Radiometric Processing of Remote Sensing Data by ltx81750

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									                           Chapter 4

  Radiometric Processing of Remote Sensing Data




  Remote Sensing                                    Ayman F. Habib
                                      1




                           Overview
• Radiometric calibration
   – Sensor calibration
        • DN/grey values → At-sensor radiance.
   – Atmospheric correction
        • At-sensor radiance → Surface radiance.
   – Solar and topographic correction
        • Surface radiance → Surface reflectance.
• Radiometric image processing:
   – Spatial/image domain.
        • Noise removal.
        • Point and edge detection.
   – Frequency domain.
  Remote Sensing                                    Ayman F. Habib
                                      2
                   Radiometric Calibration




  Remote Sensing                           Ayman F. Habib
                              3




       Recorded Digital Numbers (DN)

• Recorded grey values (digital numbers) at any
  pixel location is not a record of the true ground-
  leaving radiance.
• The signal is attenuated due to atmospheric
  absorption.
• The directional properties of the signal are altered
  by refraction and scattering.
• Incoming radiance is augmented by scattered path
  radiance.
   – Introduces haze and reduces the image contrast.

  Remote Sensing                           Ayman F. Habib
                              4
       Recorded Digital Numbers (DN)
                       Sensor




                                S1
                       S2




                   Q             P
  Remote Sensing                              Ayman F. Habib
                                 5




       Recorded Digital Numbers (DN)

• All of the signal appears to originate from point
  “P” on the ground. However:
   – The scattering at S1 redirects some of the radiation into
     the sensor’s field of view.
   – Some of the energy from point “Q” is scattered at S2
     into the sensor’s field of view.
   – The cumulative effect of the scattering at S1 and S2 is
     known as “the atmospheric path radiance”.
   – The exitance from “P” and “Q” is attenuated by the
     atmosphere.

  Remote Sensing                              Ayman F. Habib
                                 6
       Recorded Digital Numbers (DN)
• Moreover, recorded energy by the sensor depends
  on:
   – The solar elevation angle, the solar azimuth, the slope
     of the ground, and the sensor look angle.
        • The effect of these factors is described by the bidirectional
          reflectance function.
   – The Earth-Sun distance.
• There are some techniques that can be used to
  estimate the atmospheric and viewing angle
  effects: Radiometric Calibration.
                       Calibration

  Remote Sensing                                       Ayman F. Habib
                                    7




     Atmospheric Correction: Why? (I)

• Compute the ratio between two bands of a multi-
  spectral image (e.g., Normalized Difference
  Vegetation Index – NDVI).
   – The scattering effect is inversely proportional to the
     wavelength.
   – The involved channels will be unequally affected by
     scattering.
   – The computed ratio will be a biased estimate of the true
     ratio.

  Remote Sensing                                       Ayman F. Habib
                                    8
                                                              Digital Numbers
                         Digital Numbers
                                                              reduced by absorption
                         increased by scattering




                  60
Digital Numbers




                  50
                  40
                  30
                  20
                  10


                         0.5       0.6     0.7          0.8                        1.1
                                          Wavelength (µm)

            • Combined effects of scattering and absorption on Digital
              Numbers (DN) recorded by remote sensing systems.
                  Remote Sensing                                      Ayman F. Habib
                                                   9




                    Atmospheric Correction: Why? (II)

    • One might use the recorded digital numbers (grey
      values) to infer some properties of the surface:
                   – Surface normal.
                   – Surface roughness.
                   – Surface reflectance properties.
    • Reliable recovery of such properties is only
      possible if the atmospheric component of the
      signal is estimated and removed.

                  Remote Sensing                                      Ayman F. Habib
                                                   10
Object Recognition / Atmospheric Effects
 • Expected high intensity yellow color response:
           RGB: 255, 255, 0.




                                         Recorded Intensities
                                           R: 255
                                           G: 249
                                           B: 29
  Remote Sensing                           Ayman F. Habib
                               11




   Atmospheric Correction: Why? (III)

• Comparison of remote sensing data captured at
  different times.
   –   Environmental monitoring.
   –   Resource management.
   –   Evaluation of disaster effects.
   –   Change detection applications.
• Reliable comparison is only possible after
  removing the atmospheric effect.

  Remote Sensing                           Ayman F. Habib
                               12
           Change Detection Analysis




     Calgary, 1956           Calgary, 1999
Remote Sensing                   Ayman F. Habib
                      13




           Change Detection Analysis




Remote Sensing                   Ayman F. Habib
                      14
 Change Detection / Radiometric Differences




         Calgary 56                      Calgary 99
  Remote Sensing                            Ayman F. Habib
                            15




    Radiometric Calibration Procedure

• Sensor calibration:
   – DN/grey values → At-sensor radiance.
• Atmospheric correction:
   – At-sensor radiance → Surface radiance.
• Solar and topographic correction:
   – Surface radiance → Surface reflectance.




  Remote Sensing                            Ayman F. Habib
                            16
                    Sensor Calibration

         Digital Numbers → At-Sensor Radiance




   Remote Sensing                        Ayman F. Habib
                            17




              DN → At-Sensor Radiance
• Objective: Convert digital numbers (DN) to absolute
  radiance values.
• The conversion process accounts for the exact form
  of the analog to digital (A/D) response function of
  the sensor under consideration.
• Detectors are designed to have a linear response to
  incident spectral radiance.
• The sensor’s response to incoming radiance is
  monitored using onboard calibration lamps.

   Remote Sensing                        Ayman F. Habib
                            18
                           DN → At-Sensor Radiance




Remote Sensing                                                          Ayman F. Habib
                                                19




                           DN → At-Sensor Radiance
            255
     DN = Digital Number




                                             Slope = channel Gain (G)




                    0
                            Lmin   L = Spectral Radiance                Lmax
Remote Sensing                                                          Ayman F. Habib
                                                20
                            DN → At-Sensor Radiance
                                                                  DNmax
                                              DN
                                DNmin


                                Lmin            L                   Lmax

 DN = DNmin + (DNmax - DNmin)/(Lmax - Lmin) * (L – Lmin)

DN = DNmax/(Lmax – Lmin) * L - DNmax/(Lmax – Lmin) * Lmin

                            DN = Channel Gain * L + Channel Offset
 Remote Sensing                                                       Ayman F. Habib
                                                21




                            DN → At-Sensor Radiance
  Lmax
      L=Spectral radiance




                                                               Lmax − Lmin
                                                     Slope =
                                                                  255




   Lmin


                            0           DN = Digital number                      255
 Remote Sensing                                                       Ayman F. Habib
                                                22
       Lmin and Lmax for LANDSAT MSS
                                                      Spectral Bands

             Satellite              4                 5                 6                   7

                             Lmin       Lmax   Lmin       Lmax   Lmin       Lmax     Lmin       Lmax

           LANDSAT 1         0.0        24.8   0.0        20.0   0.0        17.6      0.0       40.0
           LANDSAT 2
                             1.0        21.0   0.7        15.6   0.7        14.0      1.4       41.5
         (6/22 to 7/16/75)
           LANDSAT 2
                             0.8        26.3   0.6        17.6   0.6        15.2      1.1       39.1
            (> 7/16/75)
          LANDSAT 3
                             0.4        22.0   0.3        17.5   0.3        14.5      0.3       44.1
          (3/5 to 6/1/78)
           LANDSAT 3
                             0.4        25.9   0.3        17.9   0.3        14.9      0.3       38.3
            (> 6/1/78)
           LANDSAT 4         0.2        23.0   0.4        18.0   0.4        13.0      1.0       40.0


• L = (Lmax – Lmin) / DNmax * DN + Lmin
• L is expressed in milli-Watts cm-2 sr-1 µm-1 (spectral radiance).
    Remote Sensing                                                                 Ayman F. Habib
                                                 23




                Sensor Radiance Equation




    Remote Sensing                                                                 Ayman F. Habib
                                                 24
Paths of Radiance Received by the Sensor

                                                                                Remote
                                                                                sensing
                                               Total radiance                   system
                      E0                       at the sensor L s
            Solar
         irradiance
                                                    90°   Lp      Lt
                                          Lp
                           Tθ 0     2
                                                               Tθ v
 Diffuse sky                                   4
 irradiance    Ed                                         1,3,5
                                    1                             Atmosphere
                                                    θv
                           3
                                               θ0
                                                     Li
                                     5

                       Reflectance from Reflectance from
                       neighboring area    study area
   Remote Sensing                                              Ayman F. Habib
                                     25




Paths of Radiance Received by the Sensor

• Path 1:
   – Electromagnetic energy from the sun that was attenuated
     very little before illuminating the target within the IFOV.
• Path 2:
   – Electromagnetic energy that might never reach the Earth
     surface (due to atmospheric scattering).
   – This energy might be scattered into the IFOV.
• Path 3:
   – Energy from the sun that has undergone some Rayleigh,
     Mie, and/or non-selective scattering before illuminating
     the target within the IFOV.

   Remote Sensing                                              Ayman F. Habib
                                     26
Paths of Radiance Received by the Sensor
• Path 4:
    – Reflected radiation from nearby terrain elements into
      the sensor IFOV.
• Path 5:
    – Reflected radiation from nearby terrain elements into
      the atmosphere and then scattered onto the target within
      the sensor IFOV.
• The radiance received by the sensor is the
  cumulative summation of the radiation carried by
  paths 1-5.

   Remote Sensing                                    Ayman F. Habib
                                   27




                     Target Irradiance
• For a given spectral interval (λ1 : λ2), the solar
  irradiance reaching the Earth’s surface can be
  represented by:
            λ2
    E g = ∫ ( E0λ Tθ 0 cos θ 0 + Ed λ ) dλ   (Wm − 2 )
            λ1



    E0λ Tθ 0 cos θ 0 ≡ Path 1 Spectral Radiance
    Ed λ ≡ Diffuse Sky Spectral Radiance ( Paths 3 and 5)



   Remote Sensing                                    Ayman F. Habib
                                   28
            Atmospheric Transmittance
• Atmospheric transmittance (Tθ) accounts for the
  atmospheric scattering and absorption.
• In the absence of the atmosphere, the
  transmittance of solar radiant energy to the ground
  would be 100%.
• The atmospheric transmittance (Tθ) may be
  computed as:
   – Tθ = e-τ/cosθ.
   – Where τ is the atmospheric optical thickness,
   – and θ is the solar/sensor zenith angle.

  Remote Sensing                                Ayman F. Habib
                                29




    Atmospheric Optical Thickness (τ)
• The optical thickness of the atmosphere at a
  certain wavelength, τ(λ), equals the sum of all the
  attenuating coefficients which are made up
  primarily of:
   – Rayleigh scattering τR.
   – Mie scattering τM.
   – Selective atmospheric absorption τA.

           τ (λ ) = τ R + τ M + τ A
           Where : τ A = τ H O + τ O + τ O + τ CO
                            2        2      3           2


  Remote Sensing                                Ayman F. Habib
                                30
       Radiance Received by the Sensor
• A portion of the solar irradiance onto the target
  is reflected into the sensor’s IFOV.
• Assuming a diffuse (Lambertian) target, the
  radiance received by the sensor:
           λ2
       1
LT =
       π   ∫ R Tθ
           λ
                    v
                        ( E0λ Tθ 0 cos θ 0 + Ed λ ) dλ      (W m − 2 sr −1 )
            1

    – The division by (π) is needed for the transformation
      from irradiance (Wm-2) to radiance (Wm-2sr-1).
    – R represents the target reflectance.
    – Tθv is the atmospheric transmittance from the target
      to the sensor.
 Remote Sensing                                          Ayman F. Habib
                                     31




       Radiance Received by the Sensor
 • The radiance recorded by the sensor, LS, does
   not equal LT.
       – There is some additional radiance from other paths
         (2&4).

                    LS = LT + LP (Wm −2 sr −1 )

 • LP is known as the atmospheric path radiance.
 • The first objective of atmospheric correction
   is to minimize or remove the contribution of
   the atmospheric path radiance (LP).
 Remote Sensing                                          Ayman F. Habib
                                     32
                     Atmospheric Correction

           At-sensor radiance → Surface radiance
                Atmospheric Path Radiance




    Remote Sensing                            Ayman F. Habib
                                33




              Atmospheric Path Radiance
• LP represents the scattered path radiance, which
  introduces haze in the imagery and reduces image
  contrast.
• LP is wavelength dependent.
   – Shorter wavelengths normally manifest greater scattering
     effect.
• Haze compensation aims at minimizing the influence
  of path radiance effects.
• Haze compensation of multi-spectral data can be
  achieved by observing recorded radiance from targets
  with zero reflectance.
   – Deep clear water bodies.
    Remote Sensing                            Ayman F. Habib
                                34
                 Atmospheric Path Radiance
  • Any signal observed over such an area represents
    the path radiance.
  • Observed signal can be subtracted from all pixels
    in that band.
  • Haze compensation is usually applied uniformly
    throughout the whole scene.
        – This may or may not be valid.
  • When extreme viewing angles are involved, one
    might need to compensate for varying atmospheric
    path lengths within the scene.
       Remote Sensing                                                                         Ayman F. Habib
                                                           35




                                  10,000                                                   10,000
                           Frequency




                                                                                Frequency




Original Data                          5,000                                                5,000

                                                                    Band1
                                                                                                                Band 2


                                               0          125            255                        0          125          255
                                  10,000           Brightness Values                  10,000            Brightness Values
                           Frequency




                                                                               Frequency




                                       5,000                                                5,000
                                                                                                                   Band 4

                                                                Band 3


                                  10,000 0                125            255          10,000 0                 125          255
Band   Minimum   Maximum                           Brightness Values                                    Brightness Values
 1        51       242
                                                                               Frequency
                           Frequency




 2        17       115
                                       5,000                                                5,000
 3        14       131
                                                                  Band 5
 4        4        105                                                                                               Band 7
 5        0        193

 7        0        128                         0          125            255                        0          125          255
                                                   Brightness Values                                    Brightness Values
       Remote Sensing                                                                         Ayman F. Habib
                                                           36
                                  10,000                                              10,000




                           Frequency




                                                                               Frequency
Adjusted Data                          5,000                                               5,000
                                                                 Band1
                                                                                                              Band 2




                                  10,000 0                125            255
                                                                                       10,000
                                                                                                   0          125           255
                                                   Brightness Values                                   Brightness Values




                           Frequency




                                                                               Frequency
                                       5,000                                               5,000

                                                                                                                   Band 4
                                                                Band 3


                                               0          125            255                       0          125           255
                                  10,000           Brightness Values                   10,000          Brightness Values
Band   Minimum   Maximum




                                                                               Frequency
                           Frequency




 1        0        191

 2        0        98                  5,000                                               5,000

 3        0        117                                            Band 5
                                                                                                                    Band 7
 4        0        101

 5        0        193
                                               0          125            255                       0          125           255
 7        0        128
                                                   Brightness Values                                   Brightness Values
       Remote Sensing                                                                        Ayman F. Habib
                                                           37




       Surface Radiance → Target Reflection




       Remote Sensing                                                                        Ayman F. Habib
                                                           38
                                 Target Reflection
                 λ2
             1
     LT =
            π    ∫ R Tθ
                 λ
                             v
                                 ( E0λ Tθ 0 cos θ 0 + Ed λ ) dλ      (W m − 2 sr −1 )
                     1
    • For small bandwidth, the above equation can be simplified as:
                 1
        LT =             R Tθ v ( E0∆λ Tθ 0 cos θ 0 ∆λ + Ed )      (W m − 2 sr −1 )
                 π
    • Having estimates of:
       – Solar irradiance at the top of the atmosphere (E0),
       – Diffuse sky scattering (Ed),
       – Solar zenith angle (θ0),
       – Sensor zenith angle (θv), and
       – Atmospheric optical thickness (τ);
    • One can derive an estimate of the target reflection (R).
        Remote Sensing                                            Ayman F. Habib
                                              39




                                        Example
• Solar Zenith angle (θ0) = 38°.
• Sensor Zenith angle (θv) = 0°.
• Atmospheric optical thickness (τ) = 0.15.
• Tθ0 = e-0.15/cos38° = 0.827.
• Tθv = e-0.15/cos0° = 0.861.
• Solar irradiance at the top of the atmosphere (E0) = 256
  Wm-2.
• Diffuse sky scattering (Ed) = 0 Wm-2.
• LT = 1/π R * 256 * 0.827 * 0.861 * cos(38°) = 45.72 R

        Remote Sensing                                            Ayman F. Habib
                                              40
       Sun Angle Normalization
   Sun-Earth Distance Normalization




Remote Sensing                          Ayman F. Habib
                                  41
         Ta
            ng
              en




                                             Satellite
                tp
                  lan




                               i th
                  e




                           n
                        Ze

                        Zenith angle            Summer
                                       Sun



     Equator                           Sun      Fall
                                                Spring



                                       Sun      Winter




Remote Sensing                          Ayman F. Habib
                                  42
              Sun Angle Normalization
• Sun elevation correction accounts for the seasonal
  changes in the position of the Sun relative to the
  Earth.
• Through Sun angle normalization, image data
  acquired under different solar illumination angles
  are normalized.
   – This can be done by calculating the digital numbers DN
     assuming the Sun was at the zenith.
• The correction is applied by dividing the DN by
  the cosine of Sun’s zenith angle.

  Remote Sensing                           Ayman F. Habib
                             43




              Sun Angle Normalization
                             E0
                   E




                            θ



                       E0 = E / cos(θ)

  Remote Sensing                           Ayman F. Habib
                             44
     Sun-Earth Distance Normalization
• The Earth-Sun distance normalization is applied to
  compensate for the seasonal changes in the
  distance between the Earth and the Sun.
• The Earth-Sun distance is expressed in
  astronomical units.
   – An astronomical unit is equivalent to the mean distance
     between the Earth and the Sun ≈ 149.6 x 106 km.
• The irradiance from the Sun decreases as the
  square of the Earth-Sun distance increases.

E0 (Solar radiance at mean Earth − Sun Distance) = E * d 2
  Remote Sensing                            Ayman F. Habib
                             45




               Combined Normalization
• E0 = E * d2 / cos(θ0).
• Where:
    – E = Solar irradiance.
    – E0 = Normalized solar irradiance at the mean Earth-
      Sun distance while the Sun is at the zenith.
    – θ0 = Sun’s angle from the zenith.
    – d = Earth-Sun distance in astronomical units.
• Information regarding the solar elevation angle
  and Earth-Sun distance for a given scene is
  normally part of the ancillary data supplied with
  the purchased imagery.

  Remote Sensing                            Ayman F. Habib
                             46
         Radiometric Image Processing

                        Spatial Domain




  Remote Sensing                         Ayman F. Habib
                              47




Radiometric Image Processing: Overview

• Noise Removal:
   – Median filter.
   – Neighborhood averaging filter.
• Convolution.
• Primitive extraction.
   – Interest points.
   – Edge detection.
• Image processing in the frequency domain.
   – Fourier transform.

  Remote Sensing                         Ayman F. Habib
                              48
                   Noise Removal

• Noise is present in acquired imagery due to:
   – Poor-sampling by the sensor (data recording process).
   – Atmospheric conditions.
• Noise removal precedes any subsequent image
  processing activity (e.g., classification and
  positioning).
• Principle: Apply spatial domain smoothing
  techniques in local neighborhoods within the
  acquired image.

  Remote Sensing                               Ayman F. Habib
                               49




         Noise Removal: Median Filter

 • Sort the intensity values, within a local
   neighborhood, in an ascending or descending
   order.
 • Choose the median as the new centre value.
 • Characteristics:
     – Removes pixels in the neighborhood that are
       significantly different (i.e., due to noise) from the
       rest.
     – It preserves image sharpness/details.

  Remote Sensing                               Ayman F. Habib
                               50
       Noise Removal: Median Filter

                  93 100 98
                 105 25 95 →
                           
                 107 102 100
                           
                            

                 25 93 95 98    100 100 102 105 107→

                  93 100 98
                 105 100 95
                           
                 107 102 100
                           
                            
Remote Sensing                                 Ayman F. Habib
                                  51




       Noise Removal: Median Filter




       Before                                    After
Remote Sensing                                 Ayman F. Habib
                                  52
   Noise Removal: Neighborhood Averaging

• Process of averaging all pixels in the neighborhood.



                  1 1 1  93 100 98 
              1 
                ∗ 1 1 1 * 105 25 95  = 92
                                     
              9
                  1 1 1 107 102 100
                                    



   Remote Sensing                       Ayman F. Habib
                            53




                      Convolution
• Convolution is a simple mathematical operation
  which is fundamental to many image processing
  operators.
• Convolution provides a way of multiplying
  together two arrays of numbers, generally of
  different sizes, but of the same dimensionality, to
  produce a third array of numbers of the same
  dimensionality.
• This is used in image processing to implement
  operators whose output pixel values are simple
  linear combinations of certain input pixel values.
   Remote Sensing                       Ayman F. Habib
                            54
                     Convolution
• In an image processing context, one of the input
  arrays is two-dimensional gray-level image.
• The second array is usually much smaller, two-
  dimensional, and known as the kernel or
  convolution mask.
• The convolution is performed by sliding the kernel
  over the image, generally starting at the top left
  corner.
   – The kernel is moved through all the positions where the
     kernel fits entirely within the boundaries of the image.

  Remote Sensing                              Ayman F. Habib
                              55




                     Convolution

• Each kernel position corresponds to a single
  output pixel:
   – The value at that pixel is calculated by multiplying
     together the kernel value and the underlying image
     pixel value for each of the cells in the kernel, and then
     adding all these numbers together.
• If the image has M rows and N columns, and the
  kernel has m rows and n columns, then the size of
  the output image will have:
   – (M-m+1) rows and (N-n+1) columns.

  Remote Sensing                              Ayman F. Habib
                              56
                 Convolution: Numerical Example
5 10 12 3        4   7   6   7   9   8
6 11 13 1        4 10 2      4   6   8
9   7    8 10 8      7   5   1   2   3          Mask Coefficients    Original Values
10 9 12 8 10 10 11 3             3   4   10X7
                                                  W1 W2 W3              Z1   Z2   Z3
                                                                      Z4      Z6
                                                  W4 W5 W6 Original Value Z5 Average Filter
                                                  W7 W8 W9              Z7   Z8   Z9
                                                                                  1/9 1/9 1/9
        Original Image                                                            1/9 1/9 1/9
                                                                                  1/9 1/9 1/9


         8   7   6 6     5 9 5
                                                   R = w1 z1 + w2 z 2 + L + w9 z9
                                                           9
                                                                             9
    9
                                         8X5            = ∑ wi zi
                                                          i =1




        After Processing
          Remote Sensing                                              Ayman F. Habib
                                                   57




          Remote Sensing                                              Ayman F. Habib
                                                   58
    Smoothing Using Gaussian Mask
                                                 x2 + y 2
                                             −
                                     1            2σ2
                 G ( x, y ) =            e
                                2πσ 2

                        For σ = 1.0




Remote Sensing                                              Ayman F. Habib
                                59




                   Gaussian Smoothing




Remote Sensing                                              Ayman F. Habib
                                60
                   Primitive Extraction

                      Point Primitives
                      Edge Detection



  Remote Sensing                           Ayman F. Habib
                             61




  Interest Operators for Point Primitives

• For some applications, one might be interested in
  automatic extraction of distinct points from the
  input imagery.
   – For example, photogrammetric 3-D restitution of the
     object space from overlapping 2-D imagery.
• Two common approaches for automatic point
  extraction are:
   – Moravec Interest operator.
   – Förstner Interest operator.

  Remote Sensing                           Ayman F. Habib
                             62
               Moravec Interest Operator

• Interest points (feature points) are image locations
  where the interest operator computes a high
  variance value.
• In other words, certain pixel within the image
  corresponds to an interesting point if:
   – There is a significant difference between the grey-value
     at this pixels and its neighboring pixels.
• This comparison is quantified using variance
  computation.
  Remote Sensing                                  Ayman F. Habib
                                 63




Moravec Operator (Variance Computation)
 I1 =      ∑ [ f ( x,
        ( x, y ) ∈ S
                        y ) − f ( x , y + 1)] 2

 I2 =      ∑ [ f ( x,
        ( x, y ) ∈ S
                        y ) − f ( x + 1, y )] 2

 I3 =      ∑ [ f ( x,
        ( x, y) ∈ S
                        y ) − f ( x + 1, y + 1)] 2

 I4 =      ∑ [ f ( x,
        ( x, y ) ∈ S
                        y ) − f ( x + 1, y − 1)] 2

Where S represent all the pixels in the window

  Remote Sensing                                  Ayman F. Habib
                                 64
                   Moravec Operator

• Edge pixels have no variance along the edge
  direction.
• The minimum value of the previous directional
  variances are taken as the interest value at the
  central pixel, (xc, yc):
   – I(xc, yc) =min (I1, I2, I3, I4).
• We have interest points if the interest value at their
  locations are local maxima and exceed a
  predefined threshold.

  Remote Sensing                         Ayman F. Habib
                                65




                     Original Image




  Remote Sensing                         Ayman F. Habib
                                66
                    Variance Image




Remote Sensing                       Ayman F. Habib
                           67




                 Moravec Interest Points




Remote Sensing                       Ayman F. Habib
                           68
                   Edge Detection
• Acquired imagery are rich with linear features.
• The linear features are bounded by “edges”.
• An edge represents a discontinuity in the two
  dimensional gray value distribution function.
• Abrupt change in the gray level intensity within an
  area of the image space constitutes an edge.
• Edge detection refers to the process that examines
  the digital image for discontinuities in the grey
  level function.

  Remote Sensing                       Ayman F. Habib
                         69




                   Edge Detection




     Original Image                 Detected Edges

  Remote Sensing                       Ayman F. Habib
                         70
                 Edge Detection Techniques

• Edge detection techniques can be classified into
  two categories.
      – First derivative operators.
            • For example, SOBEL and CANNY Edge Detection.
      – Second derivative operators.
            • For example, LOG - Laplacian of Gaussian.




     Remote Sensing                                   Ayman F. Habib
                                     71




                         Edge Detection

Intensity f(x)




                                                                       x



     Remote Sensing                                   Ayman F. Habib
                                     72
                       First Derivative

  • Edges are characterized by maximal values in the
    first derivative of the intensity profile.
  f´(x)




Threshold


                                                                  x


      Remote Sensing                             Ayman F. Habib
                                 73




                 Non Maximal Suppression

  • To have a single response per edge:
       – Broad ridges in the first derivative magnitude array
         must be thinned so that only the magnitudes at the
         points of greatest local change remain.
  • Non maximal suppression suppress all values
    across the direction of the line that are not peak
    values.



      Remote Sensing                             Ayman F. Habib
                                 74
              Second Derivative Operator

• Edges are characterized by zero crossings in the
  second derivative of the intensity profiles.
            f´´(x)


                                    Edge Location



                                                          x



  Remote Sensing                              Ayman F. Habib
                              75




         Edge Detection: SOBEL Filter
                              Gx                    Gy
  a       b          c   -1   -2   -1        -1       0        1
  d       e          f   0    0    0         -2       0        2
  g       h          i   1    2    1         -1       0        1


• SOBEL Filter in the x-direction:
   – Gx = (g+2h+i) - (a+2b+c).
• SOBEL Filter in the y-direction:
   – Gy = (c+2f+i) - (a+2d+g).

  Remote Sensing                              Ayman F. Habib
                              76
  Remote Sensing                             Ayman F. Habib
                             77




         Edge Detection: SOBEL Filter

• Disadvantage:
   – Only the derivatives in x and y directions are
     considered.
   – The x-y direction is ignored.
   – This will result in losing some edge pixels.
• As an improvement, we can consider an expanded
  neighborhood of “e” and use “Extended SOBEL
  Filter.”


  Remote Sensing                             Ayman F. Habib
                             78
                   Extended SOBEL Filter
• SOBEL Filter in the xy-direction:
   – Gxy = 4/6[(j+2d+2h+u) - (p+2b+2f+o)]
• SOBEL Filter in the yx-direction:
   – Gyx = 4/6[(m+2f+2h+s) - (r+2b+2d+l)]

                           p   q    r
                       j   a   b    c   m

                       k   d   e    f   n

                       l   g   h    i   o

                           s    t   u

  Remote Sensing                            Ayman F. Habib
                               79




                      Original Image




  Remote Sensing                            Ayman F. Habib
                               80
               CANNY Edge Detection




  Remote Sensing                             Ayman F. Habib
                                 81




       Edge Detection & Enhancement

• Chavez Kernel:
   – Apply the Average Filter.
   – Subtract the Average Filter from the original pixel
     value to get the high frequency (HF) component:
        • HF = pixel value - average value
   – By adding HF back to the original pixel, a high
     frequency enhancement will be achieved:
        • New value = Pixel Value + HF.




  Remote Sensing                             Ayman F. Habib
                                 82
                    Chavez Kernel
                            1 1 1
                         1       
                    AVG = ∗ 1 1 1
                         9
                            1 1 1
                                 
           0 0 0       1 1 1       − 1 − 1 − 1
           0 1 0 − 1 ∗ 1 1 1 = 1 ∗ − 1 8 − 1
      HF =        9          9                
           0 0 0 
                       1 1 1
                                     − 1 − 1 − 1
                                                  

           0 0 0       − 1 − 1 − 1     − 1 − 1 − 1
           0 1 0 + 1 ∗ − 1 8 − 1 = 1 ∗ − 1 17 − 1
NewValue =        9                9              
           0 0 0 
                       − 1 1 − 1
                                         − 1 1 − 1
                                                      
   Remote Sensing                        Ayman F. Habib
                            83




          Radiometric Image Processing

                    Frequency Domain




   Remote Sensing                        Ayman F. Habib
                            84
                                  Fourier Series
                         1

                       0.5
(1/1)sin(2*pi*1*x)
                         0

                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4


                         1

                       0.5

                         0

                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4




      Remote Sensing                                           Ayman F. Habib
                                              85




                                  Fourier Series
                         1

                       0.5
(1/1)sin(2*pi*1*x)
(1/3)sin(2*pi*3*x)       0

                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4


                         1

                       0.5

                         0

                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4




      Remote Sensing                                           Ayman F. Habib
                                              86
                                  Fourier Series
                         1

                       0.5
(1/1)sin(2*pi*1*x)
(1/3)sin(2*pi*3*x)       0
(1/5)sin(2*pi*5*x)
                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4


                         1

                       0.5

                         0

                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4




      Remote Sensing                                           Ayman F. Habib
                                              87




                                  Fourier Series
                         1

                       0.5
(1/1)sin(2*pi*1*x)
(1/3)sin(2*pi*3*x)       0
(1/5)sin(2*pi*5*x)
                       -0.5
(1/7)sin(2*pi*7*x)
                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4


                         1

                       0.5

                         0

                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4




      Remote Sensing                                           Ayman F. Habib
                                              88
                                  Fourier Series
                         1

                       0.5
(1/1)sin(2*pi*1*x)
(1/3)sin(2*pi*3*x)       0
(1/5)sin(2*pi*5*x)
                       -0.5
(1/7)sin(2*pi*7*x)
(1/9)sin(2*pi*9*x)      -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4


                         1

                       0.5

                         0

                       -0.5

                        -1
                              0   0.2   0.4    0.6   0.8   1       1.2    1.4




      Remote Sensing                                           Ayman F. Habib
                                              89




                                  Fourier Series
 • F(x) = (1/1)sin(2*pi*1*x) + (1/3)sin(2*pi*3*x) +
   (1/5)sin(2*pi*5*x) + (1/7)sin(2*pi*7*x) +
   (1/9)sin(2*pi*9*x) + ….

 • We have generated a square wave by adding different
   sine waves.

 • These sine waves have different amplitudes and
   wavelengths/frequencies.


      Remote Sensing                                           Ayman F. Habib
                                              90
                         Fourier Series

 • The reverse is the Fourier series: Any signal can
   be decomposed into many sinusoidal waves.

 • Each sine wave is characterized by its amplitude
   and wavelength (or frequency).

 • The input signal is time/location dependant or is
   said to be in time/spatial domain.

    Remote Sensing                                 Ayman F. Habib
                                      91




                         Fourier Series

 • Fourier series is the process of transforming a
   signal from time/spatial domain to frequency
   domain.
 • In this example:

                                           Summation of sine waves
f(x)                                       with different amplitudes
                     Fourier Series
Square wave                                and wavelengths that make
                                           up the signal.


    Remote Sensing                                 Ayman F. Habib
                                      92
                                 Fourier Series
                                                              Amplitude       Frequency
                                                              1               1
f(x)                    Fourier Series
                                                              1/3             3

                                                              1/5             5
Spatial domain
                                                              1/7             7

                                                              1/9             9

                                                              …               …

                                                              To infinity

                                                                  Frequency domain
       Remote Sensing                                               Ayman F. Habib
                                                      93




  Fourier Transform of Discrete Functions
           • Given a discrete function gl, where 0 ≤ l ≤ N - 1


           Fourier Transform: Spatial → Frequency Domain
                         N −1                     2π kl
                                             −i
               Gk =      ∑g
                         l =0
                                 l       e         N
                                                           0 ≤ k ≤ N −1


       Inverse Fourier Transform: Frequency → Spatial Domain
                         N −1                     2 π kl
                                              i
                 gl =    ∑G
                          k =0
                                     k   e          N
                                                           0 ≤ l ≤ N −1

       Remote Sensing                                               Ayman F. Habib
                                                      94
Image: Spatial and Frequency Domains
                 Low frequency components




Remote Sensing                              Ayman F. Habib
                           95




Image: Spatial and Frequency Domains




Remote Sensing                              Ayman F. Habib
                           96
  Fourier Transform & Image Processing
• Low frequency components correspond to the trend
  within the input image.
• High frequency components correspond to the
  details within the input image.
• Image smoothing can be established by maintaining
  low frequency components while eliminating high
  frequency components.
• Image sharpening can be established by maintaining
  high frequency components while eliminating low
  frequency components.

   Remote Sensing                            Ayman F. Habib
                               97




                Smoothing in the Frequency Domain




   Remote Sensing                            Ayman F. Habib
                               98
              Sharpening in the Frequency Domain




 Remote Sensing                             Ayman F. Habib
                              99




Fourier Transform & Image Enhancement
                  Spatial Domain



                         Frequency Domain




                  Spatial Domain



                         Frequency Domain
 Remote Sensing                             Ayman F. Habib
                             100
Fourier Transform & Image Enhancement




      Spatial Domain         Frequency Domain
  Remote Sensing                  Ayman F. Habib
                       101




Fourier Transform & Image Enhancement




   Frequency Domain           Spatial Domain

  Remote Sensing                  Ayman F. Habib
                       102

								
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