Transcript l24

Today’s Lecture
• Computational Vision
– Images
– Image formation in brief (+reading)
– Image processing: filtering
Color
code:
• Linear filters
•Done
• Non-linear operations
•Today
• Signatures
•Next class
• Edges
– Image interpretation
(or not at all)
• Edge extraction
• Grouping
– Scene recovery
– Recognition
CS-424 Gregory Dudek
Image formation
Key processes:
1. Light comes from source
2. Hits objects in scene
3. Is reflected towards
A) other objects [return to step 2]
B) the camera lens
4. Passes through lens being focussed on imaging surface
5. Interacts with transducers on surface to produce electrical signals
In the eye, the lens is that of the eye, the imaging surface is the
retina, and the transducers are rods and cones.
In a camera, the imaging surface is a CCD (charge-coupled
device) made up of transistors (or related devices).
[several other types of video camera technology are commonly available, including
newer “cheap and cheerful” CMOS cameras, and older “opticons”.]
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Scene “Reconstruction”
• Solve the inverse problem: find the scene that
produced the image.
• Things to account for:
– The camera
– The geometry of the scene
– The interaction of light with objects in the scene.
• Camera model can be:
– Perspective [ loosely: x & y -> fx/z fy/z ]
• Orthogonal & orthographic are special cases
– Paraperspective (AKA weak perspective)
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Recovery
• Typically simplified models of illumination and
reflectance are employed.
– One light source.
– All objects have the same matte reflectance.
• Sometimes: don’t worry about occlusion.
• Sometimes: don’t worry about shading.
• Recovery of geometry is known as scene
reconstruction.
We will return to this later...
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The Sobel Edge operator
• Filter for horizontal and vertical edges, combine.
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Edge extraction
• Edges: places where the intensity changes: hence
there is a large derivative.
• Each edge has an amplitude and orientation that can be
expressed as a combination of orthogonal components in the
x and y directions.
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Sobel detector specifics
• Sobel edge detector
– Convolve image with a pair of operators, S and S’
S*I and S’*I
– The edge map was the Pythagorean sum of the two convolutions
E = (S * I) 2 +(S' * I) 2
The Sobel kernel, as an example, can be broken down into two parts:
1. A smoothing operation (discussed last class)
reduces effect of noise, sets scale (i.e. size)
observe: d/dt F(w) = d/dt k e-iwt = -ikw e-iwt
2. A numerical differentiation
df/dt ≈ f(t) - f(t-1)
CS-424 Gregory Dudek
Other edge operators
• Older edge detectors neglected the smoothing step:
– Larry Roberts developed one of the first (2x2 Robert’s operator[s]).
– The Prewitt operator was based on assuming we could fit a smooth
surface to the data and then differentiate.
– Hueckel operator: use least-squares line fitting
• More recent work involves
smoothing
with a two-dimension
2
2
(x y )
Gaussian:
1
2
2
2
e
2
( t G) * I
• Gaussian provides localization in space, as well as frequency.
• Rather than explicitly compute (1D form):  (G * I)
t
we can use the fact that I is constant
to improve efficiency: ( G) * I
t
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Can be precomputed
Edges: modern methods
• Instead to looking for peaks in the derivative, look
for zero-crossings in the second derivative.
• A recent operator developed by Canny uses multiple scales
(sizes) to improve edge detection, based on optimizing the
notion of what an edge is.
Wanted:
– Detection: detect an edge iff it’s there
– Uniqueness: detect each edge just once
– Localization: detect it at the right place
– Consider an analytic step edge and derive an optimal edge
detector.
• Track edges along contours and suppress (remove) neighbors.
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Edges
• An UNREALISTICALLY simple example:
– Edges from the Canny Operator.
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Input image
• Consider: extract the edge elements + grouping them
into contours.
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Sobel detector output
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Canny operator output
• Note the effect of non-maximum suppression.
• Note how difficult naive grouping would be.
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Human Edge Detection
• Overheads
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