Edge detection

• Goal: Identify sudden changes (discontinuities) in an image

• This is where most information in an image is coded

• Example: line drawings

What causes an edge?

• Depth discontinuity

• Surface orientation discontinuity

• Changes in surface properties

• Light discontinuities (e.g. shadows)

ScaleIncreased scale:• Eliminates noisy edges• Makes edges smoother and thicker• Removes fine details

Suppression of non-maxima:• Choose the local maximum point along a perpendicular cross section of the edge.

Example: Suppression of non-maxima

courtesy of G. Loy

Original image Gradient magnitudeNon-maxima suppressed

Differentiation with a Gaussian filter

Example: Canny Edge Detection

Using Matlab with default thresholds

Corner Detector

• Compute x- and y-derivatives with a Gaussian filter

• Form the orientation tensor M for every pixel

• Compute the product of eigen-values, i.e., the determinant of M

• If both eigenvalues large (product is a local maximum), then it is a corner!

Gradient directions

Blow-up of gradient directions

Corners can be detected where the product of the ellipse axes are local maxima

Fast (bottom-up) - some methods scale

Fast (bottom-up) - some methods scale

Fast (bottom-up) - some don’t

Task: Image Retrieval• Oxford Building Data (Philbin et al. CVPR’07)

Query

Task: Image Retrieval• Oxford Building Data (Philbin et al. CVPR’07)

Query

Task: Image Retrieval• Oxford Building Data (Philbin et al. CVPR’07)

Good

mat

ch

Query

Task: Image Retrieval• Oxford Building Data (Philbin et al. CVPR’07)

Good

mat

ch

Matched?

Query

Task: Image Retrieval• Oxford Building Data (Philbin et al. CVPR’07)

Good

mat

ch

Matched?

Query

Baseline System – Bags of Words

• Interest point detection (position, scale, orientation)

- Differences of Gaussian/Harris

Baseline System – Bags of Words

• Interest point detection

- Differences of Gaussian/Harris

• Feature extraction (feature vector e g R^128)

- SIFT/SURF/DAISY

Baseline System – Bags of Words

• Interest point detection

- Differences of Gaussian/Harris

• Feature extraction

- SIFT/SURF/DAISY

• Generating vocabularies – quantization- hierarchical k-means (Nister, Stewenius CVPR’06)

- approximate k-means (Philbin et al. CVPR’08)