CS332 Visual ProcessingDepartment of Computer ScienceWellesley College

Binocular Stereo Vision

Region-based stereo matching algorithms

Properties of human stereo processing

Solving the stereo correspondence problem

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(1) sum of absolute differences

Σ | pleft

– pright

|

(2) normalized correlation

(pleft

– pleft

) (pright

– pright

)

patch

σpleft σ

pright

Σ patch

Measuring goodness of match between patches

(1/n)

(1/n)

Optional: divide byn = number of pixels

in patch

Region-based stereo matching algorithm

for each row r

for each column c

let pleft be a square patch centered on (r,c) in the left image

initialize best match score mbest to ∞initialize best disparity dbest

for each disparity d from –drange to +drange

let pright be a square patch centered on (r,c+d) in the right image

compute the match score m between pleft and pright

(sum of absolute differences)

if (m < mbest), assign mbest = m and dbest = d

record dbest in the disparity map at (r,c)

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(normalized correlation)

How are the assumptions used??

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left right

The real world works against us sometimes…

Example: Region-based stereo matching, using filtered images and sum-of-absolute differences

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(from Carolyn Kim, 2013)

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Properties of human stereo processing

Use features for stereo matching whose position and disparity can be measured very precisely

Stereoacuity is only a few seconds of visual angle

difference in depth 0.01 cm at a viewing distance of 30 cm

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Properties of human stereo processing

Matching features must appear similar in the left and right images

For example, we can’t fuse a left stereo image with a negative of the right image…

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Properties of human stereo processing

Only “fuse” objects within a limited range of depth around the fixation distanceVergence eye movements are needed to fuse objects over larger range of depths

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Properties of human stereo vision

We can only tolerate small amounts of vertical disparity at a single eye position

Vertical eye movements are needed to handle large vertical disparities

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Properties of human stereo processing

In the early stages of visual processing, the image is analyzed at multiple spatial scales…

Stereo information at multiple scales can be processed independently

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Neural mechanisms for stereo processing

G. Poggio & colleagues:

complex cells in area V1 of primate visual cortex are selective for stereo disparity

neurons that are selective for a larger disparity range have larger receptive fields

zero disparity: at fixation distance near: in front of point of fixation far: behind point of fixation

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In summary, some key points…

• Image features used for matching:simple, precise locations, multiple scales, similar between left/right images

• At single fixation position, match features over a limited range of horizontal & vertical disparity

• Eye movements used to match features over larger range of disparity

• Neural mechanisms selective for particular ranges of stereo disparity

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Matching features for the MPG stereo algorithm

zero-crossings of convolutions with 2G operators of different size

L

M

S

rough disparities over large range

accurate disparities over small range

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large w

left

large w

right

small w

left

small w

right

correct match outside search range at small scale

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large w

left

right

small w

left

right

correct match now inside search range at small scale

vergence eye movements!

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Stereo images (Tsukuba, CMU)

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Zero-crossings for stereo matching

- +

… …

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Simplified MPG algorithm, Part 1

To determine initial correspondence:(1) Find zero-crossings using a 2G operator with central

positive width w(2) For each horizontal slice:

(2.1) Find the nearest neighbors in the right image for each zero-crossing fragment in the left image(2.2) Fine the nearest neighbors in the left image for each zero-crossing fragment in the right image(2.3) For each pair of zero-crossing fragments that are closest neighbors of one another, let the right fragment be separated by δinitial from the left. Determine whether δinitial is within the matching tolerance, m. If so, consider the zero-crossing fragments matched with disparity δinitial

m = w/2

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Simplified MPG algorithm, Part 2To determine final correspondence:(1) Find zero-crossings using a 2G operator with reduced width

w/2(2) For each horizontal slice:

(2.1) For each zero-crossing in the left image:(2.1.1) Determine the nearest zero-crossing fragment

in the left image that matched when the 2G operator width was w

(2.1.2) Offset the zero-crossing fragment by a distance δinitial, the disparity of the nearest matching zero-crossing fragment found at the lower resolution with operator width w(2.2) Find the nearest neighbors in the right image for each zero-crossing fragment in the left image(2.3) Fine the nearest neighbors in the left image for each zero-crossing fragment in the right image(2.4) For each pair of zero-crossing fragments that are closest neighbors of one another, let the right fragment be separated by δnew from the left. Determine whether δnew is within the reduced matching tolerance, m/2. If so, consider the zero-crossing fragments matched with disparity δfinal = δnew + δinitial

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Coarse-scale zero-crossings:

Use coarse-scale disparities to guide fine-scale matching:

Ignore coarse-scale disparities:

w = 8m = 4

w = 4m = 2

w = 4m = 2