Distinctive Image Featuresfrom Scale-Invariant Keypoints

David G. LoweInternational Journal of Computer Vision(IJCV), 2004

Extracting distinctive invariant features

• Points are individually ambiguous• More unique matches are possible with small

regions of images

http://www.csie.ntu.edu.tw/~cyy/courses/vfx/05spring/lectures/handouts/lec04_feature.pdf

Desired properties for features

• Invariant: invariant to scale, rotation, affine, illumination and noise for robust matching across a substantial range of affine distortion, viewpoint change and so on.

• Distinctive: a single feature can be correctly matched with high probability

Moravec corner detector (1980)• We should easily recognize the point by looking

through a small window• Shifting a window in any direction should give a

large change in intensity

Moravec corner detector

flat

Moravec corner detector

flat

Moravec corner detector

flat edge

Moravec corner detector

flat edge cornerisolated point

Moravec corner detectorChange of intensity for the shift [u,v]:

2

,

( , ) ( , ) ( , ) ( , )x y

E u v w x y I x u y v I x y

IntensityShifted intensity

Window function

Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1)Problem: responds too strong for edges because only minimum of E is taken into account

Harris corner detector [1992]Consider all small shifts by Taylor’s expansion

W(x, y): Gaussian function

vu

yxIyxIyxIvyuxI yx )],(),([),(),(

( , ) ,u

E u v u v Mv

=>

M: 2x2 Hessian matrix, 1, 2 – eigenvalues of M

Harris corner detector

Classification of image points using eigenvalues of M:

1

2

Corner1 and 2 are large, 1 ~ 2;E increases in all directions

edge 1 >> 2

edge 2 >> 1

flat

Measure of corner response:

2det traceR M k M

1 2

1 2

dettrace

MM

Harris Detector: Problem

• non-invariant to image scale!

All points will be classified as edges

Corner !

Scale-invariant feature transform (SIFT)

• Scale-invariant feature transform (or SIFT) is an algorithm to detect and describe local features in images.– Distinctive features– Invariant to image scale, rotation and affine

distortion– Applied locally on key-points – Based upon the image gradients in a local

neighborhood

SIFT stages:• Scale-space extrema detection• Keypoint localization• Orientation assignment• Keypoint descriptor

local descriptor

detector

descriptor

1. Detection of scale-space extremaConvolution with a variable-scale Gaussian

Difference-of-Gaussian (DoG) filter

Scale space doubles for the next octave

K=2(1/s), s+3 images for each octave

k∙

2

DoG

• Efficient function to compute• A close approximation to the scale-normalized

Laplacian of Gaussian

2. Keypoint localization

X is selected if it is larger or smaller than all 26 neighbors

Decide scale sampling frequency

Pre-smoothing

=1.6, plus a double expansion

2. Accurate keypoint localization

If has offset larger than 0.5, sample point is changed.

If is less than 0.03 (low contrast), it is discarded.

Reject points with low contrast and poorly localized along an edge

Eliminating edge responses

r=10

Let

Keep the points with

3. Orientation assignment• By assigning a consistent orientation, the keypoint

descriptor can be orientation invariant.• For a keypoint, L is the image with the closest scale

– 36-bin orientation histogram over 360° – weighted by m– Peak is the dominant orientation– Local peak within 80% creates multiple

orientations– About 15% has multiple orientations

4. Local image descriptor• Image gradients are sampled over 16x16 array of

locations in scale space• Create array of orientation histograms• 8 orientations x 4x4 histogram array = 128

dimensions

Recognition examples