Bản chất của hình ảnh y sinh học (Phần 4)

4 Image Enhancement In spite of the signi cant advances made in biomedical imaging techniques over the past few decades, several practical factors often lead to the acquisition of images with less than the desired levels of contrast, visibility of detail, or overall quality In the preceding chapters, we reviewed several practical limitations, considerations, and trade-o s that could lead to poor images When the nature of the artifact that led to the poor quality of the image is known, such as noise as explained in Chapter 3, we may design speci c methods to remove or reduce the artifact When the degradation is due to a blur function, deblurring and restoration techniques, described in Chapter 10, may be applied to reverse the phenomenon In some applications of biomedical imaging, it becomes possible to include additional steps or modi cations in the imaging procedure to improve image quality, although at additional radiation dose to the subject in the case of some X-ray imaging procedures, as we shall see in the sections to follow In several situations, the understanding of the exact cause of the loss of quality is limited or nonexistent, and the investigator is forced to attempt to improve or enhance the quality of the image on hand using several techniques applied in an ad hoc manner In some applications, a nonspeci c improvement in the general appearance of the given image may su ce Researchers in the eld of image processing have developed a large repertoire of image enhancement techniques that have been demonstrated to work well under certain conditions with certain types of images Some of the enhancement techniques, indeed, have an underlying philosophy or hypothesis, as we shall see in the following sections however, the practical application of the techniques may encounter di culties due to a mismatch between the applicable conditions or assumptions and those that relate to the problem on hand A few biomedical imaging situations and applications where enhancement of the feature of interest would be desirable are: Microcalci cations in mammograms Lung nodules in chest X-ray images Vascular structure of the brain Hair-line fractures in the ribs © 2005 by CRC Press LLC 285 286 Biomedical Image Analysis Some of the features listed above could be di cult to see in the given image due to their small size, subtlety, small di erences in characteristics with respect to their surrounding structures, or low contrast others could be rendered not readily visible due to superimposed structures in planar images Enhancement of the contrast, edges, and general detail visibility in the images, without causing any distortion or artifacts, would be desirable in the applications mentioned above In this chapter, we shall explore a wide range of image enhancement techniques that can lead to improved contrast or visibility of certain image features such as edges or objects of speci c characteristics In extending the techniques to other applications, it should be borne in mind that ad hoc procedures borrowed from other areas may not lead to the best possible or optimal results Regardless, if the improvement so gained is substantial and consistent as judged by the users and experts in the domain of application, one may have on hand a practically useful technique (See the July 1972 and May 1979 issues of the Proceedings of the IEEE for reviews and articles on digital image processing, including historically signi cant images.) 4.1 Digital Subtraction Angiography In digital subtraction angiography (DSA), an X-ray contrast agent (such as an iodine compound) is injected so as to increase the density (attenuation coe cient) of the blood within a certain organ or system of interest A number of X-ray images are taken as the contrast agent spreads through the arterial network and before the agent is dispersed via circulation throughout the body An image taken before the injection of the agent is used as the \mask" or reference image, and subtracted from the \live" images obtained with the agent in the system to obtain enhanced images of the arterial system of interest Imaging systems that perform contrast-enhanced X-ray imaging (without subtraction) in a motion or cine mode are known as cine-angiography systems Such systems are useful in studying circulation through the coronary system to detect sclerosis (narrowing or blockage of arteries due to the deposition of cholesterol, calcium, and other substances) Figures 4.1 (a), (b), and (c) show the mask, live, and the result of DSA, respectively, illustrating the arterial structure in the brain of a subject 223, 224, 225] The arteries are barely visible in the live image Figure 4.1 (b)], in spite of the contrast agent Subtraction of the skull and the other parts that have remained unchanged between the mask and the live images has resulted in greatly improved visualization of the arteries in the DSA image Figure 4.1 (c)] The mathematical procedure involved may be expressed simply as f = f1 ; f2 or © 2005 by CRC Press LLC Image Enhancement 287 f (m n) = f1 (m n) ; f2 (m n) (4.1) where f1 is the live image, f2 is the mask image, and are weighting factors (if required), and f is the result of DSA The simple mathematical operation of subtraction (on a pixel-by-pixel basis) has, indeed, a signi cant application in medical imaging The technique, however, is sensitive to motion, which causes misalignment of the components to be subtracted The DSA result in Figure 4.1 (c) demonstrates motion artifacts in the lowest quarter and around the periphery of the image Methods to minimize motion artifact in DSA have been proposed by Meijering et al 223, 224, 225] Figure 4.1 (d) shows the DSA result after correction of motion artifacts Regardless of its simplicity, DSA carries a certain risk of allergic reaction, infection, and occasionally death, due to the injection of the contrast agent 4.2 Dual-energy and Energy-subtraction X-ray Imaging Di erent materials have varying energy-dependent X-ray attenuation coe cients X-ray measurements or images obtained at multiple energy levels (also known as energy-selective imaging) could be combined to derive information about the distribution of speci c materials in the object or body imaged Weighted combinations of multiple-energy images may be obtained to display soft-tissue and hard-tissue details separately 5] The disadvantages of dualenergy imaging exist in the need to subject the patient to two or more X-ray exposures (at di erent energy or kV ) Furthermore, due to the time lapse between the exposures, motion artifacts could arise in the resulting image In a variation of the dual-energy method, MacMahon 226, 227] describes energy-subtraction imaging using a dual-plate CR system The Fuji FCR 9501ES (Fuji lm Medical Systems USA, Stamford, CT) digital chest unit uses two receptor plates instead of one The plates are separated by a copper lter The rst plate acquires the full-spectrum X-ray image in the usual manner The copper lter passes only the high-energy components of the X rays on to the second plate Because bones and calcium-containing structures would have preferentially absorbed the low-energy components of the X rays, and because the high-energy components would have passed through low-density tissues with little attenuation, the transmitted high-energy components could be expected to contain more information related to denser tissues than to lighter tissues The two plates capture two di erent views derived from the same X-ray beam the patient is not subjected to two di erent imaging exposures, but only one Weighted subtraction of the two images as in Equation 4.1 provides various results that can demonstrate soft tissues or bones and calci ed tissues in enhanced detail see Figures 4.2 and 4.3 © 2005 by CRC Press LLC 288 Biomedical Image Analysis (a) (b) (c) (d) FIGURE 4.1 (a) Mask image of the head of a patient for DSA (b) Live image (c) DSA image of the cerebral artery network (d) DSA image after correction of motion artifacts Image data courtesy of E.H.W Meijering and M.A Viergever, Image Sciences Institute, University Medical Center Utrecht, Utrecht, The Netherlands Reproduced with permission from E.H.W Meijering, K.J Zuiderveld, and M.A Viergever, \Image registration for digital subtraction angiography", International Journal of Computer Vision, 31(2/3): 227 { 246, 1999 c Kluwer Academic Publishers © 2005 by CRC Press LLC Image Enhancement 289 Energy-subtraction imaging as above has been found to be useful in detecting fracture of the ribs, in assessing the presence of calci cation in lung nodules (which would indicate that they are benign, and hence, need not be examined further or treated), and in detecting calci ed pleural plaques due to prolonged exposure to asbestos 226, 227] The bone-detail image in Figure 4.3 (a) shows, in enhanced detail, a small calci ed granuloma near the lower-right corner of the image FIGURE 4.2 Full-spectrum PA chest image (CR) of a patient See also Figure 4.3 Image courtesy of H MacMahon, University of Chicago, Chicago, IL Reproduced with permission from H MacMahon, \Improvement in detection of pulmonary nodules: Digital image processing and computer-aided diagnosis", RadioGraphics, 20(4): 1169{1171, 2000 c RSNA © 2005 by CRC Press LLC 290 FIGURE 4.3 (b) (a) Bone-detail image, and (b) soft-tissue detail image obtained by energy subtraction See also Figure 4.2 Images courtesy of H MacMahon, University of Chicago, Chicago, IL Reproduced with permission from H MacMahon, \Improvement in detection of pulmonary nodules: Digital image processing and computer-aided diagnosis", RadioGraphics, 20(4): 1169{1171, 2000 c RSNA © 2005 by CRC Press LLC Biomedical Image Analysis (a) Image Enhancement 291 4.3 Temporal Subtraction Temporal or time-lapse subtraction of images could be useful in detecting normal or pathological changes that have occurred over a period of time MacMahon 226] describes and illustrates the use of temporal subtraction in the detection of lung nodules that could be di cult to see in planar chest images due to superimposed structures DR and CR imaging facilitate temporal subtraction In temporal subtraction, it is desired that normal anatomic structures are suppressed and pathological changes are enhanced Registration of the images is crucial in temporal subtraction misregistration could lead to artifacts similar to those due to motion in DSA Geometric transformation and warping techniques are useful in matching landmark features that are not expected to have changed in the interval between the two imaging sessions 223, 224, 225] Mazur et al 228] describe image correlation and geometric transformation techniques for the registration of radiographs for temporal subtraction 4.4 Gray-scale Transforms The gray-level histogram of an image gives a global impression of the presence of di erent levels of density or intensity in the image over the dynamic range available (see Section 2.7 for details and illustrations) When the pixels in a given image not make full use of the available dynamic range, the histogram will indicate low levels of occurrences of certain gray-level values or ranges The given image may also contain large areas representing objects with certain speci c ranges of gray level the histogram will then indicate large populations of pixels occupying the corresponding gray-level ranges Based upon a study of the histogram of an image, we could design gray-scale transforms or lookup tables (LUTs) that alter the overall appearance of the image, and could improve the visibility of selected details 4.4.1 Gray-scale thresholding When the gray levels of the objects of interest in an image are known, or can be determined from the histogram of the given image, the image may be thresholded to obtain a variety of images that can display selected features of interest For example, if it is known that the objects of interest in the image have gray-level values greater than L1 , we could create an image for display © 2005 by CRC Press LLC 292 Biomedical Image Analysis as n) L1 g(m n) = 0255 ifif ff ((m (4.2) m n) L1 where f (m n) is the original image g(m n) is the thresholded image to be displayed and the display range is 255] The result is a bilevel or binary image Thresholding may be considered to be a form of image enhancement in the sense that the objects of interest are perceived better in the resulting image The same operation may also be considered to be a detection operation see Section 5.1 If the values less than L1 were to be considered as noise (or features of no interest), and the gray levels within the objects of interest that are greater than L1 are of interest in the displayed image, we could also de ne the output image as n) L1 g(m n) = 0f (m n) ifif ff ((m (4.3) m n) L : The resulting image will display the features of interest including their graylevel variations Methods for the derivation of optimal thresholds are described in Sections 5.4.1, 8.3.2, and 8.7.2 Example: A CT slice image of a patient with neuroblastoma is shown in Figure 4.4 (a) A binarized version of the image, with thresholding as in Equation 4.2 using L1 = 200 HU , is shown in part (b) of the gure As expected, the bony parts of the image appear in the result however, the calci ed parts of the tumor, which also have high density comparable to that of bone, appear in the result The result of thresholding the image as in Equation 4.3 with L1 = 200 HU is shown in part (c) of the gure The relative intensities of the hard bone and the calci ed parts of the tumor are evident in the result 4.4.2 Gray-scale windowing If a given image f (m n) has all of its pixel values in a narrow range of gray levels, or if certain details of particular interest within the image occupy a narrow range of gray levels, it would be desirable to stretch the range of interest to the full range of display available In the absence of reason to employ a nonlinear transformation, a linear transformation as follows could be used for this purpose: 80 < f (m n);f if f (m n) f1 (4.4) g(m n) = : f2;f1 if f1 < f (m n) < f2 if f (m n) f2 where f (m n) is the original image g(m n) is the windowed image to be displayed, with its gray-scale normalized to the range 1] and f1 f2 ] is the range of the original gray-level values to be displayed in the output after © 2005 by CRC Press LLC Image Enhancement 293 (a) (b) (c) (d) FIGURE 4.4 (a) CT image of a patient with neuroblastoma The tumor, which appears as a large circular region on the left-hand side of the image, includes calci ed tissues that appear as bright regions The range of ;200 400] has been linearly mapped to the display range of 255] see also Figures 2.15 and 2.16 Image courtesy of Alberta Children's Hospital, Calgary (b) The image in (a) thresholded at the level of 200 as in Equation 4.2 Values above 200 appear as white, and values below this threshold appear as black (c) The image in (a) thresholded at the level of 200 as in Equation 4.3 Values above 200 appear at their original level, and values below this threshold appear as black (d) The range of 400] has been linearly mapped to the display range of 255] as in Equation 4.4 Pixels corresponding to tissues lighter than water appear as black Pixels greater than 400 are saturated at the maximum gray level of 255 HU HU HU HU HU HU HU © 2005 by CRC Press LLC 294 Biomedical Image Analysis stretching to the full range Note that the range 1] in the result needs to be mapped to the display range available, such as 255], which is achieved by simply multiplying the normalized values by 255 Details (pixels) below the lower limit f1 will be eliminated (rendered black) and those above the upper limit f2 will be saturated (rendered white) in the resulting image The details within the range f1 f2 ] will be displayed with increased contrast and latitude, utilizing the full range of display available Example: A CT slice image of a patient with neuroblastoma is shown in Figure 4.4 (a) This image displays the range of ;200 400] HU linearly mapped to the display range of 255] as given by Equation 4.4 The full range of HU values in the image is ;1000 1042] HU Part (d) of the gure shows another display of the same original data, but with mapping of the range 400] HU to 255] as given by Equation 4.4 In this result, pixels corresponding to tissues lighter than water appear as black pixels greater than 400 HU are saturated at the maximum gray level of 255 Gray-level thresholding and mapping are commonly used for detailed interpretation of CT images Example: Figure 4.5 (a) shows a part of the chest X-ray image in Figure 1.11 (b), downsampled to 512 512 pixels The histogram of the image is shown in Figure 4.6 (a) observe the large number of pixels with the gray level zero Figure 4.6 (b) shows two linear gray-scale transformations (LUTs) that map the range 0:6] (dash-dot line) and 0:2 0:7] (solid line) to the range 1] the results of application of the two LUTs to the image in Figure 4.5 (a) are shown in Figures 4.5 (b) and (c), respectively The image in Figure 4.5 (b) shows the details in and around the heart with enhanced visibility however, large portions of the original image have been saturated The image in Figure 4.5 (c) provides an improved visualization of a larger range of tissues than the image in (b) regardless, the details with normalized gray levels less than 0:2 and greater than 0:7 have been lost Example: Figure 4.7 (a) shows an image of a myocyte Figure 4.8 (a) shows the normalized histogram of the image Most of the pixels in the image have gray levels within the limited range of 50 150] the remainder of the available range 255] is not used e ectively Figure 4.7 (b) shows the image in (a) after the normalized gray-level range of 0:2 0:6] was stretched to the full range of 1] by the linear transformation in Equation 4.4 The details within the myocyte are visible with enhanced clarity in the transformed image The corresponding histogram in Figure 4.8 (b) shows that the image now occupies the full range of gray scale available however, several gray levels within the range are unoccupied, as indicated by the white stripes in the histogram 4.4.3 Gamma correction Figure 2.6 shows the H-D curves of two devices The slope of the curve is known as An imaging system with a large could lead to an image with © 2005 by CRC Press LLC Image Enhancement 347 (a) (b) (c) (d) FIGURE 4.40 (a) Part of a mammogram with a cluster of calci cations, true size 43 43 mm Results of enhancement by (b) adaptive-neighborhood contrast enhancement (c) gamma correction and (d) unsharp masking See also Figures 4.37 and 4.41 Reproduced with permission from W.M Morrow, R.B Paranjape, R.M Rangayyan, and J.E.L Desautels, \Region-based contrast enhancement of mammograms" IEEE Transactions on Medical Imaging, 11(3):392{406, 1992 c IEEE © 2005 by CRC Press LLC 348 Biomedical Image Analysis FIGURE 4.41 Result of enhancement of the image in Figure 4.40 (a) by global histogram equalization applied to the entire image See also Figures 4.37 and 4.40 Reproduced with permission from W.M Morrow, R.B Paranjape, R.M Rangayyan, and J.E.L Desautels, \Region-based contrast enhancement of mammograms," IEEE Transactions on Medical Imaging, 11(3):392{406, 1992 c IEEE (a) FIGURE 4.42 (b) (a) Part of a mammogram with dense masses, true size 43 43 mm (b) Result of enhancement by adaptive-neighborhood contrast enhancement Reproduced with permission from W.M Morrow, R.B Paranjape, R.M Rangayyan, and J.E.L Desautels, \Region-based contrast enhancement of mammograms," IEEE Transactions on Medical Imaging, 11(3):392{406, 1992 c IEEE © 2005 by CRC Press LLC Image Enhancement 349 (a) (b) FIGURE 4.43 (a) Part of a mammogram with a benign cyst, true size 43 43 mm (b) Result of enhancement by adaptive-neighborhood contrast enhancement Reproduced with permission from W.M Morrow, R.B Paranjape, R.M Rangayyan, and J.E.L Desautels, \Region-based contrast enhancement of mammograms," IEEE Transactions on Medical Imaging, 11(3):392{406, 1992 c IEEE to enhancement, the contrast histogram of the enhanced image should contain more counts of regions at higher contrast levels than the contrast histogram of the original image Various enhancement methods can be quantitatively compared by measuring the properties of their respective contrast histograms The spread of a contrast histogram may be quanti ed by taking the second moment about the zero-contrast level For a distribution of contrast values ci , quantized so that there are N bins over the range ;1 1], the second moment M2 is M2 = N X i=1 ci2 p(ci) (4.31) where p(ci ) is the normalized number of occurrences of seed pixels (including redundant seed pixels) that lead to the growth of a region with contrast ci A low-contrast image, that is, an image with a narrow contrast histogram, will have a low value for M2 an image with high contrast will have a broader contrast histogram, and hence a greater value of M2 For the purpose described above, image contrast needs to be recomputed after the entire image has been enhanced, because the relative contrast between adjacent regions is dependent upon the changes made to each of the regions In order to measure the contrast in an image after enhancement, region growing (using the same parameters as in the enhancement procedure) © 2005 by CRC Press LLC 350 Biomedical Image Analysis is performed on the output enhanced image, and a contrast histogram is generated In general, the nal contrast values in the output image of adaptive-neighborhood contrast enhancement will not match the contrast values speci ed by the contrast transformation in Equation 4.30 This is because Equation 4.30 is applied pixel-by-pixel to the input image, and the adaptive neighborhood for each pixel will vary Only if all the pixels in an object have exactly the same gray-level value will they all have exactly the same adaptive neighborhood and be transformed in exactly the same way Thus, the contrast enhancement curve is useful for identifying the ranges in which contrast enhancement is desired, but cannot specify the nal contrast of the regions The contrast of each region grown in the image is dependent on the value speci ed by the initial region contrast and the transformation curve, as well as the transformation applied to adjacent regions Figure 4.44 shows the contrast histograms of the complete mammograms corresponding to the images in Figure 4.40 The contrast distribution is plotted on a logarithmic scale in order to emphasize the small numbers of occurrence of features at high contrast values The wider distribution and greater occurrence of regions at high contrast values in the histogram of the adaptive-neighborhood enhanced image show that it has higher contrast The histograms of the results of gamma correction and unsharp masking also show some increase in the counts for larger contrast values than that of the original, but not to the same extent as the result of adaptive-neighborhood contrast enhancement The values of M2 for the four histograms in Figure 4.44 are 3:71 10;4 , 6:17 10;4 , 3:2 10;4 , and 4:4 10;4 The contrast histogram and its statistics provide objective means for the analysis of image enhancement 4.11 Application: Contrast Enhancement of Mammograms The accurate diagnosis of breast cancer depends upon the quality of the mammograms obtained in particular, the accuracy of diagnosis depends upon the visibility of small, low-contrast objects within the breast image Unfortunately, the contrast between malignant tissue and normal tissue is often so low that the detection of malignant tissue becomes di cult Hence, the fundamental enhancement needed in mammography is an increase in contrast, especially for dense breasts Dronkers and Zwaag 248] suggested the use of reversal lm rather than negative lm for the implementation of a form of photographic contrast enhancement for mammograms They found that the image quality produced © 2005 by CRC Press LLC Image Enhancement 351 4.5 log10 (number of regions) 3.5 2.5 1.5 0.5 −0.2 −0.15 −0.1 −0.05 0.05 adaptive−neighborhood contrast value 0.1 0.15 0.2 0.1 0.15 0.2 (a) 4.5 log10 (number of regions) 3.5 2.5 1.5 0.5 −0.2 −0.15 −0.1 −0.05 0.05 adaptive−neighborhood contrast value Figure 4.44 (b) © 2005 by CRC Press LLC 352 Biomedical Image Analysis 4.5 log10 (number of regions) 3.5 2.5 1.5 0.5 −0.2 −0.15 −0.1 −0.05 0.05 adaptive−neighborhood contrast value 0.1 0.15 0.2 0.1 0.15 0.2 (c) 4.5 log10 (number of regions) 3.5 2.5 1.5 0.5 −0.2 −0.15 −0.1 −0.05 0.05 adaptive−neighborhood contrast value (d) FIGURE 4.44 Contrast histograms of the full mammograms corresponding to the images in Figure 4.40 (a) Original, = 71 10;4 (b) adaptive-neighborhood contrast enhancement, = 17 10;4 (c) gamma correction, = 10;4 and (d) unsharp masking, = 4 10;4 Reproduced with permission from W.M Morrow, R.B Paranjape, R.M Rangayyan, and J.E.L Desautels, \Region-based contrast enhancement of mammograms," IEEE Transactions on Medical Imaging, 11(3):392{406, 1992 c IEEE M M : : M © 2005 by CRC Press LLC M : : Image Enhancement 353 was equal to that of conventional techniques without the need for special mammographic equipment A photographic unsharp-masking technique for mammographic images was proposed by McSweeney et al 249] This procedure includes two steps: rst, a blurred image is produced by copying the original mammogram through a sheet of glass or clear plastic that di uses the light then, by using subtraction print lm, the nal image is formed by subtracting the blurred image from the original mammogram Although the photographic technique improved the visualization of mammograms, it was not widely adopted, possibly due to the variability in the image reproduction procedure Askins et al 250] investigated autoradiographic enhancement of mammograms by using thiourea labeled with 35 S Mammograms underexposed as much as tenfold could be autoradiographically intensi ed so that the enhanced image was comparable to a normally exposed lm The limitations to routine use of autoradiographic techniques include cost, processing time, and the disposal of radioactive solutions Digital image enhancement techniques have been used in radiography for more than three decades (See Bankman 251] for a section including discussions on several enhancement techniques.) Ram 252] stated that images considered unsatisfactory for medical analysis may be rendered usable through various enhancement techniques, and further indicated that the application of such techniques in a clinical situation may reduce the radiation dose by about 50% Rogowska et al 253] applied digital unsharp masking and local contrast stretching to chest radiographs, and reported that the quality of images was improved Chan et al 254] investigated unsharp-mask ltering for digital mammography: according to their receiver operating characteristics (ROC) studies, unsharp masking could improve the detectability of calci cations on digital mammograms However, this method also increased noise and caused some artifacts Algorithms based on adaptive-neighborhood image processing to enhance mammographic contrast were rst reported on by Gordon and Rangayyan 242] Rangayyan and Nguyen 243] de ned a tolerance-based method for growing foreground regions that could have arbitrary shapes rather than square shapes Morrow et al 215, 123] further developed this approach with a new de nition of background regions Dhawan et al 247] p investigated the bene ts of various contrast transfer functions, including C , ln(1 + 3C ), ; e;3C , and tanh(3C ), where C is the original contrast, but used square adaptive neighborhoods They found that while a suitable contrast function was important to bring out the features of interest in mammograms, it was di cult to select such a function Later, Dhawan and Le Royer 255] proposed a tunable contrast enhancement function for improved enhancement of mammographic features Emphasis has recently been directed toward image enhancement based upon the characteristics of the human visual system 256], leading to innovative methods using nonlinear lters, scale-space lters, multiresolution lters, and © 2005 by CRC Press LLC 354 Biomedical Image Analysis wavelet transforms Attention has been paid to designing algorithms to enhance the contrast and visibility of diagnostic features while maintaining control on noise enhancement Laine et al 257] presented a method for nonlinear contrast enhancement based on multiresolution representation and the use of dyadic wavelets A software package named MUSICA 258] (MUlti-Scale Image Contrast Ampli cation) has been produced by Agfa-Gevaert Belikova et al 259] discussed various optimal lters for the enhancement of mammograms Qu et al 260] used wavelet techniques for enhancement and evaluated the results using breast phantom images Tahoces et al 261] presented a multistage spatial ltering procedure for nonlinear contrast enhancement of chest and breast images Qian et al 262] reported on tree-structured nonlinear lters based on median lters and an edge detector Chen et al 263] proposed a regional contrast enhancement technique based on unsharp masking and adaptive density shifting The various mammogram enhancement algorithms that have been reported in the literature may be sorted into three categories: algorithms based on conventional image processing methods 253, 254, 259, 261, 264, 265] adaptive algorithms based on the principles of human visual perception 123, 242, 247, 255, 256, 263, 266] and multiresolution enhancement algorithms 257, 260, 262, 267, 268, 269, 270] In order to evaluate the diagnostic utility of an enhancement algorithm, an ROC study has to be conducted however, few of the above-mentioned methods 254, 264, 266, 267, 271] have been tested with ROC procedures see Sections 12.8.1 and 12.10 for details on ROC analysis 4.11.1 Clinical evaluation of contrast enhancement In order to examine the di erences in radiological diagnoses that could result from adaptive-neighborhood enhancement of mammograms, eight test cases from the teaching library of the Foothills Hospital (Calgary, Alberta, Canada) were studied in the work of Morrow et al 123] For each of the cases, the pathology was known due to biopsy or other follow-up procedures For each case, a single mammographic lm that presented the abnormality was digitized using an Eikonix 1412 scanner (Eikonix Inc., Bedford, MA) to 096 by about 048 pixels with 12-bit gray-scale resolution (The size of the digitized image di ered from lm to lm depending upon the the size of the actual image in the mammogram.) The e ective pixel size was about 0:054 mm 0:054 mm Films were illuminated by a Plannar 1417 light box (Gordon Instruments, Orchard Park, NY) Although the light box was designed to have a uniform light intensity distribution, it was necessary to correct for nonuniformities in illumination After correction, pixel gray levels were determined to be accurate to 10 bits, with a dynamic range of approximately 0:02 ; 2:52 OD 174] The images were enhanced using the adaptive-neighborhood contrast enhancement method For all images, the tolerance for region growing was set at 0:05, the width of the background was set to three pixels, and the enhance© 2005 by CRC Press LLC Image Enhancement 355 ment curve used was that presented in Figure 4.39 The original and processed images were down-sampled by a factor of two for processing and display for interpretation on a MegaScan 2111 monitor (Advanced Video Products Inc., Littleton, MA) Although the memory bu er of the MegaScan system was of size 096 096 12 bits, the display bu er was limited to 560 048 bits, with panning and zooming facilities The monitor displayed images at 72 noninterlaced frames per second In each case, the original, digitized mammogram was rst presented on the MegaScan 2111 monitor The image occupied about 20 15 cm on the screen An experienced radiologist, while viewing the digitized original, described the architectural abnormalities that were observed Subsequently, the enhanced image was added to the display While observing both the enhanced mammogram and the original mammogram together, the radiologist described any new details or features that became apparent Case (1) was that of a 62-year-old patient with a history of di use nodularity in both breasts The MLO view of the left breast was digitized for assessment The unenhanced mammogram revealed two separate nodular lesions: one with well-de ned boundaries, with some indication of lobular calcium the other smaller, with poorly de ned borders, some spiculation, but no microcalci cations The unenhanced mammogram suggested that the smaller lesion was most likely associated with carcinoma however, there was some doubt about the origins of the larger lesion An examination of the enhanced mammogram revealed de nite calcium deposits in the larger lesion and some indication of microcalci cations in the smaller lesion The enhanced image suggested carcinoma as the origin of both lesions more strongly than the unenhanced mammogram The biopsy report for both areas indicated intraductal in ltrating carcinoma, rming the diagnosis from the enhanced mammogram Case (2) was that of a 64-year-old patient The digitized original mammogram was the CC view of the left breast The unenhanced mammogram contained two lesions The lesion in the lower-outer part of the breast had irregular edges and coarse calci cations, whereas the other lesion appeared to be a cyst Examination of the unenhanced mammogram suggested that both lesions were benign Examination of the enhanced mammogram revealed no additional details that would suggest a change in the original diagnosis The appearance of the lesions was not much di erent from that seen in the unenhanced mammogram however, the details in the internal architecture of the breast appeared clearer, adding further weight to the diagnosis of benign lesions Excision biopsies carried out at both sites rmed this diagnosis Case (3) was that of a 44-year-old patient, for whom the MLO view of the left breast was digitized The original digitized mammogram revealed multiple benign cysts as well as a spiculated mass in the upper-outer quadrant of the breast There was some evidence of calcium, but it was di cult to rm the same by visual inspection A dense nodule was present adjacent to the spiculated mass Examination of the enhanced mammogram revealed that the © 2005 by CRC Press LLC 356 Biomedical Image Analysis spiculated mass did contain microcalci cations The dense nodule appeared to be connected to the spiculated mass, suggesting a further advanced carcinoma than that suspected from the unenhanced mammogram Biopsy reports were available only for the spiculated region, and indicated lobular carcinoma No further information was available to verify the modi ed diagnosis from the enhanced mammogram Case (4) was that of a 40-year-old patient, whose mammograms indicated dense breasts The image of the right breast indicated an area of uniform density The CC view of the right breast was digitized and enhanced The digitized original mammogram indicated a cluster of microcalci cations, all of approximately uniform density, centrally located above the nipple The enhanced mammogram indicated a similar nding with a larger number of microcalci cations visible, and some irregularity in the density of the calci cations Both the original and the enhanced mammograms suggested a similar diagnosis of intraductal carcinoma Biopsy of the suspected area rmed this diagnosis Case (5) was that of a 64-year-old patient with a history of a benign mass in the right breast A digitized mammogram of the CC view of the right breast was examined The unenhanced mammogram clearly showed numerous microcalci cations that were roughly linear in distribution, with some variation in density The original mammogram clearly suggested intraductal carcinoma The enhanced mammogram showed a greater number of calci cations, indicating a lesion of larger extent The variation in the density of the calci cations was more evident Biopsy indicated an in ltrating ductal carcinoma Case (6) was that of a 59-year-old patient whose right CC view was digitized The original mammogram indicated a poorly de ned mass with some spiculations The lesion was irregular in shape, and contained some calcium The unenhanced mammogram suggested intraductal carcinoma The enhanced mammogram provided stronger evidence of carcinoma with poor margins of the lesion, a greater number of microcalci cations, and inhomogeneity in the density of the calci cations Biopsy rmed the presence of the carcinoma Case (7) involved the same patient as in Case (6) however, the mammogram was taken one year after that described in Case (6) The digitized mammogram was the CC view of the right breast The unenhanced view showed signi cant architectural distortion due to segmental mastectomy The unenhanced mammogram showed an area extending past the scarred region of fairly uniform density with irregular boundaries The unenhanced mammogram along with the patient's history suggested the possibility of cancer, and biopsy was recommended The enhanced mammogram suggested a similar nding, with added evidence of some small microcalci cations in the uniform area Biopsy of the region showed that the mass was, in fact, a benign hematoma Case (8) was that of an 86-year-old patient the MLO view of the left breast was digitized In the unenhanced mammogram, a dense region was observed © 2005 by CRC Press LLC Image Enhancement 357 with some spiculations The mammogram suggested the possibility of carcinoma and biopsy was recommended The enhanced mammogram showed the same detail as the unenhanced mammogram, with the additional nding of some microcalci cations this added to the suspicion of cancer The biopsy of the region indicated intraductal invasive carcinoma with lymph-node metastasis present In each of the eight cases described above, the overall contrast in the enhanced mammogram was signi cantly improved This allowed the radiologist to comment that \much better overall anatomical detail" was apparent in the enhanced mammograms, and that \overall detail (internal architecture) is improved" in the enhanced mammograms In all cases, the radiological diagnosis was rmed by biopsy In seven of the eight cases, the enhanced mammogram added further weight to the diagnosis made from the original mammogram, and the diagnosis was rmed by biopsy In one case, the enhanced mammogram as well as the unenhanced mammogram suggested the possibility of carcinoma however, the biopsy report indicated a benign condition This case was, however, complicated by the fact that the patient's history in uenced the radiologist signi cantly While it is not possible to make a quantitative assessment of the di erences in diagnoses from the qualitative comparison as above, it appeared that a clearer indication of the patient's condition was obtained by examination of the enhanced mammogram The adaptive-neighborhood contrast enhancement method was used in a preference study comparing the performance of enhancement algorithms by Sivaramakrishna et al 125] The other methods used in the study were adaptive unsharp masking, contrast-limited adaptive histogram equalization, and wavelet-based enhancement The methods were applied to mammograms of 40 cases, including 10 each of benign and malignant masses, and 10 each of benign and malignant microcalci cations The four enhanced images and the original image of each case were displayed randomly across three highresolution monitors Four expert mammographers ranked the images from (best) to (worst) In a majority of the cases with microcalci cations, the adaptive-neighborhood contrast enhancement algorithm provided the mostpreferred images In the set of images with masses, the unenhanced images were preferred in most of the cases See Sections 12.8.1, 12.8.2, and 12.10 for discussions on statistical analysis of the clinical outcome with enhanced mammograms 4.12 Remarks Quite often, an image acquired in a real-life application does not have the desired level of quality in terms of contrast, sharpness of detail, or the visibility © 2005 by CRC Press LLC 358 Biomedical Image Analysis of the features of interest We explored several techniques in this chapter that could assist in improving the quality of a given image The class of lters based upon mathematical morphology 8, 192, 220, 221, 222] has not been dealt with in this chapter An understanding of the exact phenomenon that caused the poor quality of the image at the outset could assist in the design of an appropriate technique to address the problem However, in the absence of such information, one could investigate the suitability of existing and established models of degradation, as well as the associated enhancement techniques to improve the quality of the image on hand It may be desirable to obtain several enhanced versions using a variety of approaches the most suitable image may then be selected from the collection of the processed images for further analysis In situations as above, there is no single or optimal solution to the problem Several enhanced versions of the given image may also be analyzed simultaneously however, this approach could demand excessive time and resources, and may not be feasible in a large-scale screening application Given the subjective nature of image quality, and in spite of the several methods we studied in Chapter to characterize image quality and information content, the issue of image enhancement is nonspeci c and elusive Regardless, if a poor-quality image can be enhanced to the satisfaction of the user, and if the enhanced image leads to improved analysis | and more accurate or dent diagnosis in the biomedical context | an important achievement could result The topic of image restoration | image quality improvement when the exact cause of degradation is known and can be represented mathematically | is investigated in Chapter 10 4.13 Study Questions and Problems (Note: Some of the questions may require background preparation with other sources on the basics of signals and systems as well as digital signal and image processing, such as Lathi 1], Oppenheim et al 2], Oppenheim and Schafer 7], Gonzalez and Woods 8], Pratt 10], Jain 12], Hall 9], and Rosenfeld and Kak 11].) Selected data les related to some of the problems and exercises are available at the site www.enel.ucalgary.ca/People/Ranga/enel697 A poorly exposed image was found to have gray levels limited to the range 25 ; 90 Derive a linear transform to stretch this range to the display range of ; 255 Give the display values for the original gray levels of 45 and 60 © 2005 by CRC Press LLC Image Enhancement 359 Explain the di erences between the Laplacian and subtracting Laplacian operators in the spatial and frequency domains Compute by hand the result of linear convolution of the following two images: 3555 66 0 77 66 4 77 42 2 25 2222 and (4.32) 351 44 35: (4.33) 132 Explain the di erences between the 3 mean and median lters Would you be able to compare the lters in the Fourier domain? Why (not)? Derive the frequency response of the 3 unsharp masking lter and explain its characteristics An image has a uniform PDF (normalized gray-level histogram) over the range 255] A novice researcher derives the transform to perform histogram equalization Derive an analytical representation of the transform Explain its e ects on the image in terms of the modi cation of gray levels and the histogram An image has a uniform PDF (normalized gray-level histogram) over the range 25 90] with the probability being zero outside this interval within the available range of 255] Derive an analytical representation of the transform to perform histogram equalization Explain its e ects on the image in terms of the modi cation of gray levels and the histogram Give an algorithmic representation of the method to linearly map a selected range of gray-level values ] to the range ] in an image of size Values below are to be mapped to , and values above mapped to Use pseudocode format and show all the necessary programming steps and details An 8 image with an available gray-level range of ; at bits/pixel has the following pixel values: 35554443 66 3 5 3 77 66 0 4 4 77 64 5 2 (4.34) 666 4 3 3 777 66 2 2 1 77 42 2 1 1 22221111 Derive the transformation and look-up table for enhancement of the image by histogram equalization Clearly show all of the steps involved, and give the : x x x y y y : © 2005 by CRC Press LLC M x N y 360 10 Biomedical Image Analysis pixel values in the enhanced image using the available gray-level range of bits/pixel Draw the histograms of the original image and the enhanced image Explain the di erences between them as caused by histogram equalization Write the expression for the convolution of an digital image with an digital image (or lter function) with Using pseudocode format, show all of the necessary programming steps and details related to the implementation of convolution as above Explain how you handle the size and data at the edges of the resulting image Prepare a 5 image with zero pixel values Add a square of size 3 pixels with the value 100 at the center of the image Apply (a) the subtracting Laplacian operator, and (b) the Laplacian operator to the image Examine the pixel values inside and around the edges of the square in the resulting images Give reasons for the e ects you nd Apply (a) the subtracting Laplacian operator, and (b) the Laplacian operator to the image in Equation 4.34 Give reasons for the e ects you nd Derive the MTF of the 3 unsharp masking operator Explain its characteristics An image is processed by applying the subtracting Laplacian mask and then by applying the 3 mean lter mask What is the impulse response of the complete system? What is the MTF of the complete system? Explain the e ect of each operator Derive the MTF of the 3 subtracting Laplacian operator and explain its characteristics What causes ringing artifact in frequency-domain ltering? How you prevent the artifact? Discuss the di erences between highpass ltering and high-frequency emphasis ltering in the frequency domain in terms of their (a) transfer functions, and (b) e ects on image features List the steps of computation required in order to perform lowpass ltering of an image in the frequency domain by using the Fourier transform N M 11 12 13 14 15 16 17 18 M © 2005 by CRC Press LLC M N N Image Enhancement 4.14 Laboratory Exercises and Projects 361 Select two underexposed images, or images with bright and dark regions such that the details in some parts are not clearly visible, from your collection Apply histogram equalization, gamma adjustment, and linear gray-level mapping transforms to the images Compare the results in terms of the enhancement of the visibility of details, saturation or loss of details at the high or low ends of the gray scale, and overall visual quality Plot the histograms of the resulting images and compare them with the histograms of the original images Comment upon the di erences Select two images from your collection, with one containing relatively sharp and well-de ned edges, and the other containing smooth features Apply the unsharp masking lter, the Laplacian operator, and the subtracting Laplacian lter to the images Study the results in terms of edge enhancement Create noisy versions of the images by adding Gaussian noise Apply the enhancement methods as above to the noisy images Study the results in terms of edge enhancement and the e ect of noise Select two images from your collection, with one containing relatively sharp and well-de ned edges, and the other containing smooth features Apply the ideal highpass lter, the Butterworth highpass lter, and the Butterworth high-emphasis lter to the images Use at least two di erent cuto frequencies Study the results in terms of edge enhancement or edge extraction Create noisy versions of the images by adding Gaussian noise Apply the lters as above to the noisy images Study the results in terms of edge enhancement or extraction and the e ect of noise © 2005 by CRC Press LLC [...]... (4.17) In the initial state at t = 0, we have g(x y 0) = f (x y) , the original image At some time instant t = > 0, the degraded image g(x y ) is observed The degraded image may be expressed in a Taylor series as 2 @2g ( x y ) ; (4.18) g(x y ) = g(x y 0) + @g @t 2 @t2 (x y ) + : Ignoring the quadratic and higher-order terms, letting g(x y 0) = f (x y) , and using the di usion model in Equation 4.16,... practice Difculty arises in the very rst step of specifying a meaningful histogram or © 2005 by CRC Press LLC Image Enhancement 309 0.09 0.08 Probability of occurrence 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0 50 100 150 200 250 150 Input gray level 200 250 Gray level (a) 250 Output gray level 200 150 100 50 0 50 100 (b) FIGURE 4.17 (a) Normalized histogram of the histogram-equalized myocyte image in Figure... transformation may yield values of sk that may not equal the sk = T (rk ) = k X pf (ri) = available quantized gray levels The values will have to be quantized, and hence the output image may only have an approximately uniform histogram In practical applications, the resulting values in the range 0 1] have to be scaled to the display range, such as 0 255] Histogram equalization is usually implemented via... bits, respectively 4.5.2 Histogram speci cation A major limitation of histogram equalization is that it can provide only one output image, which may not be satisfactory in many cases The user has © 2005 by CRC Press LLC 306 Biomedical Image Analysis (a) (b) FIGURE 4.14 (a) Part of a chest X-ray image The histogram of the image is shown in Figure 4.6 (a) (b) Image in (a) enhanced by histogram equalization... Analysis (a) (b) (c) (d) FIGURE 4.21 (a) Image of a myocyte the range from the minimum to the maximum of the image has been linearly mapped to the display range 0 255] (b) Result of unsharp masking display range ;20 180] out of ;47 201] (c) Laplacian (gradient) of the image display range ;20 20] out of ;152 130] (d) Result of the subtracting Laplacian display range ;50 200] out of ;130 282] © 2005 by... with = 0:3 and = 2:0, respectively The two results demonstrate enhanced visibility of details in the darker and lighter gray-scale regions (with reference to the original image) © 2005 by CRC Press LLC 298 Biomedical Image Analysis 0.09 0.08 Probability of occurrence 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0 50 100 150 200 250 150 200 250 Gray level (a) 0.09 0.08 Probability of occurrence 0.07 0.06 0.05... Press LLC Image Enhancement (a) 297 (b) FIGURE 4.7 (a) Image of a myocyte as acquired originally (b) Image in (a) enhanced by linear mapping of the normalized range 0:2 0:6] to 0 1] See Figure 4.8 for the histograms of the images high contrast however, the image may not utilize the full range of the available gray scale On the other hand, a system with a small could result in an image with wide latitude... correction with = 0:3 Image courtesy of W.M Morrow 215, 230] Example: Figure 4.14 (a) shows a part of a chest X-ray image part (b) of the same gure shows the corresponding histogram-equalized image Al© 2005 by CRC Press LLC 304 Biomedical Image Analysis 0.03 Probability of occurrence 0.025 0.02 0.015 0.01 0.005 0 0 50 100 150 200 250 150 200 250 Gray level (a) 0.03 Probability of occurrence 0.025 0.02 0.015... nonlinear transformation process by which we may alter the transition from one gray level to the next, and change the contrast and latitude of gray scale in the image The transformation may be expressed as 203] g(m n) = f (m n)] (4.5) where f (m n) is the given image with its gray scale normalized to the range 0 1], and g(m n) is the transformed image (Note: Lindley 229] provides a di erent de nition... Then, by specifying several histograms, it is possible to obtain a range of enhanced images, from which one or more may be selected for further analysis or use Suppose that the desired or speci ed normalized histogram is pd (t), with the desired image being represented as d, having the normalized gray levels t = 0 1 2 : : : L ; 1 Now, the given image f with the PDF pf (r) may be histogram-equalized by the