Digital Image Processing Lecture 4: Image Enhancement: Point Processing January 13, 2004 Prof. Charlene Tsai

Digital Image ProcessingLecture 4 2 Before Lecture …  Discussion group  Can be 2-4 people  Project group  3 people per group  Exceptions can be made for students outside CSIE department  Discussion group  Can be 2-4 people  Project group  3 people per group  Exceptions can be made for students outside CSIE department

Digital Image ProcessingLecture 4 3 Review  Point operations: A pixel’s gray value is changed without any knowledge of its surroundings.  Gray-level slicing  Bit-plane slicing  Point operations: A pixel’s gray value is changed without any knowledge of its surroundings.  Gray-level slicing  Bit-plane slicing

Digital Image ProcessingLecture 4 4 Arithmetic Operations  May perform arithmetic operations (+,-,*,/,neg) on an image.  Always make sure the new value, as well as the intermediate value, is within the intensity range.  Operations are straightforward.  See section 4.2 for matlab commands.  May perform arithmetic operations (+,-,*,/,neg) on an image.  Always make sure the new value, as well as the intermediate value, is within the intensity range.  Operations are straightforward.  See section 4.2 for matlab commands.

Digital Image ProcessingLecture 4 5 Image Subtraction  A more interesting arithmetic operation is pixel-wise subtraction of two images.  Refer to the fractal image again.  A more interesting arithmetic operation is pixel-wise subtraction of two images.  Refer to the fractal image again. original4 lower-order bit planes zeroed out differencecontrast enhanced

Digital Image ProcessingLecture 4 6 (con’d)  Mask mode radiography  The mask image is taken before injection of the contrast medium into patient’s bloodstream  Areas different between 2 images appear enhanced.  Mask mode radiography  The mask image is taken before injection of the contrast medium into patient’s bloodstream  Areas different between 2 images appear enhanced. Mask: h(x,y) Result: g(x,y)

Digital Image ProcessingLecture 4 7 What is a histogram?  A graph indicating the number of times each gray level occurs in the image, i.e. frequency of the brightness value in the image  The histogram of an image with L gray levels is represented by a one-dimensional array with L elements.  Algorithm:  Assign zero values to all elements of the array h f ;  For all pixels (x,y) of the image f, increment h f [f(x,y)] by 1.  A graph indicating the number of times each gray level occurs in the image, i.e. frequency of the brightness value in the image  The histogram of an image with L gray levels is represented by a one-dimensional array with L elements.  Algorithm:  Assign zero values to all elements of the array h f ;  For all pixels (x,y) of the image f, increment h f [f(x,y)] by 1.

Digital Image ProcessingLecture 4 8 Histogram Examples

Digital Image ProcessingLecture 4 9 Histogram/Contrast Stretching  To increase the dynamic range of the gray levels in the image.  Piecewise linear function  (r 1, s 1 ) & (r 2, s 2 ) control the shape of the mapping, where r 1 <r 2 & s 1 <s 2.  What if  r 1 =s 1 & r 2 =s 2 ?  r 1 =r 2, s 1 =0 & s 2 =L-1?  See section 4.3 for matlab commands.  To increase the dynamic range of the gray levels in the image.  Piecewise linear function  (r 1, s 1 ) & (r 2, s 2 ) control the shape of the mapping, where r 1 <r 2 & s 1 <s 2.  What if  r 1 =s 1 & r 2 =s 2 ?  r 1 =r 2, s 1 =0 & s 2 =L-1?  See section 4.3 for matlab commands.

Digital Image ProcessingLecture 4 10 Examples of Histogram Stretching  What is the problem here? Original (r 1 =s 1 &r 2 =s 2 ) Contrast stretched (r 1 =r min, r 2 =r max, s 1 =0,s 2 =L-1) Thresholding (r 1 =r 2,s 1 =0& s 2 =L-1)

Digital Image ProcessingLecture 4 11 Histogram Equalization: Intuition  Goal: to produce an image with equally distributed brightness levels over the whole brightness scale.  Effect: enhancing contrast for brightness values close to histogram maxima, and decreasing contrast near minima.  Result is better than just stretching, and method fully automatic.  Goal: to produce an image with equally distributed brightness levels over the whole brightness scale.  Effect: enhancing contrast for brightness values close to histogram maxima, and decreasing contrast near minima.  Result is better than just stretching, and method fully automatic.

Digital Image ProcessingLecture 4 12 Histogram equalization: How it works?  Let be the input histogram and that the input gray-scale is.  The intention is to find a monotonic pixel brightness mapping such that the output histogram is uniform over the whole output brightness scale  The monotonic property of the transform T implies  Let be the input histogram and that the input gray-scale is.  The intention is to find a monotonic pixel brightness mapping such that the output histogram is uniform over the whole output brightness scale  The monotonic property of the transform T implies

Digital Image ProcessingLecture 4 13 (con’d)  The histogram is a discrete probability density function.  The sum in the above equation can be interpreted as discrete distribution function.  Assume that the image has M rows and N columns. The equalized histogram corresponding to the uniform probability density function f whose function value is a constant:  The histogram is a discrete probability density function.  The sum in the above equation can be interpreted as discrete distribution function.  Assume that the image has M rows and N columns. The equalized histogram corresponding to the uniform probability density function f whose function value is a constant:

Digital Image ProcessingLecture 4 14 (con’d)  The equalized histogram can be obtained precisely only for the ``idealized'' continuous probability density, in which case the sum equation becomes  The desired pixel brightness transformation T can then be derived as  The equalized histogram can be obtained precisely only for the ``idealized'' continuous probability density, in which case the sum equation becomes  The desired pixel brightness transformation T can then be derived as Cumulative histogram

Digital Image ProcessingLecture 4 15 (con’d)  The discrete approximation of the continuous pixel brightness transformation from the above equation is

Digital Image ProcessingLecture 4 16 Histogram equalization - Algorithm  For an NxM image of G gray-levels (often 256), compute the image histogram H.  For the cumulative histogram H c :  Set  Rescan the image and write an output image with gray-levels  For an NxM image of G gray-levels (often 256), compute the image histogram H.  For the cumulative histogram H c :  Set  Rescan the image and write an output image with gray-levels

Digital Image ProcessingLecture 4 17 Histogram equalization: Example OriginalEqualized

Digital Image ProcessingLecture 4 18 Histogram Matching/Specification  The generalization of histogram equalization is called histogram matching.  The aim is to produce an image with desired distributed brightness levels over the whole brightness scale, as opposed to uniform distribution.  Assume the desired probability density function is G(q).  Let the desired pixel brightness transform be q=T[p].  The generalization of histogram equalization is called histogram matching.  The aim is to produce an image with desired distributed brightness levels over the whole brightness scale, as opposed to uniform distribution.  Assume the desired probability density function is G(q).  Let the desired pixel brightness transform be q=T[p].

Digital Image ProcessingLecture 4 19 (con’d)  Similarly, the cumulative histogram of the input image is  From the above eqn, it is possible to find T.  E.g. if G is the exponential distribution,  We have  Then,  Similarly, the cumulative histogram of the input image is  From the above eqn, it is possible to find T.  E.g. if G is the exponential distribution,  We have  Then,

Digital Image ProcessingLecture 4 20 Summary  Enhancement using point operations  Arithmetic operations  Histogram stretching  Histogram equalization  Histogram matching/specification  Enhancement using point operations  Arithmetic operations  Histogram stretching  Histogram equalization  Histogram matching/specification