EE 569 DiscussionZhiruo Zhou02/11/2022Discussion agenda in the next few weeks• Week 6: HW3• Week 7: Review for midterm1• Week 8: (midterm1 on Wednesday) HW4• Week 9: HW4• …2Geometric Modification• Translation• Rotation• Scaling• Shear3Geometric Modification• Translation4Geometric Modification• Rotation• Change the orientation5Geometric Modification• Scaling• Change aspect ratio• May introduce distortion6Geometric Modification• Shear• Different from rotation• Change the angles7Geometric Modification• Affine transformation• Combination of transformations• Translation, scaling, rotation, shear• Achieved by building blocks• Forward transform: 𝑇 = 𝑇1∗ 𝑇2∗ 𝑇3• Inverse transform: 𝑇−1= 𝑇3−1∗ 𝑇2−1* 𝑇1−18Image warping• Different warping methods give different effects• Usually there are some requirements on the warped image• Boundary -> boundary• Center -> center• …9Image warping• Important details• To find transformation relationship, remember to do “image coordinates -> cartesian coordinates”• For easier understanding and expression of math!• Put the origin at the location you prefer (easy for your own understanding)• When modifying the pixel values on images, find the image coordinate from its cartesian coordinate• Inverse address mapping to avoid black dots10Image warping• Forward address mapping• Some pixels in target image may be missed• Black dots in warped image• Inverse address mapping• After finding (x,y) with g(u,v) function, use the value in (x,y) to fill in (u,v) in the target image• No black dots11Image warping• Inverse address mapping (continued)• (𝑥, 𝑦) may be fractional• Bilinear interpolation12P1(a) warping into star• Requirements:• Pixels that lie on boundaries of the square should still lie on the boundaries of the star.• Pixels on the diagonal/off-diagonal of the square should remain where they are.• The thickness of the black arc region is 64 pixels.13Thickness = 64 pixelsP1(a) warping into star14P1(a) warping into star• 12 unknown parameters• Find 6 pairs to solve the linear equation15(𝑥, 𝑦)(𝑢, 𝑣)Homography Transformation & Image Stitching• Homography• Plane projective transformation• Two views of a same planar surface• Two camera share the same center• Panorama• Homography image stitching16Homography Transformation & Image Stitching• Fitting a Homography• Like affine transformations• 8 degree of freedom (scale is arbitrary)• Linear system with 8 unknowns• Each match provides 2 equations• Need at least 4 matches17Homography Transformation & Image Stitching• Image stitching• Steps:• SURF/SIFT feature detection• Find matching point pairs• Create a large enough canvas• Put left, middle, and right images on canvas• Work on the transformation18Homography Transformation & Image Stitching19Useful resources• Matlab• panorama example• https://www.mathworks.com/help/vision/ug/feature-based-panoramic-image-stitching.html• OpenCV• Basic concepts of the homography explained with code• https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html20Morphological Processing• Shrinking• Objects without holes shrink to a point, and objects with holes shrink to a connected ring halfway between each hole and the outer boundary• Thinning• Object without holes shrinks to a minimally connected stroke, and an object with holes shrinks to a connected ring halfway between each hole and the outer boundary• Skeletonizing• Removes pixels on the boundaries of objects but does not allow objects to break apart. The pixels remaining make up the image skeleton21Morphological Processing• They work on binary images• Erase white pixels• Objects must be white• Remember to binarize the image before any morphological processing!!!!• Given raw images are grayscale images, not binary ones.• Do the binarization according to instructions on the assignment file.22Morphological Processing23Morphological Processing24The input image gets modified in-place in this step! G is your output image (or the modified input image here). M is just an intermediate matrix storing the hitting status.Morphological Processing• Defect detection and counting• (1) count the number of defects25Morphological Processing• (2) different sizes and their frequency• (3) defect clearing• To know the size of a defect• “Connected-component labeling”• Check out the coding problem• https://leetcode.com/problems/number-of-islands/26Object Segmentation and Analysis• Similar to defect detection• Color image -> grayscale image -> binary