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11 ∞ Example cumulative distribution function the CDF can describe the probability of throwing a total value of less than x. 15) −∞ In a CDF, the probability of a measurement between −∞ and ∞ increases monotonically from 0 to 1, giving the CDF the following properties: 1. 2. 3. 4. 5. 16 Joint distribution functions A joint distribution function is a PDF that combines the PDFs with a number of variables R1 , R2 , . . , Rn . 10). ,Rn (x1 , x2 , . . , xn ) = PR (x) = Pr{R1 ≤ x1 AND R2 ≤ x2 AND .

That is, all processing and interface functions are incorporated into a single chip leading to an extremely compact intelligent sensing solution. FPGAs have ample I/O resources and they have the added benefit of allowing us to directly and extensively utilise parallelism while standard microprocessors do not. Given that the algorithm will be implemented in FPGA, we seek an algorithm with the following properties so that we can more easily meet our processing time constraint: • Algorithms that can be implemented in a parallel fashion are desirable since they provide a relatively simple means of decreasing processing times.

2. g. we solve for motion at each pixel of the image). In FDM, we are modelling a physical (continuous) structure, hence the discretisation must be performed explicitly. 6 Solving the membrane model An important difference between regression and membrane problems is that neighbouring parameters have no explicit relationship in regression problems. This allows a closed form, single step solution. In regularisation problems, neighbouring parameters are explicitly constrained to be similar and this in turn leads to an implied relationship between parameters that are not direct neighbours.

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