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Introduction to Computer Vision & Robotics Introduction to Computer Vision & Robotics 16 December 2020 Lecture 7 [email protected] Georg-August University, Göttingen, Germany 0 Last time we talked about 1. Morphological image processing • Erosion, dilation, opening, closing • Detection of isolated pixels or certain (simple) shapes • Convex hull • Hole filling • Morphological gradients 2. Image Features • Gradients and Edges • Corners 1 What is a feature descriptor? • useful information • simplifies an image (or image patch) • much smaller in size than a whole image • should not depend on rotation, scale, illumination and so on Descriptors are then used for matching! 2 We can use only circle and color information Example of a naive descriptor How can we describe these images in a compressed form? 3 Example of a naive descriptor How can we describe these images in a compressed form? We can use only circle and color information 3 Hough Transform Basic shape descriptors: Hough Transformation • It was invented and patented in 1960s • Then extended to arbitrary shapes in 1970s • The idea is to find imperfect instances of objects within a certain class of shapes by a voting procedure. • The simplest case of Hough transform is detecting straight lines. • Here we’ll consider lines and circles 4 Hough Lines Different Line parameterizations possible: • Cartesian Coordinates y • Parameters: (a, b) • Equation: y = ax + b • Problem: representation can not handle vertical lines • Polar Coordinates • Parameters: (r, θ) r • Equation: y = (− cos θ )x + ( r ) sin θ sin θ θ x wiki/houghtransform 5 Hough Lines − cos θ r • y = ( sin θ )x + ( sin θ ) • r = x cos θ + y sin θ • Idea of Hough algorithm: vote for possibilities • We need to discretize our voting space (called accumulator) wiki/houghtransform 6 Hough Lines 7 Hough Algorithm • Find Feature locations in Image • For each feature point xi: • For each possibility pj in the accumulator that passes through the feature point: • Increment acumulator at this position • Find the maximum element of the accumulator, it’s location reflect the according parameter values • Map back to image space 8 Example: Hough Lines Algorithm 9 wiki/houghtransform Example: Hough Lines Algorithm wiki/houghtransform 10 OpenCV Functions import cv2 import numpy as np img = cv2.imread('dave.jpg') gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY) edges = cv2.Canny(gray,50,150,apertureSize = 3) lines = cv2.HoughLines(edges,1,np.pi/180,200) for rho,theta in lines[0]: a = np.cos(theta) b = np.sin(theta) x0 = a*rho y0 = b*rho x1 = int(x0 + 1000*(-b)) y1 = int(y0 + 1000*(a)) x2 = int(x0 - 1000*(-b)) y2 = int(y0 - 1000*(a)) cv2.line(img,(x1,y1),(x2,y2),(0,0,255),2) 11 Example (Classical Hough) http://opencvexamples.blogspot.com 12 Example (Probabilistic Hough) 13 docs.opencv.org Circle Hough Transform Circle Hough Transform • We can also detect circles! • Circle with radius R and center at (a; b) has the parametric equations x = a + R cos θ y = b + R sin θ 14 Circle Hough Transform • What if circles of different radii should be detected? 15 Hough Circles: Example docs.opencv.org 16 OpenCV Circle Detector import numpy as np import cv2 as cv img = cv.imread('opencv-logo-white.png',0) img = cv.medianBlur(img,5) cimg = cv.cvtColor(img,cv.COLOR_GRAY2BGR) circles = cv.HoughCircles(img,cv.HOUGH_GRADIENT,1,20, param1=50,param2=30, minRadius=0,maxRadius=0) circles = np.uint16(np.around(circles)) for i in circles[0,:]: # draw the outer circle cv.circle(cimg,(i[0],i[1]),i[2],(0,255,0),2) # draw the center of the circle cv.circle(cimg,(i[0],i[1]),2,(0,0,255),3) 17 Practical Problem Industrial Vision: Check the status of the detail 18 Practical Problem Industrial Vision: Check the status of the detail 19 Features Why Features? • Features are used for matching • Template Matching: Find/Locate a specific object inside an image (object recognition) • Find correlating features in multiple images to reconstruct the (3D) scene (navigation, mapping, tracking) 20 Template Matching 21 Template Matching 22 Panorama Creation 23 Matching 24 Feature requirements? • Rotation invariant (e.g. Harris-Corner-Detection) • Invariant under different lighting • Scale invariant 25 David Lowe 26 Outline: SIFT • Identify Scale-Invariant Keypoint-Candidates in the Image • Filter out bad Candidates • Create one Feature Vector for each valid candidate, that describes the region around the keypoint 27 Feature descriptors • useful information • simplifies an image (or image patch) • much smaller in size than a whole image • should not depend on rotation, scale, illumination and so on • Descriptors are then used for matching! More advanced feature descriptors than basic shapes, edges, corners. 28 SIFT: Scale invariant feature transform • Invented (and patented) by David Lowe (1999, 2004) • Invariant to scale, rotation, illumination, viewpoint • It gave start to a whole family of advanced feature descriptors • It has many extensions, e.g., SURF, PCA-SHIFT • It can robustly identify objects even among clutter and under partial occlusion • Within the last decades has many applications in Computer Vision, Robotics etc. 29 Basic Idea Image content is transformed into local features that are invariant to translation, rotation, scale, and other imaging parameters courses.cs.washington.edu 30 Algorithm Overview 1. Detector • Construct a scale-space • Detect scale-space extrema • Localize keypoints 2. Descriptor • Assign orientation to each key point • Compute descriptor vectors • Normalize the vectors 31 Scale-invariant feature transform (SIFT) docs.opencv.org 32 1. Scale Space Construction • Goal: identify locations and scales that can be repeatably assigned under different views of the same scene or object. • Method: search for stable features across multiple scales using a continuous function of scale. ∗ 1 −(x2+y2)=(2σ2) • L(x; y; σ) = G(x; y; σ) I(x; y), where G(x; y; σ) = 2πσ e • The scale space of an image L(x; y; σ) is produced by progressively convolving the input image with a Gaussian kernel at different scales 33 Blob Detection • How to detect blobs of specific size? • Use Difference of Gaussians • Convolution of a Gaussian kernel on an Image: blurring (suppression of lower frequencies) • Substracting two Images that were convolved by Gaussian kernels of different sizes preserves range of frequencies courses.cs.washington.edu 34 Variable Size Blob Detection • Use filters of different sizes courses.cs.washington.edu 35 Image Pyramids • Bottom level is the original image • Each next level is derived from the previous one according to some function (e.g., Downsampling and Convolution with Gaussian kernel) courses.cs.washington.edu 36 1. Scale Space Construction • In SIFT scale-space image representation consists of N octaves, defined by two parameters s and σ • Each octave is an ordered set of s + 3 images such that m m ∗ L(x; y; k σ)p = G(x; y; k σ) fi(x; y), where k = 2, fi is i-th sub-sample of I, m = 0; 1;:::; s + 2, i = 1;:::; N 37 1. Scale Space Construction s = 2, five images in each octave David Lowe 38 1. Scale Space Construction s = 2, five images in each octave David Lowe 39 2. Extrema Detection Apply Difference of Gaussian (DoG) to approximate the Laplacian of Gaussian (LoG, which is a known blob detector) David Lowe 40 2. Extrema Detection • Detect maxima and minima of DoG in scale space • Each point is compared to its 8 neighbors in the octave and to the 9 neighbors of increased and decreased scale inside the same octave David Lowe 41 3. Extrema Detection • Local extrema are refined • Reject points with bad contrast (thresholding) • Reject points with strong edge response in one direction only • Edge points are detected using Hessian matrix (similar to Harris) • Basically, we want to keep only corner-like keypoints • Now, we can compute the descriptors 42 The aperture Problem • Why do we want corner-like patches only and not edge-like features? 43 3. Extrema Detection 44 4. Orientation Assignment • For each keypoint we have coordinates and scale (σ) • Use scale of point to choose the closest image L(x; y; σ) = G(x; y; σ) ∗ I(x; y) • Compute gradient magnitude and orientation of each keypoint pm(x; y; σ) = (L(x + 1; y; σ) − L(x − 1; y; σ))2 + (L(x; y + 1; σ) − L(x; y − 1; σ))2 L(x;y+1,σ)−L(x;y−1,σ) θ(x; y; σ) = arctan L(x+1;y,σ)−L(x−1;y,σ) 45 4. Orientation Assignment For region around keypoint • Create Histogram with 36 bins for orientation • Weight each keypoint with Gaussian window of 1:5σ • Create keypoint for all peaks with value ≥ 0:8 of max bin www.inf.fu-berlin.de 46 5. Keypoint Descriptors • Each keypoint now has • location • scale • orientation • A descriptor for the local image region around each keypoint is computed • It must be highly distinctive • Invariant to changes in viewpoint and illumination 47 5. Keypoint Descriptors • Find the blurred image of closest scale • Take a neighborhood around the keypoint (16 × 16) • Rotate the gradients and coordinates according to previously computed orientation (for rotation invariance) • Separate the region into subregions (4 × 4) • Create histogram for each subregion with 8 bins • The descriptor is 4 × 4 × 8 = 128 numbers • Normalize the 128 vector for illumination invariance http://aishack.in 48 Example matching docs.opencv.org 49 OpenCV Usage import numpy as np import cv2 from matplotlib import pyplot as plt img1 = cv2.imread('box.png',0) # queryImage img2 = cv2.imread('box_in_scene.png',0) # trainImage sift = cv2.SIFT() kp1, des1 = sift.detectAndCompute(img1,None) kp2, des2 = sift.detectAndCompute(img2,None) bf = cv2.BFMatcher() matches = bf.knnMatch(des1,des2,
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