edge and texture - web.cs.hacettepe.edu.trpinar/courses/vbm686/lectures/edg… · source: darrell,...

Edge and Texture

VBM 686 – Bilgisayarlı Görü

Pinar Duygulu

Hacettepe University

Filters for features

• Previously, thinking of filtering as a way to remove or reduce noise

• Now, consider how filters will allow us to abstract higher-level “features”.

– Map raw pixels to an intermediate representation that will be used for subsequent processing

– Goal: reduce amount of data, discard redundancy, preserve what’s useful

Source: Darrell, Berkeley

Edge detection• Goal: Identify sudden

changes (discontinuities) in an image– Intuitively, most semantic and

shape information from the image can be encoded in the edges

– More compact than pixels

• Ideal: artist’s line drawing (but artist is also using object-level knowledge)

Source: D. LoweSource: Hays, Brown

Edge detection

• Goal: map image from 2d array of pixels to a set of curves or line segments or contours.

• Why?

• Main idea: look for strong gradients, post-process

Figure from J. Shotton et al., PAMI 2007


Why do we care about edges?

• Extract information, recognize objects

• Recover geometry and viewpoint

Vanishingpoint

Vanishingline

Vanishingpoint

Vertical vanishingpoint

(at infinity)

Source: Hays, Brown

Origin of Edges

• Edges are caused by a variety of factors

depth discontinuity

surface color discontinuity

illumination discontinuity

surface normal discontinuity

Source: Steve SeitzSource: Hays, Brown

What can cause an edge?

Depth discontinuity: object boundary

Change in surface orientation: shape

Cast shadows

Reflectance change: appearance information, texture


Contrast and invariance


Closeup of edges

Source: D. HoiemSource: Hays, Brown

Characterizing edges• An edge is a place of rapid change in the

image intensity function

imageintensity function

(along horizontal scanline) first derivative

edges correspond toextrema of derivative

Source: Hays, Brown

What is an edge?

adapted from Larry Davis, University of Maryland

General Strategy

• Determine image gradient

• Mask points where gradient is particularly large with respect to neighbors (ideally curves of such points)

What is Gradient?

adapted from Michael Black, Brown University

2D edge detection


Differentiation and convolution

For 2D function, f(x,y), the partial derivative is:

For discrete data, we can approximate using finite differences:

To implement above as convolution, what would be the associated filter?

),(),(lim

),(

0

yxfyxf

x

yxf

1

),(),1(),( yxfyxf

x

yxf


CS554 Computer Vision ©Pinar Duygulu

Finite Differences


Partial Derivatives

Partial derivatives of an image

Which shows changes with respect to x?

-1 1

1 -1

or

?-1 1

x

yxf

),(

y

yxf

),(

(showing flipped filters)Source: Darrell, Berkeley

Assorted finite difference filters

>> My = fspecial(‘sobel’);

>> outim = imfilter(double(im), My);

>> imagesc(outim);

>> colormap gray;


Image gradientThe gradient of an image:

The gradient points in the direction of most rapid change in intensity

The gradient direction (orientation of edge normal) is given by:

The edge strength is given by the gradient magnitude

Slide credit S. SeitzSource: Darrell, Berkeley

Intensity profile


With a little Gaussian noise

Gradient


Effects of noise• Consider a single row or column of the image

– Plotting intensity as a function of position gives a signal

Where is the edge?Source: S. Seitz

Source: Hays, Brown

Effects of noise

• Difference filters respond strongly to noise

– Image noise results in pixels that look very different from their neighbors

– Generally, the larger the noise the stronger the response

• What can we do about it?

Source: D. ForsythSource: Hays, Brown

Solution: smooth first

• To find edges, look for peaks in )( gfdx

d

f

g

f * g

)( gfdx

d

Source: S. SeitzSource: Hays, Brown

• Differentiation is convolution, and convolution is associative:

• This saves us one operation:

gdx

dfgf

dx

d )(

Derivative theorem of convolution

gdx

df

f

gdx

d


Derivative of Gaussian filter

* [1 -1] =

Source: Hays, Brown

Derivative of Gaussian filters

x-direction y-direction

Source: L. LazebnikSource: Darrell, Berkeley

Second derivative

adapted from Martial Hebert, CMU

•Another way

to detect an

extremal first

derivative is

to look for a

zero second

derivative

Step edge


Second derivative


Sobel Operator

Laplacian of Gaussian (LOG)

• Bad idea to apply a Laplacian without smoothing

– smooth with Gaussian, apply Laplacian

– this is the same as filtering with a Laplacian of Gaussian filter

Laplacian of Gaussian (LOG)


Laplacian of Gaussian

Consider

Laplacian of Gaussianoperator

Where is the edge? Zero-crossings of bottom graphSource: Darrell, Berkeley

2D edge detection filters

• is the Laplacian operator:

Laplacian of Gaussian

Gaussian derivative of Gaussian


Smoothing with a Gaussian

Recall: parameter σ is the “scale” / “width” / “spread” of the Gaussian kernel, and controls the amount of smoothing.

…


Effect of σ on derivatives

The apparent structures differ depending on Gaussian’s scale parameter.

Larger values: larger scale edges detectedSmaller values: finer features detected

σ = 1 pixel σ = 3 pixels


So, what scale to choose?It depends what we’re looking for.

Too fine of a scale…can’t see the forest for the trees.Too coarse of a scale…can’t tell the maple grain from the cherry.Source: Darrell, Berkeley

Thresholding

• Choose a threshold value t

• Set any pixels less than t to zero (off)

• Set any pixels greater than or equal to t to one (on)


Original image


Gradient magnitude image


Thresholding gradient with a lower threshold


Thresholding gradient with a higher threshold


• Smoothed derivative removes noise, but blurs edge. Also finds edges at different “scales”.

1 pixel 3 pixels 7 pixels

Tradeoff between smoothing and localization


Designing an edge detector• Criteria for a good edge detector:

– Good detection: the optimal detector should find all real edges, ignoring noise or other artifacts

– Good localization• the edges detected must be as close as possible to

the true edges• the detector must return one point only for each

true edge point

• Cues of edge detection– Differences in color, intensity, or texture across the

boundary– Continuity and closure– High-level knowledge

Source: L. Fei-FeiSource: Hays, Brown

Canny edge detector• This is probably the most widely used edge

detector in computer vision

• Theoretical model: step-edges corrupted by additive Gaussian noise

• Canny has shown that the first derivative of the Gaussian closely approximates the operator that optimizes the product of signal-to-noise ratio and localization

J. Canny, A Computational Approach To Edge Detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8:679-714, 1986.

Source: L. Fei-FeiSource: Hays, Brown

http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=4767846&arnumber=4767851&count=16&index=4

Example

original image (Lena)

Source: Hays, Brown

Derivative of Gaussian filter

x-direction y-direction

Source: Hays, Brown

The Canny edge detector

original image (Lena)


Compute Gradients (DoG)

X-Derivative of Gaussian Y-Derivative of Gaussian Gradient Magnitude

Source: Hays, Brown


norm of the gradient



thresholding



thresholding

How to turn these thick regions of the gradient into curves?


Gradient based edge detection

adapted from David Forsyth, UC Berkeley

We wish to mark points along the curve where the magnitude is biggest.

We can do this by looking for a maximum along a slice normal to the curve

(non-maximum suppression). These points should form a curve. There are

then two algorithmic issues: at which point is the maximum, and where is the

next one?

Non-maximum suppression

Check if pixel is local maximum along gradient direction, select single max across width of the edge– requires checking interpolated pixels p and r


Non-Maximum Suppression Algorithm

Get Orientation at Each Pixel

• Threshold at minimum level

• Get orientation theta = atan2(gy, gx)

Source: Hays, Brown

Non-maximum suppression for each orientation

At q, we have a maximum if the value is larger than those at both p and at r. Interpolate to get these values.


Before Non-max Suppression

Source: Hays, Brown

After non-max suppression

Source: Hays, Brown


thinning

(non-maximum suppression)

Problem: pixels along this edge didn’t survive the thresholding


Hysteresis thresholding

• Check that maximum value of gradient value is sufficiently large

– drop-outs? use hysteresis

• use a high threshold to start edge curves and a low threshold to continue them.

Source: S. SeitzSource: Darrell, Berkeley

Hysteresis Thresholding


.

•Idea : use a high threshold to start edge curves and a low threshold to

continue them

•Start with a high threshold (strong edge)

•Apply another threshold which is lower than the higher one

•Look for the other edges which are higher than the lower

threshold and connected to the strong edges

•Add them to the edge list

Hysteresis thresholding• Threshold at low/high levels to get weak/strong edge pixels

• Do connected components, starting from strong edge pixels

Source: Hays, Brown

Hysteresis thresholding

original image

high threshold(strong edges)

low threshold(weak edges)

hysteresis threshold

Source: L. Fei-FeiSource: Darrell, Berkeley

Final Canny Edges

Source: Hays, Brown

Canny edge detector

1. Filter image with x, y derivatives of Gaussian

2. Find magnitude and orientation of gradient

3. Non-maximum suppression:– Thin multi-pixel wide “ridges” down to single pixel width

4. Thresholding and linking (hysteresis):– Define two thresholds: low and high

– Use the high threshold to start edge curves and the low threshold to continue them

• MATLAB: edge(image, ‘canny’)

Source: D. Lowe, L. Fei-FeiSource: Hays, Brown

Example


Thresholding


Different thresholds

Applied to gradient value

Non-local Maxima Suppression


LOG Operator


Effect of sigma – Detection vs. Localization


Effect of sigma


Canny’s Edge detection


Canny takes two factors into account in designing the edge detector

A model of the kind of edges to be detected

A quantitative definition of the performance this edge detector is supposed to have

Several criteria can be chosen to characterize the performance of an edge detector

Good detection, i.e. robustness to noise

Good localization

Uniqueness to response

Canny’s Edge detection


Effect of (Gaussian kernel spread/size)

Canny with Canny with original

The choice of depends on desired behavior• large detects large scale edges

• small detects fine features


Object boundaries vs. edges

Background Texture Shadows


Edge detection is just the beginning…

Berkeley segmentation database:http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench/

image human segmentation gradient magnitude

Source: L. Lazebnik

Much more on segmentation later in term…


http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench/

Texture

Easy to recognize, hard to define

Texture

Whether an effect is a texture or not depends on the scale at which it is viewed

A leaf that occupies most of the image –object

Foliage of a tree - texture

Image Segmentation

Source: ForsythSource: Hays, Brown

Texture Synthesis

Efros & Freeman

Shape from Texture

Texture looks same at different points on a surface

deformation is a cue to the shape of the surface

Adapted from David Forsyth, UC Berkeley

Texture and Material

http://www-cvr.ai.uiuc.edu/ponce_grp/data/texture_database/samples/Source: Hays, Brown

Texture and Orientation


Texture and Scale


What is texture?

Regular or stochastic patterns caused by bumps, grooves, and/or markings

Source: Hays, Brown

Pre-attentive Texture Discrimination

Adapted from Bill Freeman, MIT

Same or different textures?

Textons

Image textures generally consists of organized patterns of

regular sub-elements

One natural way to represent texture is to find the textons and

then describe the way in which they are laid out

It generally required a human to look at the texture in

order to decide what those fundamental units were...


Malik & Perona, CVPR 1989

A set of texture examples used in experiments with human subjects to tell how easily

various types of textures can be discriminated

Bergen and Adelson, Nature

1988


Representing Texture

• Instead of looking for patterns at the level of arrow-heads or triangles, look for simpler pattern elements (e.g. dots and bars)

• Easy : Find patterns by filtering the image

• Remember : There is a strong response to the filter when the image pattern in a neighborhood looks similar to the filter kernel

• Represent a texture in terms of the response of a collection of filters in different scales and orientations

How can we represent texture?

• Compute responses of blobs and edges at various orientations and scales

Source: Hays, Brown

Overcomplete representation: filter banks

LM Filter Bank

Code for filter banks: www.robots.ox.ac.uk/~vgg/research/texclass/filters.html

Source: Hays, Brown

Filter banks

• Process image with each filter and keep responses (or squared/abs responses)

Source: Hays, Brown

How can we represent texture?

• Measure responses of blobs and edges at various orientations and scales

• Idea 1: Record simple statistics (e.g., mean, std.) of absolute filter responses

Source: Hays, Brown

Can you match the texture to the response?

Mean abs responses

FiltersA

B

C

1

2

3

Source: Hays, Brown

Texture Segmentation

Squared – to count black-to-white pixels same as white-to-black pixels

Smooth – equivalent to estimating the mean of the squared filter outputs in some window

Pass to classifier – to describe the texture

Choice of statistics


• What statistics should be collected

• mean of the squared filter output

– Differentiates spoty windows from stripey windows

– (Malik and Perona)

• Use mean and standard deviation

– Texture matching

– (Ma and Manjunath)

Texture Similarity

Ma & Manjunath, CVPR 1996

Application – Satellite Images

Ma & Manjunath, CVPR 1996

Representing texture• Idea 2: take vectors of filter responses at each pixel and

cluster them, then take histograms.

Source: Hays, Brown


The Goal of Texture Analysis



The Goal of Texture Synthesis


Homage to Shannon

Hole Filling

Political Texture Synthesis!

+ =

Application: Texture Transfer

• Try to explain one object with bits and pieces of another object:

Same as texture synthesis, except an additional constraint:1. Consistency of texture

2. Similarity to the image being “explained”


Texture Transfer


Image Analogies

• Solution:

Texture by Numbers


Texture Synthesis


edge and texture - web.cs.hacettepe.edu.trpinar/courses/vbm686/lectures/edg… · source: darrell,...

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