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Thunderstorm In Situ Measurements from the Armored T28 Aircraft: Classification of 2D Probe Hydrometeor Images. Rand Feind. Overview. The problem The data Classes Feature Selection Classifiers Results. The Problem. Sensor on T-28 collects images - PowerPoint PPT Presentation

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  • Thunderstorm In Situ Measurements from the Armored T28 Aircraft: Classification of 2D Probe Hydrometeor Images

    Rand Feind

  • OverviewThe problemThe dataClassesFeature SelectionClassifiersResults

  • The ProblemSensor on T-28 collects imagesNumber of images can number in the hundreds of thousandsHydrometeor classification provides key to estimating cloud characteristics

  • 2DC and HVPS Probes

  • The DataStrips taken from the sensor Treated as black/white images2000 images extracted for training and testing

  • The Classes1. Drops - smooth perimeters; appear to be circular2. Snow - irregular, convoluted perimeters3. Hail - somewhat rough, lumpy perimeters; appear to be circular 4. Columns - linear like needles but wider; can have rough perimeters5. Needles - linear and narrow6. Dendrites - like snow but evidence of 6-way symmetry7. Plates - appear to be planar and 6-sided8. Holes - anomalous images (due to probe tip shedding)

  • Drops

    Snow

    Hail

    Columns

    Needles

    Dendrites

    Plates

    Holes

    Figure 1.

  • Drops

    Snow

    Hail

    Columns

    Needles

    Dendrites

    Plates

    Holes

    Figure 1.

  • Feature SelectionNeed to select features for classificationHow many? Literature search for ideasStart with many, eliminate (started with 25)Elimination using divergence measureProvided base set of 6Trial and errorAdd one at a time, check errorDelete one of 6, check error

  • Example : Basic MetricsX Dimension - The width of the image in pixels along the flight direction (x-dimension) (e.g., the horizontal dimension).

    Y Dimension - The height of the image in pixels perpendicular to the flight direction (y-dimension) (e.g., the vertical dimension). Note: In the case of the T-28, this orientation is perpendicular to the wingspan.

    Heymsfield Diameter - The larger of the X Dimension and the Y Dimension above.

  • Basic MetricsBottom Occulted - If the 32 photodetectors in the 2DC probe are numbered 1 through 32, this metric is the number of times photodetector 1 is shaded (i.e., the number of image pixels along the bottom edge of the image window).

    Top Occulted - Same as Bottom Occulted except photodetector 32 or the top edge of the image window.

    Total Occulted Sum of the previous two features. Used as a particle rejection criterion in Holroyd, 1987.

  • Basic MetricsPixel Area Sum of the number of pixels comprising a 2D image.

    Area Area of the particle image in square micrometers (um).

    Streak Ratio of the x-dimension to the y-dimension. Used to detect anomalous images resulting from the shedding of droplets, from the probes tips, that are moving slower than the air stream.

  • Basic MetricsPerimeter The perimeter is determined in three different ways each of which has a unique value. The first is determined by subtracting from the original particle image an eroded version of it . The second is determined by subtracting the original particle image from a dilated version of it. The second perimeter is always larger than the first. A perimeter or bug finding algorithm (Ballard and Brown, 1982) determines the third perimeter. The bug finding algorithm also provides an ordered sequence of coordinates around the perimeter which is used in the calculation of Fourier Descriptors.

    Maximum Area Area of a circle using maximum length as the diameter.

  • Divergence Jeffries-Matusita (JM) distance Values range 0 (identical) to 2 (little overlap)Hope : one feature gives value of about 2 for each pair of classes. Never happens.Assumes normal distribution

  • Divergence cont.where p(x|wi) and p(x|wj) are the normal probability distributions for the two classes i and j

  • Features selectedPDAPerimeter Diameter Area (PDA) The product of the perimeter and diameter divided by the area. Smooth, circular images give smaller values while irregular ones give larger values.LinearityLinearity The correlation coefficient for the regression. Values for linear images, such as of a needle or column, are closer to 1. This is as opposed to circularly symmetric images that have values closer to 0. A Holroyd measure.equivalent circleEquivalent Circle The diameter of a circle that has the same area as the particle image.

  • Features selectedConcavityThe ratio of the number of concave perimeter points to the distance around the convex hull. Convex images give zero or small values while images with concavities give larger values. projection fit- The standard error of a least squares quadratic regression of the projection of the number of pixels in the vertical along the horizontal. Smooth, circular images give low standard errors while irregular shapes give high errors.

  • Features selectedconvex hullThe convex hull is the distance around the perimeter of a particle image as though a rubber band were stretched around it, or the distance traversed by rolling the image along a straight line.

  • Feature DistributionsDistributions are not always:GaussianMonomodalWell separated between/among classes

  • Classification Methodologies

    Mahalanobis Minimum Distance

    Fuzzy Logic

    Backpropagation Neural Network

  • MahalanobisForm of Maximum Likelihood ClassifierAssume equal a priori probabilitiesA Euclidean distance with directionalityRichards, 1986

  • Mahalanobis(2D feature space)Richards, 1986Feature 1Feature 2PProbability of image belonging to each classClass 1Class 2Class 3

  • ResultsPerformance or accuracy of each of 3 classifiers was derived using a separate set of training and testing sample images

  • Confusion Matrices

  • Table 1. Mahalanobis Classifier Confusion Matrix

    a) Normalized by Rows - P(class j | classification i) x 100

    Classification i:

    Class j

    Drops

    Snow

    Hail

    Cols

    Need

    Dend

    Plates

    Holes

    Unk

    # Sam

    Drops

    97.1

    0.0

    2.2

    0.0

    0.0

    0.0

    0.0

    0.0

    0.7

    137

    Snow

    0.0

    75.1

    4.7

    2.3

    0.0

    16.9

    0.0

    0.0

    0.9

    213

    Hail

    33.1

    1.7

    55.1

    0.8

    0.0

    0.8

    6.8

    1.7

    0.0

    118

    Cols

    0.0

    3.7

    0.0

    85.2

    1.9

    3.7

    4.6

    0.0

    0.9

    108

    Need

    0.0

    0.0

    0.0

    1.7

    93.1

    0.0

    0.0

    1.7

    3.4

    58

    Dend

    0.0

    30.3

    6.1

    6.1

    0.0

    57.6

    0.0

    0.0

    0.0

    33

    Plates

    25.9

    0.0

    9.8

    0.7

    0.0

    0.7

    58.0

    4.9

    0.0

    143

    Holes

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    0.7

    96.5

    2.8

    144

    b) Normalized by Columns - P(classification j | class i) x 100

    Classification i:

    Class j

    Drops

    Snow

    Hail

    Cols

    Need

    Dend

    Plates

    Holes

    Unk

    Drops

    63.6

    0.0

    3.2

    0.0

    0.0

    0.0

    0.0

    0.0

    10.0

    Snow

    0.0

    90.9

    10.6

    4.9

    0.0

    59.0

    0.0

    0.0

    20.0

    Hail

    18.7

    1.1

    69.1

    1.0

    0.0

    1.6

    8.2

    1.3

    0.0

    Cols

    0.0

    2.3

    0.0

    90.2

    3.6

    6.6

    5.2

    0.0

    10.0

    Need

    0.0

    0.0

    0.0

    1.0

    96.4

    0.0

    0.0

    0.7

    20.0

    Dend

    0.0

    5.7

    2.1

    2.0

    0.0

    31.1

    0.0

    0.0

    0.0

    Plates

    17.7

    0.0

    14.9

    1.0

    0.0

    1.6

    85.6

    4.7

    0.0

    Holes

    0.0

    0.0

    0.0

    0.0

    0.0

    0.0

    1.0

    93.3

    40.0

    # Sam

    209

    176

    94

    102

    56

    61

    97

    149

    10

    Total Acc: 78.1

    Features PDA, LINEARITY, CONVEX, EQUIV_CIR, CONCAVE, PROJECTION,STREAK

  • Table 2. Fuzzy Logic Classifier Confusion Matrix

    a) Normalized by Rows - P(class j | classification i) x 100

    Classification i:

    Class j

    Drops

    Snow

    Hail

    Cols

    Need

    Dend

    Plates

    Holes

    Unk

    # Sam

    Drops

    65.7

    0.0

    11.7

    7.3

    0.0

    0.0

    11.7

    3.6

    0.0

    137

    Snow

    0.0

    62.0

    0.9

    5.6

    0.0

    31.5

    0.0