Interest Point Detection

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(1)Interest Point Detection CS485/685 Computer Vision Dr. George Bebis.

(2) Interest Points • A point in an image which has a well-defined position and can be robustly detected. • Typically associated with a significant change of one or more image properties simultaneously (e.g., intensity, color, texture)..

(3) Interest Points and Corners • A corner can be defined as the intersection of two or more edges (special case of interest points).. • In general, interest points could be: – Isolated points of local intensity maximum or minimum. – Line endings. – Points on a curve where the curvature is locally maximized..

(4) Why are interest points useful? • For establishing corresponding points between images. stereo matching left camera. right camera. panorama stitching.

(5) How could we find corresponding points? ?. (). feature descriptor. ?. =. () feature descriptor. • Need to define local patches surrounding the interest points and extract feature descriptors from every patch. • Match feature descriptors to find corresponding points..

(6) Properties of good features • Local: features are local, so robust to occlusion and clutter (no prior segmentation!). • Accurate: precise localization. • Invariant (or covariant) covariant • Robust: noise, blur, compression, etc. do not have a big impact on the feature.. Repeatable. • Distinctive: individual features can be matched to a large database of objects. • Efficient: close to real-time performance..

(7) Invariance / Covariance • A function f is invariant under some transformation T if its value does not change when the transformation is applied to its argument: if f(x) = y then f(T(x))=y • A function f is covariant when it changes in a way consistent with the transformation T: if f(x) = y then f(T(x))=T(f(x))=T(y).

(8) Interest point detectors should be covariant • Features should be detected in corresponding locations despite geometric or photometric changes..

(9) Interest point descriptors should be invariant ?. (). ?. feature descriptor. =. () feature descriptor. Should be similar despite geometric or photometric transformations.

(10) Interest point candidates. Use features with gradients in at least two, significantly different orientations (e.g., corners, junctions etc).

(11) Aperture Problem. A corner is easier to match. A point on a line is hard to match.. t. t+1. t. t+1.

(12) Interest point candidates (cont’d) auto-correlation.

(13) Steps in Corner Detection. 1. For each pixel, the corner operator is applied to obtain a cornerness measure for this pixel. 2. Threshold cornerness map to eliminate weak corners. 3. Apply non-maximal suppression to eliminate points whose cornerness measure is not larger than the cornerness values of all points within a certain distance..

(14) Steps in Corner Detection (cont’d).

(15) Corner Detection Methods • Contour based – Extract contours and search for maximal curvature or inflexion points (i.e., curvature zero-crossing) along the contour.. • Intensity based – Compute a measure that indicates the presence of an interest point (1) directly from gray (or color) values or (2) by first fitting a parametric model to the gray (or color) values. – Methods using parametric models can localize corners to sub-pixel accuracy but are more expensive..

(16) A contour-based approach: Curvature Scale Space • Parametric contour representation: (x(t), y(t)). Curvature.

(17) A contour-based approach: Curvature Scale Space g(t,σ): Gaussian. Curvature:.

(18) Curvature Scale Space (cont’d). σ. G. Bebis, G. Papadourakis and S. Orphanoudakis, "Curvature Scale Space Driven Object Recognition with an Indexing Scheme based on Artificial Neural Networks", Pattern Recognition., Vol. 32, No. 7, pp. 1175-1201, 1999..

(19) Zuniga-Haralick Detector • Approximate image function in the neighborhood of the pixel (i,j) by a bi-cubic polynomial.. measure of "cornerness”:  2(k 22 k6  k 2 k3k5  k32 k 4 ) ZH (i, j )  (k 22  k32 ) 3 / 2.

(20) Corner Detection Using Edge Detection? • Edge detectors are not stable at corners. • Gradient is ambiguous at corner tip (i.e., discontinuous near corners)..

(21) Corner Detection Using Intensity • Image gradient has two or more dominant directions near a corner. • Shifting a window in any direction should give a large change in intensity.. “flat” region: no change in all directions. “edge”: no change along the edge direction. “corner”: significant change in all directions.

(22) Moravec Detector (1977) • Idea: measure intensity variation at (x,y) by shifting a small window (3x3 or 5x5) by one pixel in each of the eight principle directions (horizontally, vertically, and four diagonals)..

(23) Moravec Detector (cont’d) • The intensity variation Sw in a given direction (∆x, ∆y) can be calculated as follows:.

(24) Moravec Detector (cont’d) • Moravec’s detector calculates Sw in all 8 directions:. ∆x, ∆y in {-1,0,1}. SW(-1,-1), SW(-1,0), ..., SW(1,1).

(25) Moravec Detector (cont’d) • The “cornerness” of a pixel is the minimum intensity variation found over the eight shift directions: Cornerness(x,y) = min{SW(-1,-1), SW(-1,0), ...SW(1,1)}. Cornerness Map (normalized) Note response to isolated points!.

(26) Moravec Detector (cont’d) • Non-maximal suppression will yield final corners..

(27) Moravec Detector (cont’d) • Does a reasonable job in finding the majority of true corners. • Edge points not in one of the eight principle directions will be assigned a relatively large cornerness value..

(28) Moravec Detector (cont’d) • The response is anisotropic as the intensity variation is only calculated at a discrete set of directions and shifts (i.e., not rotationally invariant).

(29) Harris Detector •. Improves the Moravec detector by: (1) Avoiding the use of discrete directions and discrete shifts. (2) Using a Gaussian window instead of a square window.. 1 in window, 0 outside. Gaussian. C. Harris and M. Stephens. "A Combined Corner and Edge Detector”, Proceedings of the 4th Alvey Vision Conference: pages 147—151, 1988..

(30) Harris Detector (cont’d) • Idea: decompose SW by factor out ∆x, ∆y • Use Taylor series expansion to “linearlize”.

(31) Taylor Series Expansion – Quick Review • A representation of a function f(x) as an infinite sum of terms calculated from the values of its derivatives at a single point a:. 1D. (n ) f´(a) f´´(a ) f (a ) f ( x )  f(a )  ( x  a)  ( x  a )2    ( x  a )n  O( x n 1 ) 1! 2! n!.

(32) Taylor Series Expansion – Example The exponential function (in blue), and the sum of the first n+1 terms of its Taylor series at a=0 (in red)..

(33) Taylor Series Expansion – Quick Review • Can be generalized to higher dimensions: 2D. 1 f ( x)  f (a)  f (a)( x  a )  ( x  a )T Hf (a )( x  a)  ... 2. Gradient. Hessian in n dimensions. Hessian.

(34) Harris Detector (cont’d) Using first order Taylor approximation:. f ( x)  f (a)  f ( a)( x  a). substitute.

(35) Harris Detector (cont’d). SW. rewrite using dot product.

(36) Harris Detector (cont’d) Since. :.

(37) Harris Detector (cont’d)  x  So: SW (x, y )   x y  AW ( x, y )    y . where AW(x,y)=. (. f ( xi , yi ) 2 ) x.  f x2 or AW ( x, y )    xW , yW   fx f y. (. f ( xi , yi ) 2 ) y. fx f y  2  f y . AW(x,y) is a 2 x 2 matrix called auto-correlation or 2nd order moment matrix.

(38) Harris Detector (cont’d) • Using a window function w(x,y), we rewrite SW : w(x,y) : 1 in window, 0 outside. SW (x, y )   w( xi , yi )  f ( xi , yi )  f ( xi  x, yi  y )  xi , yi. 2.

(39) Harris Detector (cont’d) •Then Aw becomes:  f x2 AW ( x, y )    xW , yW   fx f y.  f x2 AW   w( x, y )  x, y  f x f y.  2 w ( x , y ) f  x f x f y   x , y  2  f y     w( x, y ) f x f y  x, y. fx f y  2  f y   w( x, y ) f x f y   x, y   2 w( x, y ) f y   x, y .

(40) Harris Detector (cont’d) • Harris uses a Gaussian window: w(x,y)=G(x,y,σI) where σI is called the “integration” scale:. w(x,y) : Gaussian.  f x2 AW   w( x, y )  x, y  f x f y.  2 w ( x , y ) f  x f x f y   x , y  2  f y     w( x, y ) f x f y  x, y.  w( x, y ) f x f y   x, y   2 w( x, y ) f y   x, y .

(41) Properties of auto-correlation matrix. Describes the gradient distribution (i.e., local structure) inside the window!  f x2 AW   w( x, y )  x, y  f x f y. fx f y  2  f y . Does not depend on x, y.

(42) Properties of auto-correlation matrix (cont’d) Aw is symmetric and can be decomposed:. 1 0  AW  R  R   0 2  1. • We can visualize AW as an ellipse with axis lengths and directions determined by its eigenvalues and eigenvectors.. (min)1/2. (max)1/2.

(43) Harris Detector (cont’d) • The eigenvectors of AW encode. v1. direction of intensity change. • The eigenvalues of AW encode strength of intensity change.. v2. direction of the slowest change. (min)1/2. (max)1/2. direction of the fastest change.

(44) Harris Detector (cont’d) 2. Classification of pixels using the eigenvalues of AW :. “Edge” 2 >> 1. “Corner” 1 and 2 are large, 1 ~ 2; intensity changes in all directions. 1 and 2 are small; SW is almost constant in all directions. “Flat” region. “Edge” 1 >> 2 1.

(45) Distribution of fx and fy fy fx. fy. fy fx. fx.

(46) Harris Detector (cont’d) One way to compute “good” corners is by thresholding min(λ1,λ2) % assume 1 > 2 2. J. Shi and C. Tomasi, "Good Features to Track”, 9th IEEE Conference on Computer Vision and Pattern Recognition, June 1994..

(47) Harris Detector (cont’d) • To avoid computing the eigenvalues explicitly, the Harris detector uses the following function:. R(AW) = det(AW) – α trace2(AW) which is equal to:. R(AW) = λ1 λ2- α (λ1+ λ2)2. α: is a const.

(48) Harris Detector (cont’d) Classification of image. “Edge” R<0. points using R(AW):. “Corner” R>0. R(AW) = det(AW) – α trace2(AW) α: is usually between 0.04 and 0.06. |R| small “Flat” region. “Edge” R<0.

(49) Harris Detector (cont’d) • Other functions:. 2  a1 12 det A  trA 1  2.

(50) Harris Detector - Steps  f x2 AW   w( x, y )  x, y  f x f y. f ( xi , yi )   G ( x, y,  D ) * f ( xi , yi ) x x f ( xi , yi )   G ( x, y,  D ) * f ( xi , yi ) y y. fx f y   f y2 . σD is called the “differentiation” scale.

(51) Harris Detector - Steps  f x2 AW   w( x, y )  x, y  f x f y. fx f y   f y2 . (using σI). R(AW) = det(AW) – α trace2(AW).

(52) Harris Detector - Example.

(53) Harris Detector – Scale Parameters • The Harris detector requires two scale parameters: (i) a differentiation scale σD for smoothing prior to the computation of image derivatives, & (ii) an integration scale σI for defining the size of the Gaussian window (i.e., integrating derivative responses).. AW(x,y)  AW(x,y,σI,σD) • Typically, σI=γσD.

(54) Harris Detector - Example.

(55) Compute corner response R.

(56) Find points with large corner response: R>threshold.

(57) Take only the points of local maxima of R.

(58) Map corners on the original image (for visualization).

(59) Invariance to Geometric/Photometric Changes • Is the Harris detector invariant to geometric and photometric changes? – Rotation. – Scale. – Affine – Linear intensity change: I(x,y)  a I(x,y) + b.

(60) Harris Detector: Rotation Invariance • Rotation. Ellipse rotates but its shape (i.e. eigenvalues) remains the same Corner response R is invariant to image rotation.

(61) Harris Detector: Rotation Invariance (cont’d).

(62) Harris Detector: Photometric Changes • Linear intensity change: - Only derivatives are used => invariance to intensity shift I(x,y)  I (x,y) + b - Intensity scale: I(x,y)  a I(x,y) R. R. threshold. x (image coordinate). x (image coordinate). Partially invariant to affine intensity change.

(63) Harris Detector: Scale Invariance • Scaling. Corner All points will be classified as edges rather than corners. Not invariant to scaling (and affine transforms).

(64) Harris Detector: Repeatability.

(65) Harris Detector: Repeatability (cont’d).

(66) Harris Detector: Repeatability (cont’d) When two points correspond?.

(67) Harris Detector: Repeatability (cont’d) How do we find correspondences?.

(68) Harris Detector: Repeatability (cont’d) • In a comparative study of different interest point detectors, Harris was shown to be the most repeatable.. (σI=1, σD=2). C. Schmid, R. Mohr, and C. Bauckhage, "Evaluation of Interest Point Detectors", International Journal of Computer Vision 37(2), 151.172, 2000..

(69) Harris Detector: Disadvantages • Sensitive to: – Scale change – Significant viewpoint change – Significant contrast change.

(70) How can we handle scale changes? •. AW(x,y,σI,σD) must be adapted to scale changes.. •. If scale change is known, adapt the Harris detector to it by properly setting σI and σD.. •. If scale change is unknown, detect interest points at multiple scales..

(71) Multi-scale Harris Detector • Detects interest points at varying scales. R(AW) = det(AW(x,y,σI,σD)) – α trace2(AW(x,y,σI,σD)) scale. σn=knσ σD= σn σI=γσD. σn y.  Harris . x.

(72) Multi-scale Harris Detector (cont’d) Interest points detected at varying scales:. M. Brown, R. Szeliski, and S. Winder, “Multi-image matching using multi-scale oriented Patches”, IEEE Conference on Computer Vision and Pattern Recognition, vol. I, pages 510-517, 2005..

(73) Multi-scale Harris Detector (cont’d) • •. The same interest point will be detected at multiple consecutive scales. Interest point location will shift as scale increases (i.e., due to smoothing).. The size of each circle corresponds to the scale at which the interest point was detected..

(74) How do we match them? • • •. Corresponding features might appear at different scales. How do we determine these scales? Need a scale selection mechanism!.

(75) Scale Selection: Exhaustive Search • Simple approach for scale selection but not efficient!.

(76) Scale Selection: Characteristic Scale • •. Scale selection by finding the characteristic scale of each feature. This the scale revealing the spatial extent of an interest point. characteristic scale. characteristic scale.

(77) Scale Selection: Characteristic Scale (cont’d) •. Only a subset of interest points are selected using the characteristic scale of each feature  matching can be simplied. •. The size of the circles is related to the scale at which the interest points were selected..

(78) Automatic Scale Selection • Design a function F(x,σn) which provides some local measure. • Select points at which F(x,σn) is maximal over σn.. max of F(x,σn) corresponds to characteristic scale!. F(x,σn) σn. T. Lindeberg, "Feature detection with automatic scale selection" International Journal of Computer Vision, vol. 30, no. 2, pp 77-116, 1998..

(79) Lindeberg et al, 1996. Slide from Tinne Tuytelaars.

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(87) Automatic Scale Selection (cont’d) •. Using characteristic scale, the spatial extent of interest points becomes covariant to scale transformations.. •. The ratio σ1/σ2 reveals the scale factor between the images.. σ1. σ2 σ1/σ2 = 2.5.

(88) How should we choose F(x,σn) ? • What local measure F(x,σn) should we use? – Should be rotation invariant. – Should have one stable sharp peak..

(89) How should we choose F(x,σn) ? (cont’d) • Typically, F(x,σn) is defined using derivatives, e.g.:. Square gradient :  2 ( L2x ( x,  )  L2y ( x,  )) LoG : |  2 ( Lxx ( x,  )  Lyy ( x,  )) | DoG :| I ( x) * G ( n 1 )  I ( x)* G ( n ) | Harris function : det( AW )   trace 2 ( AW ) • LoG yielded best results in a evaluation study; DoG was second best. C. Schmid, R. Mohr, and C. Bauckhage, "Evaluation of Interest Point Detectors", International Journal of Computer Vision, 37(2), pp. 151-172, 2000..

(90) How should we choose F(x,σn) ? (cont’d) • Let’s see how LoG responds at blobs ….

(91) Recall: Edge detection Using 1st derivative. f. d g dx. f. d g dx. edge. derivative of Gaussian. edge = maximum of derivative.

(92) Recall: Edge detection Using 2nd derivative. f d2 g 2 dx d2 f 2g dx. edge second derivative of Gaussian (Laplacian). edge = zero crossing of second derivative.

(93) LoG’s response at a blob • Blob = superposition of two edges (blobs of different spatial extent). max. (abs value). The magnitude of the LoG response will achieve a maximum at the center of the blob, provided the scale of the LoG is “matched” to the scale of the blob (e.g, its spatial extent).

(94) How could we find the spatial extent of a blob using LoG? • Convolve blobs with LoG filters at several scales and find maximum response across scales. • Problem: LoG response decays as scale increases.. Blob. increasing σ. Why does this happen?.

(95) Gaussian derivative response • The response of the Gaussian derivative to a perfect step edge decreases as σ increases. 1  2.

(96) Normalize LoG response • To keep response the same (i.e., scale-invariant), must multiply Gaussian derivative by σ • LoG is the second Gaussian derivative, so it must be multiplied by σ2.

(97) Normalize LoG response (cont’d) Blob. Un-normalized LoG response. Scale-normalized LoG response ( σ2 x LoG). max.

(98) Spatial extent of circle • At what scale does the LoG achieve a maximum response for a binary circle of radius r?. r image.  r/. 2 (characteristic scale). LoG response. • LoG is maximized at. r/ 2. scale (σ).

(99) Spatial extent of circle (cont’d) • Spatial extent r can be determined using: r  2. characteristic scale.

(100) Harris-Laplace Detector • Multi-scale Harris with scale selection. • Uses LoG maxima to find characteristic scale.. σn.  LoG . scale. y.  Harris . x.

(101) Harris-Laplace Detector (cont’d) (1) Find interest points at multiple scales using Harris detector. - Scales are chosen as follows: σn =knσ - At each scale, choose local maxima assuming 3 x 3 window (i.e., non-maximal suppression). F ( x,  n )  F ( xW ,  n ) xW  W F ( x,  n )  t h where. F ( x,  n )  det( AW )   trace 2 ( Aw ). (σD =σn, σI =γσD ).

(102) Harris-Laplace Detector (cont’d) (2) Select points at which the normalized LoG is maximal across scales and the maximum is above a threshold. σn+1. F ( x,  n )  F ( x,  n 1 )  F ( x,  n )  F ( x,  n 1 ) F ( x,  n )  t. σn σn-1. where:. F ( x,  n ) |  2 ( Lxx ( x,  n )  Lyy ( x,  n )) |. K. Mikolajczyk and C. Schmid, “Indexing based on scale invariant interest points" IEEE Int. Conference on Computer Vision, pp 525-531, 2001..

(103) Example • Interest points detected at each scale using Harris-Laplace – Few correspondences between levels corresponding to same σ. – More correspondences between levels where ration of σ = 2.. images differ by a scale factor of 1.92. σ=1.2. σ=2.4. σ=1.2. σ=2.4. σ=4.8. σ=4.8. σ=9.6. σ=9.6.

(104) Example (cont’d) (same viewpoint – change in focal length and orientation). -More than 2000 points would have been detected without scale selection. -Using scale selection, 190 and 213 points were detected in the left and right images, respectively..

(105) Example (cont’d). 58 points are initially matched (some not correct).

(106) Example (cont’d). • Reject outliers (inconsistent matches - using RANSAC) • Left with 32 matches, all of which are correct. • •Estimated scale factor is 4:9 and rotation angle is 19 degrees..

(107) Harris-Laplace Detector (cont’d) Repeatability • Invariant to: – Scale – Rotation – Translation. • Robust to: – Illumination changes – Limited viewpoint changes.

(108) Implement Harris-Laplace using DoG • LoG can be approximated by DoG:. G ( x, y, k )  G ( x, y,  )  (k  1) 2 2G • Note: DoG already incorporates the σ2 scale normalization factor..

(109) •. Implement Harris-Laplace using DoG (cont’d) Gaussian-blurred image. L ( x, y ,  )  G ( x , y ,  ) * I ( x , y ) •. Result using DoG:. DoG ( x, y,  )  L( x, y, k )  L( x, y,  ). -. =.

(110) Implement Harris-Laplace using DoG (cont’d) G  x, y, k 2  * I G  x , y , k  * I. D  x, y ,   .  G  x, y, k   G  x, y,   * I. G  x, y ,   * I. σn =knσ. DoG.

(111) Harris-Laplace using DoG (cont’d) DoG pyramid. Look for local maxima in DoG pyramid. David G. Lowe, "Distinctive image features from scale-invariant keypoints.” Int. Journal of Computer Vision, 60 (2), pp. 91-110, 2004..

(112) Handling Affine Changes • Similarity transformations cannot account for perspective distortions; affine could be used for planar surfaces. • Similarity transform. • Affine transform.

(113) Handling Affine Changes (cont’d) • Similarly to characteristic scale selection, detect the characteristic shape of the local feature. • Need to create scale space using non-uniform Gaussian filters (i.e., Affine Gaussian Scale Space).

(114) Uniform Gaussian Scale Space. Uniform Gaussian (assuming zero mean). L ( x, y, )  G ( x, y, )  I ( x, y )  1 G ( x, y ,  )  e 2 2. 2. x y 2. 2. p  1  e 2 det().  2 0  x where p    and    2 y   0  . Only one parameter: σ.  1.  p 2. Σ: covariance matrix.

(115) Affine Gaussian Scale Space L (x, y,  )  G ( x, y,  )  I ( x, y) Non-uniform Gaussian (assuming zero mean) 1 G ( x, y ,  )  e 2 det( ). p   1 p  2.  11  12  x where p    and    ( 12   21 )   y  21  22 . Three parameters: σ11, σ12, σ22. Σ: covariance matrix.

(116) How does this affect Harris’ 2nd order moment matrix? • Assuming uniform Gaussian:. same as AW(x, σI, σD). w(x,y). • Assuming non-uniform Gaussian: σI ΣI and σD ΣD. • Not practical to compute μ for all possible parameter values!.

(117) Use Iterative Affine Adaptation (Harris Affine Detector) • Use an iterative approach: – Extract approximate locations and scales using the HarrisLaplace detector. – For each point, modify the scale and shape of its neighborhood in an iterative fashion. – Converges to stable points that are covariant to affine transformations ..

(118) Steps of Iterative Affine Adaptation 1. Detect initial locations and neighborhood using HarrisLaplace. 2. Estimate affine shape of neighborhood using 2nd order moment matrix μ(x, σI, σD)..

(119) Steps of Iterative Affine Adaptation (cont’d) 3. Normalize (i.e., de-skew) the affine region by mapping it to a circular one (i.e., “remove” perspective distortions).. 4. Re-detect the new location and scale in the normalized image. 5. Go to step 2 if the eigenvalues of μ(x, σI, σD) for the new point are not equal (i.e., not yet adapted to the characteristic shape)..

(120) Iterative affine adaptation - Examples Initial points Example 1. Example 2.

(121) Iterative affine adaptation – Examples (cont’d). Example 1. Iteration #1. Example 2.

(122) Iterative affine adaptation – Examples (cont’d) Iteration #2 Example 1. Example 2.

(123) Iterative affine adaptation – Examples (cont’d) Iteration #3, #4, … Example 1. Example 2. K. Mikolajczyk and C. Schmid, “Scale and Affine invariant interest point detectors”, International Journal of Computer Vision, 60(1), pp. 63-86, 2004.. http://www.robots.ox.ac.uk/~vgg/research/affine/.

(124) Iterative affine adaptation – Examples (cont’d).

(125) De-skewing • Consider a point xL with 2nd order matrix ML xL. • The de-skewing transformation is defined as follows:.

(126) De-skewing corresponding regions • Consider two points xL and xR which are related through an affine transformation: xL. xR.

(127) De-skewing corresponding regions (cont’d). Normalized regions are related by pure rotation R..

(128) Resolving orientation ambiguity • •. Create histogram of local gradient directions in the patch. Smooth histogram and assign canonical orientation at peak of smoothed histogram. Dominant gradient direction!. 2. 0. (36 bins).

(129) Resolving orientation ambiguity (cont’d) • Resolve orientation ambiguity.. Compute R.

(130) Other Affine Invariant Blob/Region Detectors • There are many other techniques for detecting affine invariant blobs or regions, for example: – Intensity Extrema-Based Region (IER) – Maximally Stable Extremal Regions (MSERs) • No need to detect interest points..

(131) Intensity Extrema-Based Region Detector (1) Take a local intensity extremum as initial point. (2) Examine the intensity along “rays” from the local extremum. (3) The point on each ray for which fI(t) reaches an extremum is selected (i.e., invariant). (4) Linking these points together yields an affinely invariant region, to which an ellipse is fitted. d>0: small const Tuytelaars, T. and Van Gool, L. “Matching Widely Separated Views based on Affine Invariant Regions”, International Journal on Computer Vision, 59(1):61–85, 2004..

(132) Intensity Extrema-Based Region Detector (cont’d) • The regions found may not exactly correspond, so we approximate them with ellipses using 2nd order moments..

(133) Intensity Extrema-Based Region Detector (cont’d) • Double the size of the ellipse to make regions more distinctive. • Final ellipse is not necessarily centered at original anchor point..

(134) Intensity Extrema-Based Region Detector (cont’d) Ellipses, computed from corresponding regions, also correspond!.

(135) Intensity Extrema-Based Region Detector (cont’d).

(136) Intensity Extrema-Based Region Detector (cont’d).

(137) Intensity Extrema-Based Region Detector (cont’d) • Region extraction is robust to inaccurate localization of intensity extremum..

(138) Maximally Stable Extremal Regions (MSERs) • Consider all possible thresholdings of a gray-scale image: If I(x,y) > It then I(x,y)=0; else I(x,y)=255. Matas, J., Chum, O., Urban, M. and Pajdla, T., “Robust wide-baseline stereo from maximally stable extremal regions”, British Machine Vision Conf, pp. 384–393, 2002..

(139) Maximally Stable Extremal Regions (MSERs) • Extermal Regions – All regions formed using different thresholds. – Can be extracted using connected components.. • Maximally Stable Extremal Regions – Regions that remain stable over a large range of thresholds.. • Approximate MSER by an ellipse.

(140) Example • Extermal regions can be extracted in O(nlog(logn)) time where n is the number of pixels. •Sensitive to image blur..

(141)

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