Description

Feature extraction: Corners and blobs. Why extract features?. Motivation: panorama stitching We have two images – how do we combine them?. Step 2: match features. Why extract features?. Motivation: panorama stitching We have two images – how do we combine them?. Step 1: extract features.

Transcripts

Include extraction: Corners and blobs

Why extricate highlights? Inspiration: display sewing We have two pictures – how would we consolidate them?

Step 2: coordinate elements Why extricate highlights? Inspiration: scene sewing We have two pictures – how would we join them? Step 1: remove highlights

Why separate components? Inspiration: scene sewing We have two pictures – how would we join them? Step 1: separate components Step 2: coordinate elements Step 3: adjust pictures

Characteristics of good elements Repeatability similar element can be found in a few pictures regardless of geometric and photometric changes Saliency Each element has a particular depiction Compactness and productivity Many less elements than picture pixels Locality An element involves a moderately little range of the picture; hearty to disorder and impediment

Applications Feature focuses are utilized for: Motion following Image arrangement 3D reproduction Object acknowledgment Indexing and database recovery Robot route

Finding Corners Key property: in the area around a corner, picture inclination has at least two overwhelming headings Corners are repeatable and unmistakable C.Harris and M.Stephens. "A Combined Corner and Edge Detector." Proceedings of the fourth Alvey Vision Conference : pages 147- - 151.

"level" locale: no adjustment every which way "edge" : no alter along the edge course "corner" : huge change every which way The Basic Idea We ought to effortlessly perceive the point by looking through a little window Shifting a window in any heading ought to give a huge change in power Source: A. Efros

Window work Shifted power Intensity Window work w(x,y) = or 1 in window, 0 outside Gaussian Harris Detector: Mathematics Change in appearance for the move [ u,v ]: Source: R. Szeliski

Harris Detector: Mathematics Change in appearance for the move [ u,v ]: Second-arrange Taylor development of E ( u , v ) around (0,0) (bilinear estimation for little moves):

M Harris Detector: Mathematics The bilinear guess disentangles to where M is a 2 2 framework processed from picture subsidiaries:

Interpreting the second minute grid The surface E ( u , v ) is privately approximated by a quadratic shape. We should attempt to comprehend its shape.

Interpreting the second minute grid First, consider the pivot adjusted case (angles are either even or vertical) If either λ is near 0, then this is not a corner, so search for areas where both are expansive.

bearing of the speediest alter course of the slowest change ( max ) - 1/2 ( min ) - 1/2 General Case Since M is symmetric, we have We can picture M as a circle with hub lengths controlled by the eigenvalues and introduction dictated by R Ellipse condition:

Visualization of second minute networks

Visualization of second minute lattices

Interpreting the eigenvalues Classification of picture focuses utilizing eigenvalues of M : 2 "Edge" 2 >> 1 "Corner" 1 and 2 are vast, 1 ~ 2 ; E increments every which way 1 and 2 are little; E is practically steady every which way "Edge" 1 >> 2 "Level" district 1

Corner reaction work α : consistent (0.04 to 0.06) "Edge" R < 0 "Corner" R > 0 |R| little "Edge" R < 0 "Level" area

Harris identifier: Steps Compute Gaussian subsidiaries at every pixel Compute second minute grid M in a Gaussian window around every pixel Compute corner reaction work R Threshold R Find neighborhood maxima of reaction capacity (nonmaximum concealment)

Harris Detector: Steps

Harris Detector: Steps Compute corner reaction R

Harris Detector: Steps Find focuses with huge corner reaction: R> edge

Harris Detector: Steps Take just the purposes of nearby maxima of R

Harris Detector: Steps

Invariance We need elements to be recognized regardless of geometric or photometric changes in the picture: in the event that we have two changed variants of similar picture, components ought to be distinguished in relating areas

Models of Image Change Geometric Rotation Scale Affine legitimate for: orthographic camera, locally planar question Photometric Affine power change ( I an I + b )

Harris Detector: Invariance Properties Rotation Ellipse turns yet its shape (i.e. eigenvalues) continues as before Corner reaction R is invariant to picture pivot

Intensity scale: I an I R limit x (picture arrange) x (picture organize) Harris Detector: Invariance Properties Affine force change Only subsidiaries are utilized => invariance to power move I I + b Partially invariant to relative force change

Harris Detector: Invariance Properties Scaling Corner All focuses will be named edges Not invariant to scaling

Scale-invariant element identification Goal: freely identify comparing areas in scaled adaptations of similar picture Need scale choice component for discovering trademark locale measure that is covariant with the picture change

Scale-invariant elements: Blobs

Recall: Edge discovery Edge f Derivative of Gaussian Edge = most extreme of subsidiary Source: S. Seitz

Edge recognition, Take 2 Edge f Second subsidiary of Gaussian (Laplacian) Edge = zero intersection of second subordinate Source: S. Seitz

most extreme From edges to blobs Edge = swell Blob = superposition of two swells Spatial choice : the greatness of the Laplacian reaction will accomplish a most extreme at the focal point of the blob, gave the size of the Laplacian is "coordinated" to the size of the blob

unique flag (radius=8) expanding σ Scale choice We need to locate the trademark size of the blob by convolving it with Laplacians at a few scales and searching for the greatest reaction However, Laplacian reaction rots as scale builds: Why does this happen?

Scale standardization The reaction of a subordinate of Gaussian channel to an impeccable stride edge diminishes as σ increments

Scale standardization The reaction of a subsidiary of Gaussian channel to a flawless stride edge diminishes as σ increments To keep reaction the same (scale-invariant), should increase Gaussian subsidiary by σ Laplacian is the second Gaussian subordinate, so it must be duplicated by σ 2

Scale-standardized Laplacian reaction greatest Effect of scale standardization Original flag Unnormalized Laplacian reaction

Blob discovery in 2D Laplacian of Gaussian: Circularly symmetric administrator for blob location in 2D

Blob identification in 2D Laplacian of Gaussian: Circularly symmetric administrator for blob recognition in 2D Scale-standardized:

Scale determination At what scale does the Laplacian accomplish a most extreme reaction for a twofold hover of span r? r picture Laplacian

Scale choice The 2D Laplacian is given by Therefore, for a paired hover of span r, the Laplacian accomplishes a greatest at (up to scale) Laplacian reaction r scale ( σ ) picture

Characteristic scale We characterize the trademark scale as the scale that produces pinnacle of Laplacian reaction trademark scale T. Lindeberg (1998). "Feature recognition with programmed scale selection." International Journal of Computer Vision 30 (2): pp 77- - 116.

Scale-space blob identifier Convolve picture with scale-standardized Laplacian at a few scales Find maxima of squared Laplacian reaction in scale-space

Scale-space blob locator: Example

Scale-space blob indicator: Example

Scale-space blob finder: Example

Efficient execution Approximating the Laplacian with a distinction of Gaussians: (Laplacian) (Difference of Gaussians)

Efficient usage David G. Lowe. "Distinctive picture highlights from scale-invariant keypoints." IJCV 60 (2), pp. 91-110, 2004.

From scale invariance to relative invariance

heading of the speediest alter course of the slowest change ( max ) - 1/2 ( min ) - 1/2 Affine adjustment Recall: We can imagine M as an oval with hub lengths dictated by the eigenvalues and introduction controlled by R Ellipse condition:

Affine adjustment case Scale-invariant districts (blobs)

Affine adjustment case Affine-adjusted blobs

Affine standardization The second minute oval can be seen as the "trademark shape" of an area We can standardize the locale by changing the oval into a unit circle

Orientation vagueness There is no novel change from an oval to a unit circle We can pivot or flip a unit circle, regardless it remains a unit circle

p 2 0 Orientation uncertainty There is no one of a kind change from an oval to a unit circle We can turn or flip a unit circle, despite everything it remains a unit hover So, to allot a remarkable introduction to keypoints: Create histogram of neighborhood angle bearings in the fix Assign sanctioned introduction at pinnacle of smoothed histogram

Affine adjustment Problem: the second minute "window" dictated by weights w ( x , y ) must match the trademark state of the district Solution: iterative approach Use a round window to register second minute lattice Perform relative adjustment to discover an oval molded window Recompute second minute network utilizing new window and emphasize

Iterative relative adjustment K. Mikolajczyk and C. Schmid, Scale and Affine