Unit 2. Image Enhancement in Spatial Domain.pptx

Unit 2. Image Enhancement in Spatial Domain

1. Unit No. 2 Image Enhancement in Spatial Domain Dr. S. M. Karve Assistant Professor Dept. of Electronics & Telecommunication Engineering

2. Image Enhancement Definition Image Enhancement: is the process that improves the quality of the image for a specific application

3. Image Enhancement Methods Spatial Domain Methods (Image Plane) Techniques are based on direct manipulation of pixels in an image Frequency Domain Methods Techniques are based on modifying the Fourier transform of the image. Combination Methods There are some enhancement techniques based on various combinations of methods from the first two categories

4. E nh a nce m e n t Techniques Spatial Operates on pixels Frequency Domain Operates on FT of Image

5. Spatial domain Methods  The simplest form of T is when the neighbourhood is of size 1x1, that is a single pixel.  Then g depends only on the value of f, at (x,y) or the gray level f(x,y), and T becomes a gray level transformation function of the form  s = T(r). s – Output gray level of g(x,y) r – Input gray level of f(x,y) at any point (x,y)   This type of processing is known as point processing , because the processing depends only on the gray level at that point.

6. When T operates on the neighbourhood of f(x,y), the processing is done by the use of masks (say a 3x3 2-D array) and is known as mask processing. The mask coefficients determine the nature of process. Spatial domain Methods

7. Point Operation Operation deals with pixel intensity values individually. The intensity values are altered using particular transformation techniques as per the requirement. The transformed output pixel value does not depend on any of the neighbouring pixel value of the input image. Examples: Image Negative. Contrast Stretching. Thresholding. Brightness Enhancement . 3

8. Examples of Enhancement Techniques • Contrast Stretching : If T(r) has the form as shown in the figure below, the effect of applying the transformation to every pixel of f to generate the corresponding pixels in g would: Produce higher contrast than the original image, by: Darkening the levels below m in the original image Brightening the levels above m in the original image So, Contrast Stretching: is a simple image enhancement technique that improves the contrast in an image by ‘stretching’ the range of intensity values it contains to span a desired range of values. Typically, it uses a linear function

9. Examples of Enhancement Techniques • Thresholding I s a l i m i t e d ca se o f c on t r a st s t r e t c h i n g , it p r o d uc e s a t w o - l e v e l (binary) image. Some fairly simple, yet powerful, processing approaches can be formulated with grey-level transformations. Because enhancement at any point in an image depends only on the gray level at that point, techniques in this category often are referred to as point processing .

10. Basic Intensity ( Gray-level) Transformation Functions • Grey-level transformation functions (also called, intensity functions), are considered the simplest of all image enhancement techniques. The value of pixels, before and after processing, will be denoted by r and s , respectively. These values are related by the expression of the form: s = T (r) where T is a transformation that maps a pixel value r into a pixel value s. • •

11. Consider the following figure, which shows three basic types of functions used frequently for image enhancement: Basic Intensity (Gray-level) Transformation Functions

12. Basic Intensity (Gray-level) Transformation Functions • The three basic types of functions used frequently for image enhancement: Linear Functions: Negative Transformation Identity Transformation Logarithmic Functions: Log Transformation Inverse-log Transformation Power-Law Functions: n th power transformation n th root transformation

13. Linear Functions Identity Function Output intensities are identical to input intensities This function doesn’t have an effect on an image, it was included in the graph only for completeness Its expression: s = r

14. Linear Functions • Image Negatives (Negative Transformation) – The negative of an image with gray level in the range [0, L-1], where L = Largest value in an image, is obtained by using the negative transformation’s expression: s = L – 1 – r W h i c h r e v e r se s t h e i n t e n s i t y l e v e ls o f a n i np u t i m a g e , i n t h is manner produces the equivalent of a photographic negative. – The negative transformation is suitable for enhancing white or gray detail embedded in dark regions of an image, especially when the black area are dominant in size

15. Image Negatives

16. Logarithmic Transformations • Log Transformation The general form of the log transformation: s = c log (1+r) Where c is a constant, and r ≥ Log curve maps a narrow range of low gray-level values in the input image into a wider range of the output levels. Used to expand the values of dark pixels in an image while compressing the higher-level values. It compresses the dynamic range of images with large variations in pixel values.

17. Logarithmic Transformations

18. Logarithmic Transformations • Inverse Logarithm Transformation Do opposite to the log transformations Used to expand the values of high pixels in an image while compressing the darker-level values.

19. Power-Law Transformations Power-law transformations have the basic form of: s = c . r ᵞ Where c and ᵞ are positive constants

20. Power-Law Transformations Different transformation curves are obtained by varying ᵞ (gamma)

21. Power-Law Transformations • Variety of devices used for image capture, printing and display respond according to a power law. The process used to correct this power-law response phenomena is called gamma correction . For example, Cathode Ray Tube (CRT) devices have an intensity-to- voltage response that is a power function, with exponents varying from approximately 1.8 to 2.5 .With reference to the curve for g=2.5 in Fig. 3.6, we see that such display systems would tend to produce images that are darker than intended. This effect is illustrated in Fig. 3.7. Figure 3.7(a) shows a simple gray-scale linear wedge input into a CRT monitor. As expected, the output of the monitor appears darker than the input, as shown in Fig. 3.7(b). Gamma correction. In this case is straightforward. All we need to do is preprocess the input image before inputting it into the monitor by performing the transformation. The result is shown in Fig. 3.7(c).When input into the same monitor, this gamma-corrected input produces an output that is close in appearance to the original image, as shown in Fig. 3.7(d).

22. Power-Law Transformation

23. Power-Law Transformation • In addition to gamma correction, power-law t ra n s f o rmati o ns are useful for general- p urp o s e contrast man i pu l a t i o n . See figure 3.8

24. Power-Law Transformation • Another illustration of Power-law t ra n s f o rmati o n

25. Piecewise-Linear Transformation Functions Principle: Rather than using a well defined mathematical function we can use arbitrary user defined transforms Advantage: Some important transformations can be formulated only as a piecewise function. Disadvantage: Their specification requires more user input that previous transformations

26. Types of Piecewise transformations Contrast Stretching Gray-level Slicing Bit-plane slicing

27. Contrast Stretching O n e o f functions th e s i m p l es t p ie ce w i s e li ne ar is a contrast-stretching transformation, which is used to enhance the low contrast images . Low contrast images may result from: Poor illumination W r o n g s e t t in g o f l e n s a p e r t u r e du r in g i m age acquisition.

28. Contrast Stretching

29. Contrast Stretching • Figure 3.10(a) shows a typical transformation used for contrast stretching. The locations of points (r1, s1) and (r2, s2) control the shape of the transformation function. If r1 = s1 and r2 = s2, the transformation is a linear function that produces no changes in gray levels. If r1 = r2, s1 = and s2 = L-1, the transformation becomes a Thresholding function that creates a binary image. Intermediate values of (r1, s1) and (r2, s2) produce various degrees of spread in the gray levels of the output image, thus affecting its contrast. In general, r1 ≤ r2 and s1 ≤ s2 is assumed, so the function is always increasing. • • • • •

30. Contrast Stretching • Figure 3.10(b) shows an 8-bit image with low contrast. • F i g . 3 . 1 ( c ) s h o w s t h e r e su l t o f c on t r a st s t r e t c h i n g , ob t a i n e d b y setting (r1, s1) = (r min , 0) and (r2, s2) = (r max ,L-1) where r min and r max denote the minimum and maximum gray levels in the image, respectively. Thus, the transformation function stretched the levels linearly from their original range to the full range [0, L-1]. • Finally, Fig. 3.10(d) shows the result of using the thresholding function defined previously, with r1=r2=m, the mean gray level in the image.

31. Gray-level Slicing or Intensity-level Slicing • This technique is used to highlight a specific range of gray levels in a given image. It can be implemented in several ways, but the two basic themes are: One approach is to display a high value for all gray levels in the range of interest and a low value for all other gray levels. This transformation, shown in Fig 3.11 (a), produces a binary image. The second approach , based on the transformation shown in Fig 3.11 (b), brightens the desired range of gray levels but preserves gray levels unchanged . Fig 3.11 (c) shows a gray scale image, and fig 3.11 (d) shows the result of using the transformation in Fig 3.11 (a). •

32. Gray-level Slicing

33. Bit-plane Slicing • • Pixels are digital numbers, each one composed of bits. For example, the intensity of each pixel in a 256 gray – scale image is composed of 8 bits (ie 1 byte) • I n ste a d o f h i gh li gh t i ng g r a y - l e v el r ang e, we c o u l d highlight the contribution made by each bit. This method is useful and used in image compression. •

34. Bit-plane Slicing

35. Bit-plane Slicing • Assuming that each pixel is represented by 8 bits, the image is composed of eight 1-bit planes Plane containing the lowest order bit of all pixels in the image and plane 7 all the higher order bits Only the most significant bits contain the majority of visually significant data. The other bit planes constitute the most suitable details Separating a digital image into its bits planes is useful for analyzing the relative importance played by each bit of the image It helps in determining the adequacy of the number of bits used to quantize each pixel • • • •

36. Histogram Processing Histograms are the basis for numerous spatial domain processing techniques. Histogram manipulation can be used effectively for image enhancement. The histogram of a digital image with gray levels in the range [0,L-1] is a discrete function h( rk )= nk , where rk is the kth gray level and nk is the number of pixels in the image having gray level rk . It is common practice to normalize a histogram by dividing each of its values by the total number of pixels in the image, denoted by n.Thus , a normalized histogram is given by p( rk )= nk /n, for k=0,1,p,L-1.Loosely speaking, p( rk ) gives an estimate of the probability of occurrence of gray level rk . Note that the sum of all components of a normalized histogram is equal to 1. (negative and identity transformations )

37. Histogram Processing Histograms are simple to calculate in software and also lend themselves to economic hardware implementations, thus making them a popular tool for real-time image processing. The horizontal axis of each histogram plot corresponds to gray level values, rk . The vertical axis corresponds to values of h( rk )= nk or p( rk )= nk /n if the values are normalized. Thus , as indicated previously , these histogram plots are simply plots of h( rk )= nk versus rk or p( rk )= nk /n versus rk .

38. Histogram Processing Fig: Four basic image types : dark, light , low contrast, high contrast ,and their corresponding histograms.

39. Histogram Processing (a)Original Image (b)Negative Transformation 1. Histogram Equalization: I t is a technique for adjusting image intensities to enhance contrast. Let f be a given image represented as a mr by mc matrix of integer pixel intensities ranging. So L is the number of possible intensity values, often 256. Let p denote the normalized histogram of f with a bin for each possible intensity. So Pn = number of pixels with intensity n /total number of pixels Where n = 0,1,...,L − 1.

40. Histogram Processing Histogram Matching (Specification): In image processing , histogram matching or histogram specification is the transformation of an image so that its histogram matches a specified histogram. When automatic enhancement is desired, this is a good approach because the results from this technique are predictable and the method is simple to implement. In particular, it is useful sometimes to be able to specify the shape of the histogram that we wish the processed image to have. The method used to generate a processed image that has a specified histogram is called histogram matching or histogram specification. Here we want to convert the image so that it has a particular histogram that can be arbitrarily specified. Such a mapping function can be found in three steps: Equalize the histogram of the input image Equalize the specified histogram Relate the two equalized histograms

41. Histogram Processing We first equalize the histogram Px of the input image x : We then equalize the desired histogramPz of the output image z : The inverse of the above transform is As the two intermediate images Y andY’ both have the same equalized histogram, they are actually the same image, i.e., Y=Y’ , and the overall transform from the given image x to the desired image z can be found to be: 2. Histogram Matching (Specification):

42. Enhancement Using Arithmetic/Logic Operations : Arithmetic/logic operations involving images are performed on a pixel-by-pixel basis between two or more images (this excludes the logic operation NOT, which is performed on a single image).As an example , subtraction of two images results in a new image whose pixel at coordinates (x,y)is the difference between the pixels in that same location in the two images being subtracted. Depending on the hardware and/or software being used, the actual mechanics of implementing arithmetic/logic operations can be done sequentially done. When dealing with logic operations on gray-scale images, pixel values are processed as strings of binary numbers. For example, performing the NOT operation on a black, 8-bit pixel (a string of eight 0’s) produces a white pixel (a string of eight 1’s). Intermediate values are processed the same way, changing all 1’s to 0’s and vice versa. In the AND and OR image masks, light represents a binary 1 and dark represents a binary 0.Masking sometimes is referred to as region of interest (ROI) processing

43. Enhancement Using Arithmetic/Logic Operations : (a ) Original image . ( b)AND image mask . ( c) Result of the AND d ) Original image . ( e) OR image mask . ( f) Result of operation OR

44. Enhancement Using Arithmetic/Logic Operations : There are 2 methods of Enhancement Using Arithmetic/Logic Operations : Image Subtraction Image Averaging

45. Enhancement Using Arithmetic/Logic Operations : 1. Image Subtraction : Image subtraction or pixel subtraction is a process whereby the digital numeric value of one pixel or whole image is subtracted from another image. This is primarily done for one of two reasons – levelling uneven sections of an image such as half an image having a shadow on it, or detecting changes between two images. This detection of changes can be used to tell if something in the image moved. This is commonly used in fields such a s astrophotograph y to assist with the computerized search for asteroids in which the target is moving and would be in one place in one image, and another from an image one hour later and where using this technique would make the fixed stars in the background disappear leaving only the target. The difference between two images f(x, y) and h(x, y), expressed as

46. Enhancement Using Arithmetic/Logic Operations : 2. Image Averaging : Consider a noisy image g(x, y) formed by the addition of noise N(x, y) to an original image f(x, y);that is, where the assumption is that at every pair of coordinates (x,y)the noise is uncorrelated† and has zero average value. The objective of the following procedure is to reduce the noise content by adding a set of noisy images, {gi(x, y)} If the noise satisfies the constraints just stated, that if an image is formed by averaging K different noisy images,