therefore, a threshold on the intensity of the maximum modulus is said to a criterion to separate the real edges from the false edges and finally edges are retained and their characteristics are preserved when compared to spatial domain. 6.5.2.2 Fractional Wavelet Transform approach Unser.M & Blu.T introduced new family of wavelets based on B-Splines. Singularities and irregular structures carry useful information in two dimensional signals and the conventional edge detection techniques using gradient operator’s work well for truly smooth images and not for noisy images. FrWT has all the features of WT and it represents the signal in Fractional domain and projects the data in time–fractional-frequency plane. The FrWT of a 2Dfunction is given by , where along { ( )}- (6.19) in equation (6.19) are dilation and translation parameters and directions. It has been recognized by several researchers that there exists a strong connection between wavelets and differential operators [Jun Li, 2003]. So, transient features such as discontinuities are characterized by wavelet coefficients in their neighborhood, the same way as a derivative acts locally too. One of the primary 140 reasons for the success of FrWT in edge detection application is that they can be differentiated simply by taking finite differences. Wavelet Transform Modulus Maxima (WTMM) developed by Mallat, carries the properties of sharp signal transitions and singularities whereas FrWT acts as a multiscale differential operator. The derivative like behavior of FrWT provides promising results when compared to DWT approach. The new family of the WT is constructed using linear combinations of the integer shifts of the one-sided power functions: ̂ * + Where α is the fractional degree (6.20) is the gamma function. One of the primary reasons for the success of FrWT is that they can be differentiated at fractional order by taking finite differences. This is in contrast with the classical wavelets whose differentiation order is constrained to be an integer. This property is well suited for image edge detection. The fractional derivative can be defined in Fourier domain as ̂ Where ̂ ∫ (6.21) denotes the Fourier Transform of [Unser. M & Blu.T, 2003]. Singularities detection can be carried out finding the local maxima of the FrWT which is clearly evident in Figure 6.5 (c). The magnitude of the wavelet transform modulus at the corresponding locations indicates the strength of the edges caused by sharp transitions. 6.5.2.3 Steerable Wavelet Transform approach An appropriate edge detection technique which ensures that the fine edges of image without false edge detection are necessary for biomedical imagery. Machine vision and many image processing applications require oriented filters. It is often required to use the same set of filters for rotation at different angles and different orientation under adaptive control. [Freeman, 1991] developed the need of designing a filter, with filter response as a function of orientation and named it steerable. The 141 term ‘steerable’ (rotated) is used to describe a separate category of filters in which a filter of arbitrary orientation is synthesized as linear combination of a set of basis kernels. These filters provide components at each scale and orientation separately and its non-aliased subbands are good for texture and feature analysis. The steerable transform of a two dimensional function is written as linear sum of rotated version of itself and is given by the expression as ∑ (6.22) represents interpolation functions, ‘n’ is the number of terms required Where for summation. Any two filters are said to be quadrature if they possess same frequency response and differ in phase by 90° (Hilbert Transform).The design of quadrature pair of steerable filter is given by frequency response of second order derivative of a Gaussian function and its Hilbert Transform pair These pairs pave way for analyzing spectral strength representation of signals independent of phase. We design steerable basis set for the second derivative of a Gaussian .This is the product of even parity polynomial and a radially symmetric Gaussian function. For edge detection the quadrature pairs set and are utilized. The squared magnitude of the quadrature pair filter response steered everywhere in the direction of dominant orientation is given by * A given point + * + (6.23) is an edge point if direction perpendicular to the local orientation is at local maximum in the .Steering and along the dominant orientation gives the phase φ of edge points. (6.24) The steerable pyramid constitutes four band pass filters form a steerable basis kernel set at each level of pyramid and these basis functions are derived by dilation, translation and rotation of a single function. The orientation of these basis filters were at 0°,45°,90°,135° and the coefficients of these filters obtained at any 142 orientation can also be obtained at any linear combination of these basis filters. The original image with perfect reconstruction can be obtained, when these basis filters are applied again at each level and the pyramid collapses to the original version [Douglas Shy & Pietro Perona, 1994]. It consists of permanent, dedicated basis filters, which convolve the image as it comes in, their outputs are multiplied by gain masks with appropriate interpolation functions at each time and position and the final summation produces adaptively steered filter. Steerable filters are useful in various tasks: shape from shading, orientation and phase analysis, edge detection and angularly adaptive filtering [Freeman et. al., 1991]. The focus of this paper is to provide edge detection technique with good visual perception, undoubtly it is provided by steerable filters by avoiding spurious edges caused by noise and detecting real edges. Simulation results were performed to demonstrate the edge detections of images are shown in Figure 6.5 (e,f,g) and that this technique of using Steerable Wavelet Transform competes with other transform can be observed by means of visual perception. 6.6 INFLUENCE OF NOISE ON EDGE DETECTION The principal sources of noise in digital images arise during image acquisition and/or transmission. The performance of imaging sensors is affected by a variety of factors, such as environmental conditions during image acquisition and by the quality of the sensing elements themselves. For instance, in acquiring the images with a CCD camera, light levels and sensor temperature are major factors affecting the amount of noise in the resulting image. Edges in images are susceptible to noise and this is due to the fact that the edge detector algorithms are designed to respond to sharp changes, which can be caused by noisy pixels. Noise may occur in digital images for a number of reasons. The most commonly studied noises are white noise, salt & pepper noise and speckle noise. To reduce the effects of noise, preprocessing of the image is required. The preprocessing can be performed in two ways, filtering the image with a Gaussian function, or by using a smoothing function. The problem with the above approaches is that the optimal result may not be obtained by using a fixed operator. Simulation results were carried out to discuss the influence of noise on edge detection and the performance of edge detectors are discussed in forthcoming topics. 143 6.7 SIMULATION RESULTS In a 2-D image signal, intensity is often proportional to scene radiance, physical edges corresponding to the significant variations in reflectance, illumination, orientation and depth of scene surfaces are represented in the image by changes in the intensity function. Some types of edges results from various phenomena; for example when one object hides another, or when there is shadow on a surface. Noises are unwanted contamination that is intruded in an image acquisition because of several factors: such as poor illumination settings, sensors fault etc. The detection of edges are challenging task in noisy images. These are demonstrated through numerical results in this section. 6.7.1 Numerical Results of edge detection using spatial domain techniques The performance of various edge detectors in spatial domain are validated for biomedical images such as narrowed artery nerve of a human heart and for an iris image with cancer tissues are shown in Figure 6.3 and 6.4 respectively. These operators are widely used for their simplicity. (a) Narrowed artery nerve of a human heart (b) Prewitt image (c)Canny image (d) Laplacian image (e) Sobel image (f) Roberts image Fig. 6.3: Performance of edge detectors for an image of narrowed artery nerve in spatial domain. 144 (a)Iris image with cancer (b) Prewitt image (c)Canny image (d) Laplacian image (e) Sobel image (f) Roberts image Fig. 6.4: Performance of edge detectors for an iris image with cancer tissues in spatial domain The Roberts exhibits poor performance and Prewitt, Sobel performs moderately whereas Canny’s edge detection algorithm provides better performance but requires more overhead when compared to Sobel, Prewitt and Robert’s operator. The Canny operator provides better results and spurious edges can be avoided by hysteresis thresholding and can detect edges of an image but fails to detect lines. The advantages of the zero crossing operators (Laplacian) are detecting edges and their simple orientations, due to the approximation of the gradient magnitude and their possession of fixed characteristics in all directions. The disadvantages of these operators are sensitivity to the noise and detecting the edges and their orientations of noisy image eventually degrading the magnitude of the edges. 6.7.2 Numerical Results of edge detection using spatial domain techniques with noise The influences of noise on biomedical images are discussed by taking into consideration salt and pepper noise. 145 (a) Noisy image (b) Prewitt image (c)Canny image (d) Laplacian image (e) Sobel image (f) Roberts image Fig. 6.5: Performance of gradient edge detectors for image of narrowed artery nerve with noise (a) Noisy image (b) Prewitt image (c)Canny image (d) Laplacian image (e) Sobel image (f) Roberts image Fig 6.6: Performance of gradient edge detectors of an iris image with cancer tissues influenced by noise 146 The primary advantages of the classical operator are simplicity but most of these partial derivative operators are sensitive to noise. Use of these masks result in thick edges or boundaries, in addition to spurious edge pixels due to noise. The increase of noise in an image will eventually degrade the magnitude of the edges. The streaking effect can be observed with noise, it is an effect caused due to breaking up of edge contours. The major disadvantage is the inaccuracy, as the gradient magnitude of the edges decreases; accuracy also decreases as shown in Figure 6.5 and 6.6. The second disadvantage is that, the operation gets diffracted by some of the existing edges in the noisy image. These gradient based operators produce false edges in and around salt and pepper noise. The Prewitt and Roberts operator completely fails for noisy images. Moderate performances are observed by Laplacian and Sobel and much better results are obtained by Canny. 6.7.3 Numerical Results of edge detection using transform domain techniques (a)Narrowed artery nerve of a human heart (b) DWT image (d) Steerable wavelets (c) FrWT image (e)Steerable wavelets with (f)Adaptively oriented refined features steered filtering Fig. 6.7. Performance of gradient edge detectors for an image of narrowed artery nerve in transform domain 147 The tumor cells in eye do not only supply blood to the photoreceptors (rods and cones) of the retina and enables ophthalmologist to treat patients with large tumors. The edge detection techniques help to diagnose whether the cells are benign and malignant type and generally treated with enucleation, with or without preoperative radiation. (a)Cancer affected iris image (b) DWT image (c) FrWT image (d) Steerable wavelets (e)Steerable wavelets with (f)Adaptively oriented refined features steered filtering Fig. 6.8: Performance of gradient edge detectors of an iris image with cancer tissues in transform domain As most of the gradient operators fail to detect edges of an image with noises, some of the transform domain techniques discussed here are: DWT, FrWT, StWT. These transforms extract salient features of the scene with no loss of edge information when compared to spatial domain techniques and do not produce false edges and are observed in Figure 6.7 and 6.8. As natural images contain spots, lines and edges it is optimal to find an edge detector which responds to images with noise. FrWT and StWT which possess local energy measure provides peak responses at points of constant phase as a function of spatial frequency and corresponds to edge 148 points where human observers localize contours [Simina Emerich, 2008]. It is further observed that edges are well covered visually but textures and fine structures are removed in DWT domain. In FrWT and StWT operated images the textures and fine structures are observed which clearly states the superiority of transform domain. By use of angularly adaptive filtering the denoising and enhancement of orientated structures can be done simultaneously. 6.7.4 Numerical results of edge detection using transform domain techniques with noise The transform domain techniques outperform the gradient operators under noisy environment which are evident in Figure 6.9. (a)Narrowed artery nerve with Salt & Pepper noise (b) DWT image (c) FrWT image (d) Steerable wavelets (e) Steerable wavelets with refined features (f) Adaptively oriented steered filtering Fig 6.9: Performance of gradient edge detectors for an image of narrowed artery nerve with noise 149 (a)Cancer affected iris image with Salt & Pepper noise (b) DWT image (c) FrWT image (d) Steerable wavelets (e) Steerable wavelets (f) Adaptively oriented with refined features steered filtering Fig 6.10: Performance of gradient edge detectors of an iris image with cancer tissues influenced by noise in transform domain The edges are not affected by streaking effect due to noise in transform domain which is essential in biomedical applications. The steerable wavelet based edge detector which has adaptive in nature is used to eliminate streaking of edge contours and is evident in the Fig.6.10. The physician can vary the scale based on the level of details required and view the delicate details of the artery nerve and cancer tissues in eye and arrive at an amicable solution for subsequent treatments. Thus decision making is simple and eases him to diagnose most sensitive issues related to heart and eye diseases. 150 6.8 SUMMARY Comparison of various edge detection techniques and to analyze the performance of the various techniques under noisy conditions are evaluated. The classical operators possess some of the features like simplicity, detection of edges and their orientations, sensitivity to noise and are inaccurate. In this chapter, different approaches of edge detection techniques like Gradient-based, Laplacian based and Transform domain based techniques are presented. Edge detection techniques are compared with case studies of identifying a narrowed artery nerve of a human heart and iris image with cancer cells which provides the physician, information in making decision to perform Coronary Artery Block Surgery or Stent placement and in case of iris cells, assists to categorize whether benign and malignant tissues are present and to treat with enucleation(removal of the eye), with or without preoperative radiation. Gradient-based algorithms have major drawback as they are sensitive to noise. The dimension of the kernel filter in spatial domain and its coefficients are static and it cannot be adapted to a given image. It has been observed that evaluation of spatial domain operators like Canny, Laplacian, Sobel, Prewitt, Roberts’s exhibited poor performance with noise. Though Laplacian performs better for some features, it suffers from mismapping which represents edges. The edges are not continuous hence called streaking effect is severe in noisy images. Performance evaluation of edge detection techniques with DWT, FrWT and StWT were discussed. The fine to coarse information related to edge detection can be obtained through DWT based edge detection which provides the band passed representation, with threshold limits. Computational tasks in FrWT such as differentiation, integration and search for extrema are quite simple in transformed coefficients. The noise components are optimally separated and hence FrWT provides perfect localization. These estimating derivatives are helpful in edge detection and the edge points are well localized. Thus it is less sensitive to noise and provides robust edge detection with adjustable scale parameter which will be helpful for the physician to diagnose the intensity of the disease with ease. 151 The steerable filters can measure local orientation, direction, strength and phase at any orientation provides sophisticated results as these filters are oriented and non-aliased subbands provide us elegant edge detection and can be used for texture and feature analysis of the image. Further it is concluded that FrWT & StWT are convenient and perspective tools for edge detection analysis in bio-medical domain problems. The problem of streaking effect was addressed in spatial domain and predominantly suppressed and visualized in FrWT and StWT domain. 152