Feature Detection and Matching Reading: Szeliski Chapter 4 Pages: 208~266 http://staff.ustc.edu.cn/~xjchen99/teaching/teaching.html

COMPARE with WHAT we learn before? How to UNDERSTAND? COMPARE with WHAT we learn before?

Image Matching TexPoint fonts used in EMF. by Diva Sian by swashford TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

Harder Case by Diva Sian by scgbt

Even Harder Case “How the Afghan Girl was Identified by Her Iris Patterns” Read the story

Harder still? NASA Mars Rover images

Answer below (look for tiny colored squares…) NASA Mars Rover images with SIFT feature matches Figure by Noah Snavely

Features Readings Szeliski, Ch 4.1 All is Vanity, by C. Allan Gilbert, 1873-1929 Readings Szeliski, Ch 4.1 (optional) K. Mikolajczyk, C. Schmid,  A performance evaluation of local descriptors. In PAMI 27(10):1615-1630 http://www.robots.ox.ac.uk/~vgg/research/affine/det_eval_files/mikolajczyk_

Image Matching

Image Matching

Invariant Local Features Find features that are invariant to transformations geometric invariance: translation, rotation, scale photometric invariance: brightness, exposure, … Feature Descriptors

Advantages of Local Features Locality features are local, so robust to occlusion and clutter Distinctiveness: can differentiate a large database of objects Quantity hundreds or thousands in a single image Efficiency real-time performance achievable Generality exploit different types of features in different situations

More Motivation… Feature points are used for: Image alignment (e.g., mosaics) 3D reconstruction Motion tracking Object recognition Indexing and database retrieval Robot navigation … other

Features Point/patch, Edge/curve Region

Want Uniqueness Look for image regions that are unusual Lead to unambiguous matches in other images How to define “unusual”?

Corner Detection Basic idea: Find points where two edges meet—i.e., high gradient in two directions “Cornerness” is undefined at a single pixel, because there’s only one gradient per point Look at the gradient behavior over a small window Categories image windows based on gradient statistics Constant: Little or no brightness change Edge: Strong brightness change in single direction Flow: Parallel stripes Corner/spot: Strong brightness changes in orthogonal directions

Matching Criterion (weighted) Summed Square Difference – SSD Compare an image patch against itself

Local Measures of Uniqueness Suppose we only consider a small window of pixels What defines whether a feature is a good or bad candidate? High level idea is that corners are good. You want to find windows that contain strong gradients AND gradients oriented in more than one direction Slide adapted from Darya Frolova, Denis Simakov, Weizmann Institute.

Feature Detection Local measure of feature uniqueness How does the window change when you shift it? Shifting the window in any direction causes a big change “flat” region: no change in all directions “edge”: no change along the edge direction “corner”: significant change in all directions Slide adapted from Darya Frolova, Denis Simakov, Weizmann Institute.

Feature Detection: Mathematics Consider shifting the window W by (u,v) how do the pixels in W change? compare each pixel before and after by summing up the squared differences (SSD) this defines an SSD “error” of E(u,v): W

Harris Detector: Mathematics Change of intensity for the shift [u,v]: Auto-correlation function Window function Intensity Shifted intensity or Window function w(x,y) = Gaussian 1 in window, 0 outside

Auto-Correlation Function

Auto-Correlation Function Good unique minimum 1D aperture problem No good peak

Small Motion Assumption Taylor Series expansion of I: If the motion (u,v) is small, then first order approx is good

Feature Detection: Mathematics Image gradient Harris detector with a [-2,-1,0,1,2] filter for Ix Gaussian filter

Small Motion Assumption Plugging this into the formula on

Feature Detection: Mathematics W

Feature Detection: Mathematics This can be rewritten: x- Auto-correlation matrix x+

Feature Detection: Mathematics

Feature Detection: Mathematics For the example above You can move the center of the blue window to anywhere on the blue unit circle Which directions will result in the largest and smallest E values? We can find these directions by looking at the eigenvectors of H

Quick eigenvalue/eigenvector review The eigenvectors of a matrix A are the vectors x that satisfy: The scalar  is the eigenvalue corresponding to x The eigenvalues are found by solving: In our case, A = H is a 2x2 matrix, so we have The solution: Once you know , you find x by solving

Feature Detection: Mathematics This can be rewritten: x- x+ Eigenvalues and eigenvectors of H=A Define shifts with the smallest and largest change (E value) x+ = direction of largest increase in E. + = amount of increase in direction x+ x- = direction of smallest increase in E. - = amount of increase in direction x+

Feature Detection: Mathematics Intensity change in shifting window: eigenvalue analysis 1, 2 – eigenvalues of H If we try every possible orientation n, the max. change in intensity is 2 Ellipse E(u,v) = const (max)-1/2 (min)-1/2

Feature Detection: Mathematics 2 Classification of image points using eigenvalues of H: “Edge” 2 >> 1 “Corner” 1 and 2 are large, 1 ~ 2; E increases in all directions 1 and 2 are small; E is almost constant in all directions “Edge” 1 >> 2 “Flat” region 1

Feature Detection: Mathematics How are +, x+, -, and x+ relevant for feature detection? What’s our feature scoring function?

Feature Detection: Mathematics How are +, x+, -, and x+ relevant for feature detection? What’s our feature scoring function? Want E(u,v) to be large for small shifts in all directions the minimum of E(u,v) should be large, over all unit vectors [u v] this minimum is given by the smaller eigenvalue (-) of H

Feature Detection Here’s what you do Compute the gradient at each point in the image Create the H matrix from the entries in the gradient Compute the eigenvalues. Find points with large response (- > threshold) Choose those points where - is a local maximum as features

Feature Detection Here’s what you do Compute the gradient at each point in the image Create the A matrix from the entries in the gradient Compute the eigenvalues. Find points with large response (- > threshold) Choose those points where - is a local maximum as features [Shi and Tomasi 1994]

Harris Detector Measure of corner response: Harris and Stephens 1988 (k – empirical constant, k = 0.04-0.06) The trace is the sum of the diagonals, i.e., trace(H) = h11 + h22 Very similar to - but less expensive (no square root)

Harris Detector: Mathematics 2 “Edge” “Corner” R depends only on eigenvalues of H R is large for a corner R is negative with large magnitude for an edge |R| is small for a flat region R < 0 R > 0 “Flat” “Edge” |R| small R < 0 1

Harris Detector The Algorithm: Find points with large corner response function R (R > threshold) Take the points of local maxima of R

Harmonic Mean Smoother function in the region where Brown, M., Szeliski, R., and Winder, S. (2005). Smoother function in the region where

Isocontours of Response

Harris Detector: Workflow

Harris Detector: Workflow Compute corner response R

Harris Detector: Workflow Find points with large corner response: R>threshold

Harris Detector: Workflow Take only the points of local maxima of R

Harris Detector: Workflow

Example: Gradient Covariances Corners are where both eigenvalues are big from Forsyth & Ponce Detail of image with gradient covar- iance ellipses for 3 x 3 windows Full image

Example: Corner Detection (for camera calibration) courtesy of B. Wilburn

Example: Corner Detection courtesy of S. Smith SUSAN corners

Harris Detector: Summary Average intensity change in direction [u,v] can be expressed as a bilinear form: Describe a point in terms of eigenvalues of H: measure of corner response A good (corner) point should have a large intensity change in all directions, i.e. R should be large positive

Outline of Feature Detection Compute the horizontal and vertical derivatives of the image Ix and Iy by convolving the original image with derivatives of Gaussians Compute the three images corresponding to the outer products of these gradients. (The matrix H is symmetric, so only three entries are needed.) Convolve each of these images with a larger Gaussian. Compute a scalar interest measure using one of the formulas discussed above. Find local maxima above a certain threshold and report them as detected feature point locations.

Adaptive Non-Maximal Suppression (ANMS) (a) Strongest 250 (b) Strongest 500 Local maxima Response value should be significantly (10%) larger than all of its neighbors within a radius (r)

Adaptive Non-Maximal Suppression (ANMS) (a) Strongest 250 (b) Strongest 500 (c) ANMS 250, r = 24 (d) ANMS 500, r = 16

Invariance Suppose you rotate the image by some angle Will you still pick up the same features? What if you change the brightness? Scale? Rotation: yes (with some caveats—image resampling errors…) Change brightness: probably, but will have to adjust thresholds Scale: no, generally.

Invariance Repeatability of feature detector: frequency with which keypoints are detected in one image are found within ε (ε=1.5) pixels of the corresponding location in a transformed image

Scale Invariance Detect features at a variety of scales Multiple resolutions in a pyramid Matching in all possible levels

Multi-Scale Oriented Patches

Scale invariant detection Suppose you’re looking for corners Show other scales and how the feature looks less corner like

Feature Detection Key idea: find scale that gives local maximum of f f is a local maximum in both position and scale Common definition of f: Laplacian Difference between two Gaussian filtered images with different sigmas

Feature Detection Stable features in both location and scale Laplacian of Gaussian (LoG) Difference of Gaussian

Lindeberg et al., 1996 Lindeberg et al, 1996 Slide from Tinne Tuytelaars Slide from Tinne Tuytelaars

Scale-Space Feature Detection Empirical number of levels in each octave = 3

SIFT Feature Detection Scale Invariant Feature Transform

Feature Detector Sample image Harris response DoG response Harris and DoG detectors tend to respond at complementary locations.

Rotation Invariance and orientation estimation Dominant orientation Average gradient within a region around the keypoint (larger window than detection window to make it more reliable) Orientation histogram

Affine Invariance For wide baseline stereo matching or object recognition

Affine Invariance For a small enough patch, any continuous image wrapping can be well approximated by an affine deformation Eigenvalue analysis for Hessian matrix or auto-correlation: using the principle axis and ratios to fit the affine coordinate frame (Lindeberg and Garding 1997; Baumberg 2000; Mikolajczyk and Schmid 2004; Mikolajczyk, Tuytelaars, Schmid et al. 2005; Tuytelaars and Mikolajczyk 2007)

Affine Invariance Maximally Stable Extremal Region (MSER) Algorithm Matas, Chum, Urban et al. (2004) Algorithm Binary regions by thresholding the image at all possible gray levels Region area changes as the threshold changes D_area/D_t is minimal  maximal stable

Keypoint Detection Very active area (Xiao and Shah 2003; Koethe 2003; Carneiro and Jepson 2005; Kenney, Zuliani, and Manjunath 2005; Bay, Tuytelaars, and Van Gool 2006; Platel, Balmachnova, Florack et al. 2006; Rosten and Drummond 2006 Invariance to transformation such as scaling, rotations, noise, and blur These experimental results, code, and pointers to the surveyed papers can be found on their Web site at http://www.robots.ox.ac.uk/vgg/research/affine/ (Mikolajczyk, Tuytelaars, Schmid et al. 2005)

4.1.2 Feature Descriptor TBD

SIFT Feature Scale Invariant Feature Transform (SIFT) Distinctive Image Features from Scale-Invariant Keypoints, David G. Lowe Scale Invariant Feature Transform (SIFT) Detect features that densely cover the image over the full range of scales and locations

Points and Patches Two approaches to finding feature points and their correspondences detect in one, then track For video sequence application, tracking, stereo… Detect independently, then match For image stitching, recognition …

Keypoint Detection and Matching Four steps: Feature detection Feature description Feature matching Feature tracking