3 Affine TransformsAffine transforms cover a linear combination of translations, scale, and rotationI(x,y) is the original imageI’(x’,y’) is the transformed imageTypePropertiesMeaningTranslationaij = 0; i,j = 1,2Scalinga12=a21=0Rotationa11= a12=-a21= a22=Slanta11= a12=a21= a22= 1: rotation angle: slant angle
4 Linear Filters Convolution Equation Smoothing Low pass filter Vertical Line Sensitive filterVertical edgeSensitive filterEnhancement filterLaplacian Edge Operator
6 DilationFor each background pixel superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel position.If at least one pixel in the structuring element coincides with a foreground pixel in the image underneath, then the input pixel is set to the foreground value.If all the corresponding pixels in the image are background, however, the input pixel is left at the background value.
7 ErosionFor each foreground pixel superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel position.If every pixel in the structuring element coincides with a foreground pixel in the image underneath, then the input pixel is left as is.If any pixel coincides with background, however, the input pixel is changed to background.
8 Opening and ClosingOpening: Erosion followed by Dilation using the same kernelClosing: Dilation followed by Erosion using the same kernel
9 Hit and Miss Kernel has 1s, 0s, and don’t-care If the 1s and 0s in the kerenel exactly match 1s and 0s in image, then the pixel underneath the origin is set to 1 else 0Corner finding kernelsFinal result is “OR” of the outputsused to locate isolated points in a binary image.used to locate the end points on a binary skeleton -four hit-and-miss passes - one for each rotationused to locate the triple points (junctions) on a skeleton.
10 ThinningNT(P1) = no. of 0 to 1 transitions in the ordered sequence ,<P2, P3, P9, P2>NZ(P1) = no. of non-zero neighbors of P1Set P1 to 0If 1<NZ(P1)<7 ANDIf NT(P1) = 1 ANDP2.P4.P8 = 0 OR NT(P2) .NE. 1 ANDP2.P4.P6 = 0 OR NT(P4) .NE. 1Use both kernels and their 90o variationsConsider all pixels on the boundaries of foreground regions. Delete pixel that has more than one foreground neighbor, as long as doing so does not locally disconnectIterate until convergence.
11 Vornoi Diagrams and Convex Hulls Thickening can be performed by thinning the backgroundConvex hull of a binary shape can be visualized by imagining stretching an elastic band around the shape. The elastic band will follow the convex contours of the shape, but will `bridge' the concave contours.1a and 1b are used for skeletonization of background.On each thickening iteration till convergence, each element is used in turn, and in each of its 90° rotations.Structuring elements 2a and 2b are used similarly to prune the skeleton until convergence to get VORNOI diagram.
12 Connected Component Labeling Scan the image by moving along a row reach a point p to be labeledExamines neighbors of p which have already been encountered in the scan(i) to the left of p, (ii) above it, and (iii and iv) the two upper diagonal terms.If all four neighbors are 0, assign a new label to pelse if only one neighbor is 1 assign its label to pelse if one or more of the neighbors are 1 assign one of the labels to p and note the equivalences.After completing the scan, the equivalent label pairs are sorted into equivalence classes and a unique label is assigned to each class.
14 Adaptive Thresholding Adaptive (T= mean) threshold with 7x7 neighborhoodOriginal gray scaleGlobal thresholdAdaptive (T=mean-C) threshold with 7x7 neighborhood; C=7 and C=10Using T= median instead of the mean
17 Features Geometrical Features Structural Features Moments Sizes in x and y direction, aspect ratio, perimeter, areaMaximum and minimum distances from boundary to center of massCompactness = Perimeter2 / (4 Pi . Area)Signatures = projection profilesStructural FeaturesNumber of holesEuler Number = no. of components – no. of holesMoments= area of the object= center of mass
18 X-Y CutsAutocorrelation function of the projection profile, k is the lag parameterIf k=kp is the first peak following the peak at k=0, sharpness of peak is given by
25 Docstrum Slope Histograms Use local information Connect a mark (component) with K (=4..6) neighborsHistogram of the slopesMore efficient than projection profilesDocstrum is the radius and angle plot of the slopes