Sayısal görüntülerde kenar tanıma metodları

Abstract

Görüntü işleme konusunda temel Öneme sahip konulardan biriside kenar tanımadır. Görüntülerin gri seviyelerindeki ani değişikliklerin olduğu bölgelere kenar denir. Cisimlerin, fiziksel özellikleri İle kenarları arasında direkt bir ilişki vardır, görüntünün birçok fiziksel özelliği kenarlarından çıkarılabilir. Bu nedenle görüntü işleme sistemlerinin ilk basamaklarında kenar tanıma işlemleri önem taşımaktadır. Kenar tanıma metodları gri seviyeli görüntüleri kenar görüntülerine çevirmektedir. Bu değişim orijinal görüntüdeki birçok. yararlı fiziksel özelliği degi şti r meden ak tar ir. Bundan sonr ak i gör ünt ü i şl eme basamaklarına basit formlara indirgenmiş verilerin uygulanmasına imkan verir. Bu tezde genel kenar tanıma metodları incelenmiştir. En yaygın kullanım olan türev yöntemleri içerik olarak oldukça eksik olmalarına ragmen hale kullanımdadır ve hale teorilerinin geliştirilmesine çalışılmaktadır. Yöresel ortalama değişimleri incelenerek istatistiksel testle kenar bulunması incelenen diğer bir konudur. GürUltüyüde hesaba katan stokastik modeller kullanarak yapılan Wiener filtresi ile kenar tanıma metodu özellikle gürültülü ortamalar için incelediğimiz diğer bir bölümdür. FIR filtre kullanılarak yapılan enerjiyi maksimize etmeye çalışan yöntem filtreleme yöntemlerini incelediğimiz bölümdür. Son yöntem olarakta yeni bir konu olan morfolojik kenar operatörü incelenmiştir. ? Son bölümde de buraya kadar incelenen metodların genei bir karşılaştırılması yapılacak ve performasları incelenecek tir.

A problem of fundamental importance in image analysis is edge detection. Edge points can be thought of as pixel locations of abrupt gray-level change. As there is a direct relationship between the edges and the physical properties of a scene, much of the scene information can be recovered from an edge image. Thus edge detection is a key step in the early processing of a computer vision system. Edge detection converts gray scale image into a binary edge image which may have, direction information. The transformation preserves a great deal of the useful information in the orijinal image. The rest of the vision processes can deal with the simple form, Instead of dealing with gray scale image Information. Therefore edge detection has been a topic of fruitful research in recent years. S different approach to the problem are analyzed. They can be grouped in the following categories." 1. Differentiation techniques 2. Local statistical technique 3. Filtering technique 4. Stochastic gradient technique 5. Morphological technique Abrupt changes in gray level can take several different forms. The most common is the step edge. This is, of course, the ideal case. A step edge seper,ates two regions in each of which the gray level, is relatively uniform with different Values on the" two sides of the edge. But the presence of blur and noise turns steps into noisy ramps edges which have a transition region between two different gray levels. Another important type of gray level discontinuity is the line, which is a thin strip that differs from the regions on both sides of it. Also abrupt changes in the rate of change of gray can also be defined as edges. A difficulty with edge detection is that the detected edges often have gaps in them at places where the transitions between regions are not abrupt enough. Moreover, edges may be detected at points that are not part of region boundaries, if the given picture is noisy. For a continues image /Cx,y} its derivative assumes, a local maximum in the direction of the edge. VIII ! Threfore one of the most fruitful ways to produce an edge image based on differentiation. At this edge detection techniques, the gradient of the input image is measured at a specific direction and, then magnitude of the gradient thresholded with a appropriate threshold value. Performance of this method depends on both choice of gradient type and threshold value. threshold value / figure: Procedure for producing edge images.1 Based on this gradient method two types of edge detection developed. These are gradient operators and compass operators. Gradient operators can be classfied into two system. Directional- and non-direct i onl operators, for example, if the system uses \Öftx,y3/âvı\ this system can detect edges at vertical direction, but can not detect edges at other directions. Since this function that has a bias toward one parti culr direction, it is called directional edge detector. If the system uses |7/Ci,JD| since this system do not have a bias toward any particular direction, this method called non-directional detector. For digital images the operators also called mask. These mask represents finite difference approximation of directional masks. Once the magnitude of the gradient calculated, pixel location Cm,nD is declared as an edge point if gradient at Cm,a> exceeds some threshold t. ' The locations of edge points constitude an edge map, e<$m,u3 which is defined as e {1, 0, other e I g otherwise I = t> Edge map gives the necessary data for tracing the object boundries in an image. Typically, t may be selected using the cumulative histogram of gCm,nD so that pixel magnitude of which 3 to 10% of the largest gradient magnitude are declared as edges. Some of the common gradient operators are Prewitt, Robert, Isotropic and Sobel. IX Compass operators measure gradients in a selected number of directions. An counterclockwise circular shift of the eight boundary elements of these mask gives a 43° rotation of the gradient direction. Another frequently encountered operator is the Laplacian, defined as vV = a2/ a2/ ax2 ay2 Because of the second order derivatives, this gradient operator is more sensitive to noise than those previously defined. Also, thresholded magnitude produce double edges. For thee reasons, together with inability detect edge directions, the- Laplacian as such is not a good edge detection algoritms. A better utilization of the Laplacian operator, Laplacian of Gaussian functions is a powerfull zero crossing. Laplacian of Gaussian functions is defined as **hC*.y:> - i - C x* + y2 - En** D OıaO* where a controls the width of the Gaussion kernel and k normalizes the sum of the elements of a given size mask to unity. Such kind of zero crossing edge detector is equivalent to a low pass filter having a Gaussian impulse response followed by a Laplace operator. The low pass filter serves to noise sensitivity of the Laplacin.Laplacian of Gaussian is notated as LoG.. LoG filters was, first, defined by Marr and Hi 1 bert. Previous derivative methods fails in the noisy pictures. Using local average changes instead of gray values gives better performance in the noisy pictures. But, using local averages detect edges very abruptly. At this method, local averages of small windows are calculated, if average changes of adjacent windows exceed; some threshold, this means an edge region exist between this two adjacent windows. Dividing this windows into smaller windows, then calculating the average changes of this small windows, give more accurate edge regions. At the second step, to detect edge pixels, threshold the small edge windows with both their own average value and local variance. With this two step algorihtm, edges can be detected abruptly even at the high noise levels. Another powerful edge detection algoritm is stok ast i k gradient method. To detect the presence of n edge at locattion P calculate the horizantal gradient as, gCm,rO = u.Cm,n-13-u.Cm,n+lD where u.Cm.nD and u.Cm,n} are the optimum forward and 1 o backward estimates of uCm,rO based on the noisy- observations given over some regions W of khe left and right half -planes, respectively. Thus ufCm,n2? and u.Cm.nU are semicausel estimates. For observations, we o can find the best linear mean square semicausel FIR estimate of the form u.CnuiO = E E aCk,lDvCm-k,n-lD W=: |k|<p,0<l r k,l eW Where aCk,13 is the Wiener filter weights. The backward semicausel estimate employs. the same filter weights but backward. Using the gradient definitions in ^stochastic model, horisantal mask can be obtained from ufCm,rp ahd u.Cm,nD. Vertical mask would be the 90 counterclockwise b rotation of horizantal mask. Using this mask in the directional gradient method, better peformance would be obtained. In order to detect meaningful edges in noisy pictures, edge detection filters should operate on a global basis and should optimize a givin performance measure. In this chapter, we derive an optimal edge detection filter which produces maximum energy within a resolution interval of specified width in the vicinity of the edge. The product of the resolution and bandwidth of the filter can be set at any desired value. We show that, in the continuous case, the filter transfer function is specified in terms of the prolate spheroidal wave function. In the discrete case, the filter transfer function is specified in terms of the sampled values of the first-order prolate spheroidal wawe function or in terms of the sampled values of an asymptotic approximation of the wave function. Both version can be implamented by FFT transform. By adjusting a single parameter of the filter, it is possible to trade off edge resolution for output signal to noise ratio An other method of edge detection is morphological methods. The morfological approach is generally based upon the analysis of two valued image in terms of some predetermined geometric shape known as a structuring element. Essentially, the manner in which the structuring element fits into the image is studied. A simple method of edge detection is to take the difference between an image and its erosion by a small rod shape structuring element. Then choosing an appropriate threshold value, we can get edge image. An improved verson of this method is to take minimum of dilation and erosion residue of the blured image XI Edge detection algorithms can be compared in a number of different ways. Quantltavely, the performance in noise of an edge detection operator may be measured as follows, n is the number of pixel» decl eared and n is the number of false edge points after adding noise. </p,0<l