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Chapter 21 Machine Vision

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Chapter 21

Machine Vision

- Human Vision
- Image Processing
- Edge Detection
- Convolution and the Canny Edge Detector
- Segmentation
- Classifying Edges

- Using Texture
- Structural Texture Analysis
- Determining Shape and Orientation from Texture
- Interpreting Motion
- Making Use of Vision
- Face Recognition

- Image Processing consists of the following components:
- Image capture
- Edge detection
- Segmentation
- Three dimensional segmentation
- Recognition and analysis

- Image capture is the process of converting a visual scene into data that can be processed.

- Edge detection is the first phase in processing image data.
- The following images show a photograph of a hand and the edges detected in this image.

- Every edge represents some kind of discontinuity in the image.
- Most edges are depth discontinuities.
- Other discontinuities are:
- Surface orientation discontinuities
- Surface reflectance discontinuities
- Illumination discontinuities (shadows)

- One method of edge detection is to differentiate the image:
- Discontinuities will have the highest differentials.

- This does not work well with noisy images
- Convolution is better for such images.

- The convolution of two discrete functions f(a, b) and g(a, b) is defined as follows:
- The convolution of continuous functions f(a,b) and g(a,b) is defined as follows:
- An image can be smoothed, to eliminate noise, by convolving it with the Gaussian function:

- The image, after smoothing, can be differentiated to detect the edges.
- The peaks in the differential correspond to the edges in the original image.
- In fact, the same result can be obtained by convolving the image with the differential of G:

- This method only works with one-dimensional edges. To detect two dimensional egdes we convolve with two filters, and square and add the results:
- where I(x, y) is the value of the pixel at location (x, y) in the image.
Filter 1 is G’σ(x) Gσ(y)

Filter 2 is G’σ(y) Gσ(x)

- This is the Canny edge detector.

- Once the edges have been detected, this can be used to segment the image.
- Segmentation involves dividing the image into areas which do not contain edges.
- These areas will not have sharp changes in colour or shading.
- In fact, edge detection will not always entirely segment an image.
- Another method is thresholding.
- Thresholding involves joining pixels together that have similar colors.

- After extracting edges, it is useful to classify the edges.
- A convex edge is an edge between two faces that are at an angle of more than 180° from each other.
- A concave edge is an edge between two faces that are at an angle of less than 180° from each other.
- An occluding edge is a depth discontinuity.

- The following diagram shows a line drawing that has had all its edges classified as convex (+), concave (-) or occluding (arrow):

- Most vertices represent a meeting of three faces.
- There are onlysixteen possible ways these trihedral vertices can be labeled:

- The Waltz algorithm uses this constraint.
- This works as follows:
- The first edge that is visited is marked with all possible labels.
- Then the algorithm moves onto an adjacent edge, and attempts to label it.
- If an edge cannot be labeled, the algorithm backtracks.
- Thus, depth-first search is applied to attempt to find a consistent labeling for the whole image.

- Textures, such as these, tell us a great deal about images, including:
- Orientation
- Shape

- We can also determine what the pictures on the right are showing, simply by their textures.

- A statistical method of determining texture is to use co-occurrence matrices.
- D(m, n) is the number of pairs of pixels in our picture, P, for which:
P(i, j) = m

P(i + δi, j + δj) = n

i and j are pixels in P, and δi and δj are small increments.

- D defines how likely it is that any two pixels a particular distance apart (δi and δj) will have a particular pair of values.
- The co-occurrence matrix is defined as:
C = D + DT where DT is the transposition of D.

- The structural approach treats textures as being made up of individual units called texels.
- In this image, each tileis a texel.
- Texel analysis involvessearching for repeatedpatterns and shapeswithin an image.

- These are good examples of pictures where texture helps to determine the shape and orientation.
- Note that the second image, although it is a flat, two dimensional shape, looks like a sphere.
- This is because this is the only sensible way for our brains to explain the texture.

- One way to determine orientation is to assume that each texel is flat.
- Thus the extent of distortion of the shape of the texel will tell us what angle it is being viewed at.
- Orientation involves determining slant (σ) and tilt (τ) , as shown here:

- Detecting motion is vital in mammalian vision.
- Similarly, agents that interact with the real world need to be able to interpret motion.
- We are interested in two types of motion:
- Actual motion of other objects
- Apparent motion caused by the motion of the agent.

- Detecting motion is vital in mammalian vision.
- Similarly, agents that interact with the real world need to be able to interpret motion.
- We are interested in two types of motion:
- Actual motion of other objects
- Apparent motion caused by the motion of the agent.

- This apparent motion is known as optical flow, and the vectors that define the apparent motion are the motion field.

- The arrows on this photo show the motion field.

- What purpose does machine vision really serve?
- It can be used to control mobile agents or unmanned vehicles such as those sent to other planets.
- Another purpose is to identify objects in the agent’s environment.
- If the agent is to interact with these objects (pick them up, sit on them, talk to them) it must be able to recognize that they are there.

- An example of a problem that humans are extremely good at solving, but computers are very bad at.
- Faces must be recognized in varying lighting conditions, from different angles and distances, and with other variable elements such as facial hair, glasses, hats and natural aging.
- Methods used in face recognition vary, but many involve principle component analysis:
- Identifying those features that most differentiate one face from another, and treating those as a vector which is to be compared.