Today we consider the basic convolutions that seem necessary to support basic visual processes, including brightening, sharpening, and edge detection.

1. Computing general functions.
2. The Perceptron Model. A system for weighing evidence about the state of the environment
   1. Inputs are either 0 or 1.
   2. Inputs have weights associated with them.
   3. Output is 1 if and only if the combined inputs exceed a threshold.
   4. Minsky and others demonstrated that there certain types of general computation that perceptrons were not able to perform. (See readings about the connectedness problem.)
3. The neural network model, a classifier system.
   1. Outputs can be used to identify various inputs that are members of a class.
   2. Networks are trained on inputs with known classifications. Weights associated with neural connections are then adjusted given known errors in the classification of the training set. Networks must often consider training data multiple times.
   3. Common method for adjusting weights can be thought of as a gradient descent approach to adjusting the weights to minimize error.
      1. Large error is never completely eliminated in a single step: unstable.
      2. The learning rate can be thought of as controlling the percent of the error eliminated; may not actually occur, because the weight-error space has local extrema.
   4. Trained networks can be used to classify inputs with unknown classifications.
   5. Batch training: Errors from all training instances are grouped together before adjusting the weights.
   6. On-line training: Individual training instances are used to make adjustments to the weights. Advantages include:
      1. On-line training allows fine control over the adjustments of weights.
      2. On-line training can be be an on-going process that may track moving targets. Batch training is, in some sense, monotonic, or focused on a static identification of the problem.
4. Applications:
   1. Working example: Code recognition.
   2. Handwriting recognition in PDA's (Newton was one of the first).
   3. Voice recognition (Octel's word-recognition system)
5. Convolution: the controlled mixing of data to serve a purpose.
   1. An Excel example.
   2. Notions borrowed from analysis of frequency-based signals.
   3. Concept: JPEG encodes images using frequency-based encoding; it's a "lossy" encodoing.
   4. Filters: low-pass, high-pass, and band-filters.
   5. Bluring. Accentuating low-pass filter.
   6. Edge-detection. High-pass filter.
   7. Sharpening. Enhancing edges, attenuating low-frequency components of the image.

Resources needed for this class:

• Selections from the Algorithmic Beauty of Plants, by Przemyslaw Prusinkiewicz and Aristid Lindenmayer. We will be using this material in lab next week.
• Turing's Chemical Basis for Morphogensis. This is a technically demanding, but interesting foundation paper; the basis for this field of biology. Most of the ideas presented here have since been discounted, but it remains an important interdisciplinary essay.

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