Manav Goyal

Image Enhancement - Image Processing

  • Spatial and Frequency domain
  • Image Enhancement Methods
    • The principal objective of enhancement is to process an images so that the result is more suitable than the original image for a SPECIFIC application
    • Uses
      • Highlighting interesting details in the images
      • Removing noise from the images
      • Making images more visually appealing
      • Enhance hidden information
      • Filter important image features
      • Discard unimportant image features
    • Types
      • Spatial Domain Methods (Image Plane)
        • Techniques are based on direct manipulation of pixels in an image
        • Methods
          • Point Processing
            • s = T(r)
            • Gray-Level Transformation Function
              • Types
                • Contrast stretching
                • Thresholding
              • Basic Gray Level Transformation
                • log, nth root, identity, nth power, inverse log
              • Digital/Image Negative
                • It is useful when for enhancing white details embedded in dark regions of the image
                • S = L-1-r
                • r = pixel value of given image
                • L = grey-level value
                  • 256 for 8-bit per pixel image
              • Log Transformations
                • Expands the details of darker regions in an image
                • s = c * log(1+r)
              • Power-Law Transformations
                • s = cry
                • Gamma Correction
            • Piecewise-Linear Transformation Functions
              • Arbitrarily complex
              • More user input
              • Type of Transformations
                • Contrast stretching
                  • Increase the dynamic range of the gray levels in the image
                  • S = r - c[b-a/d-c] + a
                    • a = s1, b = s2, c = r1, d = r2
                  • Causes for poor image
                    • Poor illumination
                    • Wrong lens aperture
                    • Wrong shutter speed
                    • Lack of dynamic range in the imaging sensor
                • Gray-level slicing
                  • Highlighting a specific range of gray levels in an image
                • Bit-plane slicing
                  • It divides the image into bit planes on the basis of contribution of each bit in the image
                  • Steps
                    • Convert each pixel into binary
                    • Create "n" planes where "n" is number of bits
                    • Fill first plane by taking first bit of each binary and so on
          • Mask Processing
            • g(x,y) = T[f(x,y)]
      • 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
  • Histogram processing
    • Image Not Loaded
    • Histogram Equalization
      • The intensity levels in an image may be viewed as random variables in the interval [0, L-1]
      • Let pr(r) and ps(s) denote the probability density function (PDF) of random variables "r" and "s"
      • s = T(r), 0 ≤ r ≤ L-1
        • T(r) is a strictly monotonically increasing function, one-to-one mapping, continuous and differentiable
        • 0 ≤ T(r) ≤ L-1 for 0 ≤ r ≤ L-1
      • ps(s)ds = pr(s)dr
      • Image Not Loaded
      • Steps
        • Image Not Loaded - If grey level is not given directly then Take maximum value > Represent it in power of 2 > Take that as L
        • Create table for new Grey level (Equal to histogram equalization level obtained from previous table) & No. of Pixel
        • Plot histogram and calculate Output image
  • Spatial Filtering
    • Used to Smoothing and Sharpening of images by removing very High/Low frequency components
    • Spatial filtering is defined by
      • A neighborhood
      • An operation that is performed on the pixels inside the neighborhood
    • Types in Frequency Domain
      • Low pass (preserve low frequencies)
        • Remove High frequency components, Keeps Low frequency
        • Used to Smoothen the image
        • Removes noise (as noise is mostly High frequency)
        • Types and their Transformation function
          • Ideal low Pass
            • Image Not Loaded
          • Butterworth low Pass
            • Image Not Loaded
          • Gaussian low Pass
            • Image Not Loaded
      • High pass (preserve high frequencies)
        • Remove Low frequency components, Keeps High frequency
        • Used to Sharpen the image
        • No background
        • Types
          • Ideal low Pass
            • Image Not Loaded
          • Butterworth low Pass
            • Image Not Loaded
          • Gaussian low Pass
            • Image Not Loaded
      • Band-pass (preserve frequencies within a band)
      • Band-reject (reject frequencies within a band)
    • Spatial Filtering Methods
      • Linear
        • A filtering method is linear when the output is a weighted sum of the input pixels
        • T[a1f1(t,z) + a2f2(t,z)] = a1T[f1(t,z)] + a2T[f2(t,z)]
        • Linear Spatial Filtering Methods
          • Correlation
            • Often used in applications where we need to measure the similarity between images or parts of images (Pattern matching)
            • Image Not Loaded
          • Convolution
            • Similar to correlation except that the mask is first flipped both horizontally and vertically
            • If symmetric, w(s,t) = w(-s,-t), then convolution is equivalent to correlation
            • Image Not Loaded
      • Non-Linear
    • Steps for Filtering in the Frequency Domain
      • Take image f(x,y) of dimension MxN
      • Give padding to form fp(x,y) of dimension PxQ, where P = 2M and Q = 2N
        • Zero Padding
        • Replicate Edge Pixels
        • Wrap Around Edge Pixels
      • To centralize image multiply
        • fp(x,y) * (-1)x+y
      • Filter is H(u,v), Fourier transform the image F(x,y)
        • G(u,v) = H(u,v) * F(x,y)
      • Find inverse of DFT
        • g(x,y) = T-1[g(u,v)] (-1)x+y
    • Steps for Filtering in the Spatial Domain
      • Slower than Frequency Domain
      • Convolution is used
  • Statistical Order/Non-Linear Filters
    • Mean Filter
    • Weighted Average Filter
      • Weighted Matrix * Elements/Sum of all Elements
      • In Weighted Matrix we gave more weight to the center value
        • Take centre value of filter as whatever value you want and others as 1
    • Median Filter
      • Sometimes a median filter works better than an averaging filter
    • Min Filter
    • Max Filter
  • Smoothening Spatial Filters
    • Useful in removing noise from images, Highlighting gross detail
      • Blurring -=> Pixel Averaging
    • Types
      • Simple averaging filter
        • Average all of the pixels in a neighborhood around a central value
        • Sum of all Elements/Total number of elements
        • Image Not Loaded
      • Weighted Smoothing Filters
        • Pixels closer to the central pixel are more important
        • Image Not Loaded
    • Approaches to dealing with missing edge pixels
      • Omit missing pixels
        • Only works with some filters
        • Can add extra code and slow down processing
      • Pad the image
        • Typically with either all white or all black pixels
      • Replicate border pixels
      • Truncate the image
      • Allow pixels wrap around the image
        • Can cause some strange image artifacts
  • Sharpening Spatial Filters
    • Sharpening spatial filters seek to highlight fine detail based on spatial differentiation
      • Remove blurring from images
      • Highlight edges
    • Applications
      • Electronic Printing, Medical imaging, Industrial inspections, Autonomous guidance
    • Spatial Differentiation
      • Differentiation measures the rate of change of a function
      • Requirements for digital derivative
        • First derivative
          • Must be zero in flat segment
          • Must be nonzero along ramps
          • Must be nonzero at the onset of a gray-level step or ramp
          • 1st Derivative -=> f(x+1) - f(x)
        • Second derivative
          • Must be zero in flat segment
          • Must be zero along ramps
          • Must be nonzero at the onset and end of a gray-level step or ramp
          • 2nd Derivative -=> f(x+1) - f(x-1) - 2f(x)
      • Comparing the response between first- and second-ordered derivatives
        • First-order derivative produce thicker edge
        • Second-order derivative have a stronger response to fine detail, such as thin lines and isolated points
        • First-order derivatives generally have a stronger response to a gray-level step
        • Second-order derivatives produce a double response at step changes in gray level
        • In general the second derivative is better than the first derivative for image enhancement
        • The principle use of first derivative is for edge extraction
      • Sharpening Filters
        • Laplacian Image Enhancement
          • Isotropic
          • One of the simplest sharpening filters
          • We will look at a digital implementation
          • Steps
            • Image Not Loaded
            • Subtract the Laplacian result from the original image to generate our final sharpened enhanced image
              • g(x,y) = f(x,y) - ∆2f
          • Variant
            • Image Not Loaded
            • Enhanced Laplacian filter -=> Add 1 in the middle pixel
          • Use of First Derivative for Edge Extraction
            • Image Not Loaded
            • Roberts operator (Cross gradient)
            • Roberts cross operator
            • Prewitt operator
            • Sobel operator
          • Zero crossing property of Laplacian filter
    • Un-sharp Masking
      • Primarily used in the printing and publishing industry to sharpen images
      • Process of subtracting an un-sharp (smoothed) version of image from the original
        • Blur the original image
        • Subtract the blurred image from the original (Result is called mask)
          • Sharpened = Original - Blurred image
        • Add the mask to the original
      • Image Not Loaded
  • Discrete Fourier Transform
    • Image Not Loaded
    • N is number of values
    • k is from 0 to N-1
    • Image Not Loaded
    • Image Not Loaded
    • In Continuous Fourier Transform, don't divide by N
  • Convert filter from
    • Spatial to Frequency
      • Fourier Transform
      • Take average of points, g(x,y)
      • G(u,v) = H(u,v) * F(x,y) = Filter * Image
    • Frequency to Spatial
      • Inverse Fourier Transform
  • Homomorphic Filtering
    • f(x,y) is categorized by
      • Illumination
        • Light falling on the object
      • Reflectance
        • Light reflecting from the object
    • Approach is to separate illumination and reflectance components
      • f(x,y) = i(x,y) * r(x,y)
      • F(u,v) ≠ F(i(x,y) * r(x,y)) -=> Fourier transform is not possible directly
      • Z(x,y) = ln(f(x,y))
      • Z(u,v) = Fi(u,v) + Fr(u,v) -=> Transform of Z(x,y)
        • Fi(u,v) = F[ln(i(x,y))]
        • Fr(u,v) = F[ln(r(x,y))]
      • S(u,v) = Z(u,v) * H(u,v)
        • H(u,v) is filter
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