# Rank-order and morphological enhancement of

Rank-order and morphological enhancement of image details with an optoelectronic processor Tomasz Szoplik, Javier Garcia, and Carlos Ferreira In all-optical processors, enhancement of image details is the result of high-pass filtering. We describe an optoelectronic processor in which detail enhancement results from the digitally calculated difference between an original input image and its low-pass filtered version. The low-pass filtering is realized through the rank-order median and the morphological opening and closing operations calculated by use of the optical convolver. It is shown that the normalized difference between the morphological white and black top hats enhances bright and dark image details analogously to the rank-order unsharp masking. Key words: Optoelectronic image processing, optoelectronic image enhancement, rank-order filters, morphological filters. 1. Introduction Two important methods of nonlinear image processing are rank-order1–4 and morphological5–7 filtering. Though different from the point of view of mathematical approach, they may lead to similar image modifications. It was proven that rank-order filters are equivalent to those morphological filters that commute with thresholding.8,9 This condition is met for the cases of set- and function-processing 1i.e., binary and gray-scale image-processing2 morphological filters that involve a binary structuring element 1that is, a flat kernel of local convolution2. Thus rankorder and morphological filtering can be performed in linear optical systems complemented with electronics, which adds nonlinear thresholding to the optical convolution. In both methods, processing of a grayscale image slice by slice is based on the threshold decomposition concept,1 which led to the definition of the stacking property2 of Boolean functions 1operators2. Nonlinear image processing based on the thresholded local convolution approach permits operations on image details of the size smaller than or equal to that of the convolution kernel. The processing results in modifications of local histograms calcuWhen this research was performed, the authors were with the Departamento Interuniversitario de Optica, Universitat de Valencia, Burjassot 46100, Spain. T. Szoplik’s permanent address is the Instytut Geofizyki, Universytet Warszawski, Pasteura 7, Warszawa 02-093, Poland. Received 7 December 1993; revised manuscript received 25 July 1994. [email protected]@[email protected] r 1995 Optical Society of America. lated for neighborhoods contained within the kernel windows. The purpose of local histogram modifications can be various, examples of which are noise removal, image detail enhancement, skeletonization, and segmentation. In both rank-order and morphological processing the mechanism of detail enhancement is quite similar. The details are extracted as the difference 1residue2 between the original image and its nonlinearly processed versions, which are low-pass filtered. In rank-order processing the usual low-pass filter is the median one, which neglects extreme image pixel values contained within the local convolution window. In morphological processing the opening and closing transformations have selective low-pass filter properties. In binary images the opening filters out small sets and small convex details of objects. Thus the gray-scale images are smoothed by the opening owing to removal of convex details that on each grade of gray are thinner than the structuring element. The morphological closing operation is dual to the opening. Therefore in binary images the closing fills in small dark holes within objects and connects closely disjointed parts of objects into one. The gray-scale images are smoothed by the closing owing to removal of concave details that are smaller than the kernel. In terms of intensity the opening removes bright details of an image, while the closing removes dark details. Low-pass filtering is easily performed in an optical system because of its limited modulation transfer function. Thus the efficiency of optical systems in low-pass filtering results in good performance of hybrid high-pass filtering processors. In both methods the size and the shape 10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS 267 of preserved details depend on the neighborhoods within which the operations are realized. There are several optoelectronic implementations of morphological and rank-order nonlinear processors.10–19 In all of them, because of optical convolution, the digital computations are reduced to calculating the maximum, minimum, and other rank-order values and depend less on the neighborhood shape and size. In the first demonstration of the optoelectronic rank-order processor a binary spatial light modulator 1SLM2 was employed to introduce simultaneously into an optical convolver all of the binary slices of an input image.10 A computer-generated hologram played a double role of an image beam deflector for slices and a structuring element. In this experiment a gray-scale image of 48 3 48 pixels with 16 gray levels was processed in real time. In another hybrid morphological processor the real-time programmable processing of limited-size images was presented.12 A binary input image and a structuring element were introduced into an optical system by means of two SLM’s. The use of a lenslet array illuminator yielded a convolution due to angular projection. The convolution with angular projection was also employed in the morphological processor with a laser beam scanner.14 In the morphological processor based on a coherent 4-f type correlator the impulse response of the Fourier-plane holographic filter played the role of a structuring element.15,16 In other realizations of rank-order and morphological processors, noncoherent convolvers by use of either a plane of misfocus or shadow casting were applied.11,17–19 The slices of the gray-scale input images were introduced into the convolvers by means of photographic transparencies, a TV monitor, or an SLM. In all of the above-mentioned systems, looping and sequential regime of work were necessary as a consequence of the sequential structure of rank-order and morphological filters on the one hand and the threshold decomposition concept and stacking property on the other. Recently Tasto and Rhodes showed that both rankorder and morphological filtering of threshold decomposed images realized in optoelectronic processors exhibits a high degree of noise immunity and permits high-accuracy processing.20 Their assessment as well as the progress in real-time processing techniques encourages continuation of research on hybrid optoelectronic systems for both rank-order and morphological processing. Our aim here is to demonstrate the feasibility and quality of optoelectronic experimental results of three algorithms for enhancement of image details: rankorder unsharp masking and morphological black and white top hats. To establish a link between unsharp masking and morphological top hats, we define the normalized difference between white and black top hats. The difference algorithm enhances both bright and dark details. The experiment is done on a realistic-size image with rich texture. 268 APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995 2. Rank-Order and Morphological Algorithms for Enhancement of Image Details Rank-order and morphological methods of image improvement can be divided into two broad groups of algorithms, which aim at either image smoothing or enhancement of image details.3–7,18,21 Image-smoothing algorithms are used for removal of noise that has one of several possible properties or that is a mixture of different types of noise. At the same time, information about fine image details is preserved. The noisesuppression algorithms are used for preprocessing of images that afterward are subjects of enhancement operations such as, for instance, histogram modifications or edge extraction. A sequence of proper operations may lead to a considerable image improvement appreciated by a human observer. Application of smoothing and enhancing algorithms may also precede pattern-recognition tasks. A. Rank-Order Algorithms for Enhancement of Image Details Let 5V1k26 be a discrete input image with Q gray-scale levels of intensity quantization: k 5 1k1, k22 is a vector coordinate of an input image element; k1 5 1, . . . , N1 and k2 5 1, . . . , N2; N1 3 N2 5 N is the image matrix size. According to the threshold decomposition concept,1 the kth element V1k2 of an input image is represented as a sum of kth elements of all binary slices as Q21 V1k2 5 o X 1k2, 112 q q51 where Xq1k2 is the kth element of a binary slice of an input image obtained through decomposition with a threshold q; that is, Xq1k2 5 1 50 if V1k2 $ q otherwise . For each slice 5Xq1k26, where braces denote the whole set of q-level elements, local operations are performed within a spatial neighborhood S of arbitrary size and shape that is similar for each kth input-image element. The spatial neighborhood S is cast by a scanning binary 1flat2 structuring element that characterizes the local convolution. The local-convolution operation can be very efficiently performed in a computer unless the structuring elements do not become too large. Alternatively, local convolutions can be accomplished in parallel in optical correlators. We believe that fully programmable correlators for processing of large images by means of large and arbitrarily shaped structuring elements should become feasible soon. The possibility of parallel optical calculation of local convolutions was the basis of a recently proposed optical–digital method of local histogram calculation.17 This method results from a theorem proved in Ref. 17, which says that the local q-level histogram of an arbitrary neighborhood in an input image is equal to the pointwise difference of the two convolution pat- terns obtained by convolving the slices at the levels q 1 1 and q with a binary mask, thereby defining the neighborhood. We note that, for each pixel of the input image, the pixel value in the convolution pattern of the q-level binary slice and the kernel is equal to the number of pixels in the neighborhood that are on the q-level and higher values. Detail-enhancing algorithms are designed to increase local nonhomogeneities of intensity distribution of an input image. An increase of local contrast can be accomplished in a variety of ways. A simple and linear method is to enhance these pixels that differ from average pixel values calculated within its spatial neighborhoods S: Y1k2 5 mean5S3V1k246 1 GAV1k2 2 mean5S3V1k246B, 122 where the output pixel value Y1k2 is given by the sum of a bias term equal to the average pixel value calculated within neighborhood S of the input pixel V1k2 and another term that is a difference between the input pixel value and the before-mentioned average enhanced by a gain coefficient G. The above algorithm becomes nonlinear when the mean operation is replaced with the med operation; that is, the median value of the neighborhood S is considered as a reference. The most general nonlinear rank-order unsharp masking algorithm 1UM2 is defined as follows22: UM3V1k24 5 A 1 GAV1k2 2 med5S3V1k246B, 132 where S3V1k24 is an arbitrary neighborhood of the kth element of an input image, A is the offset, G is the gain coefficient of input-image details that differ from the median value, and minus denotes a pointwise subtraction. Taking advantage of the threshold decomposition concept, we process in sequence binary slices 5Xq1k26 of the input image rather than the gray-scale input image 5V1k26 itself. For each kth input slice element a local convolution is made and the median value med5S3Xq1k246 is calculated within the kth-element neighborhood, S, defined by the binary convolution kernel. The pointwise sum of all processed slices gives the output gray-scale image. Coefficients A and G are image dependent and are calculated as follows. Pointwise subtracting the median from the original, we find minimum 12n2 and maximum 1m2 difference pixel values as well as the zero level 1as a fraction f of the full range 32n, m42. Then the gain coefficient is calculated as G 5 [email protected] 1 n2 and the offset A 5 255f. B. Morphological Algorithms for Enhancement of Image Details Morphological filters are composed of two basic operations: erosion and dilation. The erosion is defined as the locus of the center of the structuring element S when S is included in the binary slice X, such that in the extreme case it follows the border tangentially from inside. The dilation is defined as the locus of the center of the structuring element when S intersects X, such that in the extreme case it follows the border tangentially from outside. The simplest morphological filters are the opening and closing. The morphological opening is defined as follows: gS5Xq1k26 5 dSeS5Xq1k26, 142 where the erosion eS of the image slice 5Xq1k26 by the structuring element S is followed by the dilation dS of the looped eroded slice by the same kernel. The opening filters out bright details of an input image and is frequently used to remove salt elements of the two-sided impulsive noise. The opening of a grayscale image gS5V1k26 is obtained by stacking of the processed binary slices. The morphological white-tophat algorithm 1WTH2, which enhances bright details, is defined as the difference 1residue2 between the input image and its opening23: WTH5V1k26 5 5V1k26 2 gS5V1k26, 152 where minus denotes pointwise subtraction, which results in a positive representation of high-intensity details. In the black-top-hat algorithm 1BTH2 the morphological closing is employed. This operation, dual to opening, is defined as wS5X1k26 5 eSdS5X1k26, 162 where dilation and erosion are made in reverse order to that of the opening. The closing filters out dark details of an input image and is frequently used to remove pepper elements of the two-sided impulsive noise. Here also the closing of a gray-scale image wS5V1k26 results from summing up the processed binary slices. The morphological black-top-hat algorithm, which enhances dark features, is defined23 as BTH5V1k26 5 wB5V1k26 2 5V1k26, 172 where minus denotes pointwise subtraction of an original from its closing, which results in a negative representation of low-intensity details. For the purpose of comparison of results of rankorder and morphological methods for image detail enhancement we propose to combine white and black top hats. The aim is to unite bright and dark details obtained with top hats, as in the case of unsharp masking. The difference D5V1k26 between white and black top hats, which retrieves the original contrast of details, is defined as follows: D5V1k26 5 A 1 G3WTH5V1k26 2 BTH5V1k264, 182 where A is a normalization constant and G is the gain coefficient of extracted details, both of which are calculated similarly as in the case of Eq. 132. Analogy between the unsharp masking and the difference of top-hats algorithms is straightforward. In the first one, bright and dark details that outlie from the local median values are properly increased by a factor of G 10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS 269 and displayed on a bias level A calculated for the whole image. In the second one, bright and dark details are obtained from calculated differences between the input image and its morphological opening and closing, then are multiplied by the gain coefficient G, which depends on the dynamic range of the difference of top hats, and the details are displayed on a bias level A calculated for the whole image. Both algorithms are very good contrast detectors suitable for enhancement of bright and dark details that are smaller than or equal in size and shape to the structuring element used to modify the input image. 3. Experiment and Results A. Characteristic of an Optoelectronic Experiment Using Thresholded Convolution Let us discuss a few sources of noise usually present in optoelectronic processors composed of one or two SLM’s, which introduce an input image and a structuring element into the system, a CCD camera, and a frame grabber. Frequently, an input image is introduced into the optical convolver by means of an SLM in the form of a liquid-crystal display 1LCD2. Because of nonuniform thickness of the liquid-crystal sandwich and nonuniform illumination, the intensity values corresponding to logic ones and zeros vary from one element to another at random for both. For LCD pixels the contrast ratio C is defined as C 5 [email protected], 192 where Imax and Imin are the intensities transmitted by LCD pixels that are on and off. According to Ref. 24 the minimum contrast ratio for each pixel of the Epson VP-100PS-type LCD used in our experiment is 40. According to Laude et al.,25 the corresponding maximum contrast ratio for the white-light illumination reaches 60. We want to have an image input device with as a high contrast ratio as possible. If it is equal to k, then for a slice that has k times more pixels in the zero level than in the one level, the background contains the same amount of energy as the foreground. A limited value of the contrast ratio results in a high background level; therefore proper adjustment of offset and gain in the frame grabber is necessary to optimize the dynamic range of recorded images. At present the best low-end LCD that is commercially available does not exceed 480 3 440 pixels in size and has a contrast ratio on the level of 100:1. In fully programmable optical convolvers it can be used for introduction of large structuring elements of arbitrary shape. The recent development of verticalcavity surface-emitting lasers gives hope that, in the near future, microlaser arrays can be used as image input devices in optical convolvers. Nowadays vertical-cavity surface-emitting laser arrays are easily switched from the fully on to the fully off state with frequencies lower than 100 MHz.26 If a structuring element is introduced into the system by means of an SLM, the threshold level 270 APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995 depends also on the number of pixels in the kernel. The bigger the structuring element, the higher the threshold.12 Recent analysis of noise effects in optoelectronic order-statistics filtering concludes that operations using higher thresholds have higher probabilities of error.20 Consequently, instead of erosion, it is advisable to make a binary logic inversion of a slice, calculate dilation, and again make a complement. In principle, the idea is correct. However, in the case of realistic-size images with full gray scale and rich texture it should be used cautiously. In such images the first slice is mostly composed of ones and the last one of zeros. Thus routine use of the above method of complement processing with respect to all of the slices makes no sense. With the same method one cannot improve the results of processing the first and the last slices. There is a possibility of using the method in an image-dependent way, in which case the contrast ratio of the SLM’s used should be taken into account. In our experiment, dilations, medians, and erosions are calculated directly. For the past 20 years LCD’s have been produced in thin-film-transistor technology.27 In this technology each pixel of a LCD array has a thin-film transistor that permits active addressing. The transistor gate is attached to a horizontal row electrode, the drain is attached to a vertical column electrode, and the source is attached to the liquid-crystal electrode. The pixel array is activated a row at a time by activating the gate lines. In principle this technology ensures accurate switching on and off of individual pixels. Because of cross talk, however, some of the pixels may switch to another state. Let us consider possible consequences on the example of the image of a wedge with uniform distribution of shade, composed of 256 3 256 pixels, and having 256 grayscale levels. For such an image the difference in the population of ones between two subsequent slices is 256, that is, 0.004 of the total number of pixels. For an arbitrary image, such a difference can be even smaller. The cross talk may disturb this small difference considerably. We conclude that, for our purpose, low-pass filtering in an optoelectronic convolver, the limitation of the number of gray-scale levels is justified and advisable. The use of 16 gray-scale levels of the original picture instead of all 256 ensures that the number of zeros in subsequent slices does not decrease when threshold q increases. In this way, cross talk increases the level of noise, but it does not cause inversion of the population of ones in a sequence of slices. In an optoelectronic system composed of a liquidcrystal SLM, a CCD camera, and a frame grabber, there are two more sources of noise, which enter the information channel. First, the analog signals are resampled three times with different resolutions on their loop between the frame grabber, the SLM, and the CCD camera. Second, the random noise of the CCD camera and the SLM reduces the dynamic range of convolution patterns. The morphological opening and closing given with Eqs. 132 and 152 employ thresholds on minimum 1dilation2 and maximum 1erosion2 levels, which in digital processing correspond to 0 and 255 levels, respectively. In optoelectronic implementations the minimum and maximum threshold levels are located just above and below the levels of noise, which comes from the above-mentioned sources. For each pixel of the input image the pixel value in the convolution pattern of the q-level binary slice and the kernel is equal to the number of pixels in the neighborhood that are at the q level value and higher. To find the threshold levels, we use the theorem on local histogram calculation,17 which was recalled in Section 2. In principle, both local and global histograms, which are functions of the q argument, should be nondecreasing for zeros and nonincreasing for ones. The existence of noise, however, may cause small discrepancies between theory and practice, especially for extreme q levels. B. Experimental System In our experiment an optoelectronic morphological image processor with feedback was used, which was a modified version of that described in a previous paper.19 Figure 1 shows a block diagram of the processor. An input gray-scale image is digitally threshold decomposed into a stack of binary slices. The next operation is performed in the optical whitelight convolver with a plane of misfocus. Binary slices are displayed in time sequence on the Epson VP-100PS-type LCD and imaged with a camera lens onto the Pulnix TM-765 CCD camera. The system point-spread function is controlled by misfocusing and the use of a diaphragm. The point-spread function plays the role of a structuring element. In this manner every binary slice is optically convolved with a binary convolution kernel, which results in a stack of gray-scale convolution patterns. Convolution patterns recorded by the CCD camera are sent to the Matrox PIP-1024B video digitizer board. After proper thresholding in the frame grabber, the following pointwise operations on the binary convolution patterns and further processing are made on a microcomputer. In the case of morphological filters, results of intermediate operations are reintroduced into the LCD as looped inputs. The processor is equipped with TV monitors for observation of input slices, recorded convolution patterns, thresholded convolution patterns, and final results. The white-light convolver with a plane of misfocus is one of the few possible convolver configurations. The others are angular projection convolvers and shadow-casting correlators.28 Frequent use of whitelight convolvers in morphological processors and optical parallel logic processors with shadowgrams has triggered recent interest in their performance.29,30 C. Comparison of Experimental Optical Results and Digital Results Performance of detail-enhancement algorithms is demonstrated on the input image of 256 3 256 pixels and 16 gray levels, which is shown in Fig. 21a2. Figure 21b2 presents the results of a digital median filter with a binary kernel of 5 3 5 pixels. Figure 21c2 shows an example of the output of an optical median filter with a flat structuring element of the same size. Visual examination of both results confirms good performance of the optoelectronic processor. For the purpose of quantitative comparison we use the mean absolute error 1MAE2 as a measure of similarity. The MAE, which is frequently used in filter optimization problems,31 is defined as follows: MAE 5 Fig. 1. Block diagram of the morphological optoelectronic image processor. Operations are shown in circles, and data arrays are shown in squares. 1 N o 0med 5S3V1k246 2 med d op5S3V1k2460, 1102 k where subscripts d and op indicate digitally and optically calculated medians. The absolute value of the difference 1i.e., error2 between optical and digital results is summed over the whole image matrix, normalized to the 256 gray-levels score, and divided by the total number of pixels. Analogously, MAE can be defined for morphological operations and filters used in our experiment. Table 1 details values of such experimental parameters as MAE, minimum error, maximum error, and threshold value. In the first row, experimental parameters of optoelectronic calculation of the median are presented. The MAE equals 2.4 6 0.1 gray-scale levels of the 0–255 range, which means that the optical median filtration is made within 1% accuracy with respect to the digital calculations. For some pixels the maximum difference between optical and digital results reaches almost half of the gray-scale range, however. In principle the threshold value for obtaining the median should be on the level of 0.5. Nevertheless, the 10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS 271 Fig. 2. Experimental results of digital and optoelectronic calculations: 1a2 input image of 256 3 256 pixels with 16 gray levels, 1b2 digital median filtration with a square binary kernel of 5 3 5 pixels 31c2–1h2 are also obtained with a square binary kernel of 5 3 5 pixels4 1c2 optical median filtration, 1d2 digital unsharp masking, 1e2 optical unsharp masking, 1f 2 optical morphological black top hat, 1g2 optical morphological white top hat, 1h2 normalized difference of optical white and black top hats. above-discussed sources of noise can produce a shifting of the experimental local histograms. Therefore the experimental threshold value is 0.55 6 0.05. With this threshold value the MAE is minimized. According to Eq. 122, the results of digital and optical median filtering are used to calculate unsharp masking. Pointwise subtracting the median from the original, we find minimum 12n2 and maximum 1m2 difference pixel values as well as the zero level 1as 272 APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995 a fraction f of the full range 32n, m42. The gain coefficient is calculated as G 5 [email protected] 1 n2. The offset equals A 5 255f. In Figs. 21d2 and 21e2 the results of digital and optical unsharp masking are presented, respectively. Obviously they preserve the similarity of digital and optical results of median filtration. Intermediate optoelectronic operations necessary to obtain morphological white and black top hats are Fig. 2. continued. summarized in Table 1. The second and the third rows contain experimental parameters of the calculated erosion and dilation. In contrast to theoretical predictions the difference between digital and optical dilations is greater than in the case of the median filter. The accuracy of optical calculation decreases to ,1.6%. For erosion we obtain, in accordance with expectations, the worst result. The accuracy of optical calculation in comparison with the digital one decreases to ,3.2%. The last two rows of Table 1 present parameters of optical calculating of opening and closing, which simultaneously correspond with Table 1. Values of Experimental Parametersa Filter Type MAE min er max er th Median Erosion Dilation Opening Closing 2.4 6 0.1 7.9 6 0.7 4.0 6 0.2 8.0 6 0.3 6.9 6 0.1 0 0 0 0 0 104 6 8 160 6 16 144 6 16 128 6 16 144 6 16 0.55 6 0.05 0.975 6 0.005 0.025 6 0.005 0.12 6 0.03 0.955 6 0.005 a Mean absolute error (MAE), minimum error (min er), maximum error (max er), and threshold value (th) are listed for optoelectronic calculation of the following filters: median, erosion, dilation, opening, and closing. 10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS 273 calculating white and black top hats, respectively. In the case of opening we list parameters of the second operation, that is, of dilation made on the eroded image. The MAE and the minimum and maximum errors have values similar to the case of regular erosion. Thus errors made in two subsequent steps do not accumulate in a direct way. The threshold level of dilation made on the eroded image is 5 times higher than in the case of regular dilation. Finally, for closing, that is, erosion made on the dilated image, we find the experimental parameters comparable to those obtained for the case of regular erosion. Figures 21f 2 and 21g2 show black and white top hats calculated optically according to Eqs. 162 and 142, respectively. We note that both results of morphological processing are satisfactory. The wide presence of a black background confirms the good quality of optically calculated opening and closing. Figure 21h2 presents the result of the difference between optical white and black top hats calculated according to Eq. 172. The normalization constant A and the gain coefficient G are calculated in exactly the same way as in the case of the unsharp masking algorithm. We note that the experimental morphological result that combines bright and dark details of the image is easier to examine visually than the results of a rank-order unsharp masking algorithm calculated either digitally or optically. It is a consequence of the opening, closing, and median filter definitions that the combination of white and black top hats has a broader histogram than unsharp masking. Thus in the case of the morphological difference of top hats the dynamic range of the output image is more evenly employed than in the unsharp masking case. 4. Concluding Remarks Optoelectronic implementation of the rank-order and morphological algorithms for image detail enhancement has been presented and compared with digitally calculated results. High-pass morphological and rank-order filtering based on calculation of a residue of an input image and its processed version does not depend strongly on the quality of optically realized low-pass filtering. The optical part of the system is a white-light convolver using the plane of misfocus. The input image is introduced into the system by means of the Epson VP-100PS-type LCD, which is built in thin-film-transistor technology. Owing to cross talk, error in row- and column-wise addressing of pixels may result in that a kth pixel value in the upper slice 5Xq111k26 being bigger than the same kth pixel value in the lower qth slice. Therefore for the purpose of optical low-pass filtering it is advisable to use a limited number of slices, which in consequence are more sparse. In this way the benefits of using an optical convolver are twofold: first, convolutions are made in parallel, and calculation time does not depend on the structuring-element size and shape; second, processing of a fraction of the whole set of 255 274 APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995 slices is sufficient. From the point of view of a human interpreter, however, the quality of results remains good. The experimental optical results of the median filtering and the morphological erosion, dilation, opening, and closing are compared with the digitally calculated correspondents. The mean absolute error defined by Eq. 192 describes the average per image pixel distance between digitally and optically calculated results. An optical median is calculated within 1% accuracy with respect to the digital calculations. For optical dilation the accuracy decreases to 1.6%. For optically calculated closing, accuracy decreases to 2.7%. The lowest accuracy is found for the cases of optical erosion and opening, only 3.1%. In this paper we have defined the normalized difference between morphological white and black top hats, which enhances bright and dark details of an input image simultaneously. The experimental result of the difference algorithm is favorably compared with that of the rank-order unsharp masking algorithm, the reason being the better use of the dynamic range of the output image. Both algorithms give image-dependent results; however, probably in most of the cases, the top-hats difference algorithm gives an output image with a bigger number of wellpopulated gray-scale levels in the histogram than the unsharp masking algorithm. This results from the fact that the top-hat difference algorithm is defined by combination of erosions and dilations, that is, through maximum and minimum thresholds. Consequently, visual inspection of the top-hats difference algorithm output is easier than in the other case, as the overall contrast is higher. The optoelectronic processor performance depends on the level of noise present in the system. Several sources of noise have been discussed. One of the most important is the limited contrast ratio of the LCD used. Nevertheless, we believe that improvement of the accuracy of optical calculations of rankorder and morphological filters will take place in the near future. This work was supported by the Spanish project of the Comisión Interministerial de Ciencia y Tecnologı́a 1project TAP93-0667-C03-032. T. Szoplik acknowledges a GO WEST grant from the Commission of the European Communities, Cooperation in Science and Technology with Central and Eastern European Countries 1grant CIPA3511CT9206482. C. Ferreira acknowledges a GO EAST grant from the Commission of the European Communities, Cooperation in Science and Technology with Central and Eastern European Countries 1grant ERB-CIPA-CT-93-16712. References 1. J. P. Fitch, E. J. Coyle, and N. C. Gallagher, Jr., ‘‘Median filtering by threshold decomposition,’’ IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183–1188 119842. 2. P. D. Wendt, E. J. Coyle, and N. C. Gallagher, Jr., ‘‘Stack filters,’’ IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898–911 119862. 3. V. Kim and L. Yaroslavskii, ‘‘Rank algorithms for picture processing,’’ Comput. Vis. Graph. Image Process. 35, 234–258 119862. 4. I. Pitas and A. N. Venetsanopoulos, Nonlinear Digital Filters. Principles and Applications 1Kluwer, Dordrecht, The Netherlands, 19902, pp. 63–150. 5. J. Serra, Image Analysis and Mathematical Morphology 1Academic, London, 19822. 6. J. Serra, ‘‘Introduction to morphological filters,’’ in Image Analysis and Mathematical Morphology. Theoretical Advances, J. Serra, ed. 1Academic, London, 19882, pp. 101–114. 7. E. R. Dougherty and R. P. Loce, ‘‘Efficient design strategies for the optimal binary digital morphological filter: probabilities, constraints, and structuring-element libraries,’’ in Mathematical Morphology in Image Processing, E. R. Dougherty, ed. 1Dekker, New York, 19932, pp. 43–120. 8. P. Maragos and R. W. Schafer, ‘‘Morphological filters. I. Their set-theoretic analysis and relations to linear shiftinvariant filters,’’ ‘‘Morphological filters. II. Their relations to median, order-statistics, and stack filters,’’ IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1153–1184 119872. 9. P. Maragos, ‘‘Tutorial on advances in morphological image processing and analysis,’’ Opt. Eng. 26, 623–632 119872. 10. E. Ochoa, J. P. Allebach, and D. W. Sweeney, ‘‘Optical median filtering using threshold decomposition,’’ Appl. Opt. 26, 252– 260 119872. 11. J. M. Hereford and W. T. Rhodes, ‘‘Nonlinear optical image filtering by time-sequential threshold decomposition,’’ Opt. Eng. 27, 274–279 119882. 12. Y. Li, A. Kostrzewski, D. H. Kim, and G. Eichmann, ‘‘Compact parallel real-time programmable optical morphological image processor,’’ Opt. Lett. 14, 981–983 119892. 13. P. Cambon and J.-L. Bougrenet de la Tocknaye, ‘‘Mathematical morphology processor using ferroelectric liquid crystal light valves: principle,’’ Appl. Opt. 28, 3456–3460 119892. 14. B. D. Duncan, T.-C. Poon, and R. J. Pieper, ‘‘Real-time nonlinear image processing using an active optical scanning technique,’’ Opt. Laser Technol. 23, 19–24 119912. 15. E. Botha, J. Richards, and D. Casasent, ‘‘Optical laboratory morphological inspection processor,’’ Appl. Opt. 28, 5342–5350 119892. 16. D. Casasent, R. Schaefer, and R. Sturgill, ‘‘Optical hit-miss morphological transform,’’ Appl. Opt. 31, 6255–6263 119922. 17. V. Kober, T. Cichocki, M. Gedziorowski, and T. Szoplik, ‘‘Opticaldigital method of local histogram calculation by threshold decomposition,’’ Appl. Opt. 32, 692–698 119932. 18. V. Kober, J. Garcia, T. Szoplik, and L. P. Yaroslavsky, ‘‘Nonlinear image processing based on optical-digital method of local histogram calculation,’’ Intl. J. Opt. Comput. 2, 367–383 119932. 19. J. Garcia, T. Szoplik, and C. Ferreira, ‘‘Optoelectronic morphological image processor,’’ Opt. Lett. 18, 1952–1954 119932. 20. J. L. Tasto and W. T. Rhodes, ‘‘Noise immunity of threshold decomposition optoelectronic order-statistic filtering,’’ Opt. Lett. 18, 1349–1351 119932. 21. Y. S. Fong, C. A. Pomalaza-Ráez, and X. H. Wang, ‘‘Comparison study of nonlinear filters in image processing applications,’’ Opt. Eng. 28, 749–760 119892. 22. W. F. Schreiber, ‘‘Wirephoto quality improvement by unsharp masking,’’ J. Pattern Recog. 2, 111–121 119702. 23. F. Meyer, ‘‘Contrast feature extraction,’’ Pract. Metallogr. 8, 374–380 119782. 24. Seiko Epson Corporation, Epson liquid-crystal video projector VP-100PS service manual 1Seiko Epson Corporation, Nagano, Japan, 19902. 25. V. Laude, S. Mazé, P. Chavel, and Ph. Réfrégier, ‘‘Amplitude and phase coding measurements of a liquid crystal television,’’ Opt. Commun. 103, 33–38 119932. 26. M. Osinski, Center for High Technology Materials, University of New Mexico, Albuquerque, N.M. 87131-6081 1personal communication2. 27. W. E. Howard, ‘‘[email protected] crystal display technology: An introduction,’’ IBM J. Res. Dev. 36112, 3–10 119922. 28. J. Knopp and M. F. Becker, ‘‘Generalized model for noncoherent optical convolvers and correlators,’’ Appl. Opt. 17, 984–985 119782. 29. K. Raj, D. W. Prather, R. A. Athale, and J. N. Mait, ‘‘Performance analysis of optical shadow-casting correlators,’’ Appl. Opt. 32, 3108–3112 119932. 30. M. Gedziorowski, T. Szoplik, and C. Ferreira, ‘‘Resolution of a lensless shadow casting correlator with partially coherent illumination,’’ Opt. Commun. 106, 167–172 119942. 31. E. J. Coyle and J.-H. Lin, ‘‘Stack filters and the mean absolute error criterion,’’ IEEE Trans. Acoust. Speech Signal Process. 36, 1244–1254 119882. 10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS 275

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

### Related manuals

Download PDF

advertisement