3Computer and Robot Vision I IntroductionRegion Properties
4Region Properties Introduction Region Description Region is a segment produced by connected component labeling or signature segmentation.The computation of region properties can be the input for further classification.Gray-Level Value AnalysisShape Property Analysis
5Simple Global Properties Region PropertiesSimple Global PropertiesRegion AreaCentroidA=21r=3.476c=4.0951234567
6Simple Global Properties Region PropertiesSimple Global PropertiesPerimeter DescriptionIt is a sequence of its interior border pixels.Border pixels are the pixels that have some neighboring pixel outside the region.Types of Perimeter4-Connected Perimeter : Use 8-Connectivity to determine the border pixel.8-Connected Perimeter :Use 4-Connectivity to determine the border pixel.
7Simple Global Properties Region PropertiesSimple Global Properties4-Connected Perimeter
8Simple Global Properties Region PropertiesSimple Global Properties8-Connected Perimeter
9Simple Global Properties Region PropertiesSimple Global PropertiesPerimeter RepresentationIt is a sequences of border pixels in orare neighborhood
10Simple Global Properties Region PropertiesSimple Global PropertiesPerimeter LengthVertical or Horizontal LineDiagonal Line
11Simple Global Properties Region PropertiesSimple Global PropertiesCompactness MeasureIt is used as a measure of a shape’s compactness.Its smallest value is not for the digital circularity, but it would for continuous planar shapesOctagonsDiamonds
12Simple Global Properties Region PropertiesSimple Global PropertiesCircularity MeasureBoundary Pixels
13Simple Global Properties Region PropertiesSimple Global PropertiesCircularity MeasurePropertiesDigital shape circular, increases monotonically.It is similar for similar digital/continuous shapesIt is orientation and area independent.Polygon Side Estimation
14Simple Global Properties Region PropertiesSimple Global PropertiesGray-Level MeanGray-Level VarianceRight hand equation lets us compute variance with only one pass
15Simple Global Properties Region PropertiesSimple Global PropertiesMicrotexture PropertiesCo-occurrence MatrixS : a set of all pairs of pixels that are in some defined spatial relationship (4-neighbors)
16Simple Global Properties Region PropertiesSimple Global Properties123DC & CV Lab.CSIE NTU
17Simple Global Properties Region PropertiesSimple Global PropertiesMicrotexture PropertiesTexture Second MomentTexture EntropyTexture Homogeneity
18Simple Global Properties Region PropertiesSimple Global PropertiesMicrotexture PropertiesContrastCorrelation
19Definition of Extremal Points Region PropertiesExtremal PointsDefinition of Extremal PointsIt has an extremal coordinate value in either its row or column coordinate positionThey can be as many as eight distinct extermal points.
26Length of Respective Axes Region PropertiesExtremal PointsLength of Respective Axes: one end point of respective axes: the other point of respective axesQuantization ErrorCompensation Term
27Orientation of Respective Axes Region PropertiesExtremal PointsOrientation of Respective AxesOrientation of a line segment is taken as counterclockwise with respect to column axis.Quantization ErrorCompensation Term
28Properties of Line-like Region Region PropertiesExtremal PointsProperties of Line-like RegionMajor Axis : the axis with the largest length.The length and orientation of major axis stands for the same thing for this region.
29Region PropertiesExtremal PointsProperties of Line-like Region
30Properties of Triangular Shapes Region PropertiesExtremal PointsProperties of Triangular ShapesApex Selection: Find the extremal point having the greatest sum of its two largest distances.Extremal Point DistanceObjective Function
31Properties of Triangular Shapes Region PropertiesExtremal PointsProperties of Triangular ShapesSide LengthBase LengthAltitude Height
33Second-Order Spatial Moments Region PropertiesSpatial MomentsSecond-Order Spatial MomentsRow MomentMixed MomentColumn Moment
34Second-Order Spatial Moments Region PropertiesSpatial MomentsSecond-Order Spatial MomentsThey have value meaning for a region of any shapeSimilarly, the covariance matrix has value and meaning for any two-dimensional pdf.Example: An ellipse A whose center is the origin.
35Mixed Spatial Gray Level Moments Region PropertiesMixed Spatial Gray Level MomentsDescriptionA property that mixes up two properties.Spatial Properties: Region Shape, PositionIntensity propertiesTwo Second-order Mixed Spatial Gray Properties
36Mixed Spatial Gray Level Moments Region PropertiesMixed Spatial Gray Level MomentsApplication: Determine the least-square, best-fit gray level intensity plane.Unknowns Variables:Objective Function
37Mixed Spatial Gray Level Moments Region PropertiesMixed Spatial Gray Level MomentsApplication: Determine the least-square, best-fit gray level intensity planeTake partial derivative of with respect toLeast Square Method
38Mixed Spatial Gray Level Moments Region PropertiesMixed Spatial Gray Level MomentsApplication: Determine the least-square, best-fit gray level intensity plane
40Computer and Robot Vision I IntroductionSignature Properties
41Signature Properties Introduction Signature Review Remark: Signature analysis is importantbecause of easy, fast implementation in pipeline hardware
42Signature Computation Signature PropertiesSignature ComputationCentroidSecond-Order Moment
43Signature Computation Signature PropertiesSignature ComputationSecond-Order Moment
44Circle Center Determination Signature PropertiesCircle Center DeterminationDescriptionWe can determine the center position of circular region from signature analysis.
45Circle Center Determination Signature PropertiesCircle Center DeterminationDerivation
46Circle Center Determination Signature PropertiesCircle Center DeterminationDerivationCompute by a table-look-up technique
47Circle Center Determination AlgorithmStep 1: Partition the circuit into four quadrants formed by two orthogonal lines intersecting inside the circle.Step 2: Using signature analysis to compute the areas A, B, C, and, D.Step 3: Compute using the derived equation.
48Computer and Robot Vision I IntroductionContour-BasedShape Representation
49Chain Code Description It describes an object by a sequence of unit-size line segment with a given orientation.The first element must bear information about its position to permit region reconstruction.Chain Code: 3, 0, 0, 3, 0, 1, 1, 2, 1, 2, 3, 2
50Chain Code Matching Requirement It must be independent of the choice of the first border pixel in the sequence.It requires the normalization of chain codeInterpret the chain code as a base 4 number.Find the pixel in the border sequence which results in the minimum integer number.Chain Code: ( )4Chain Code: ( )4
51Curvature Description Curvature is defined as the rate of change of slope in the continuous case.The evaluation algorithm in the discrete case is based on the detection of angles between two lines.Values of the curvature at all boundary pixels can be represented by a histogram for matching.
53Signature Description The signature is a sequence of normal contour distances.It can be calculated for each boundary elements as a function of the path length.
54Definition of Chord Distribution DescriptionChord is a line joining any two points of the region boundary.The distribution of lengths and angles of all chords may be used for shape description.Definition of Chord Distribution: contour points: all other points
55Chord DistributionRotation-Independent Radial Distribution
56Recursive Boundary Splitting Segment SequenceDescriptionIt is a way to represent the boundary using segments with specified properties.Recursive Boundary Splitting
57Chromosomes Representation. Segment SequenceStructure DescriptionCurves are segmented into several typesCircular ArcsStraight LineSegments are considered as primitives for syntactic shape recognitionChromosomes Representation.
58Scale-Space Image Description Approach Properties Sensitivity of shape descriptors to scale (image resolution) is an undesirable feature.Some curve segmentation points exist in one resolution and disappear in others.Approach PropertiesOnly new segmentation points can appear at higher resolution.No existing segmentation points can disappear.
59Scale-Space Image Approach Description It is based on application of a unique Gaussian smoothing kernel to a one-dimensional signal.The zero-crossing of the second derivative is detected to determine the peak of curvature.The positions of zero-crossing give the positions of curve segmentation points.