PART I (Live Wire) The programming for this part requires mostly changing code in function "compute_paths" (inside wire.cpp). Provided starter project has BFS traversal of the graph. Instead, you should implement Dijkstra. Weight edges using direct approach on slides 8-12 (topic 5) using Gaussian function "g(x)=const*exp(-x*x/(2*sigma*sigma))" where "sigma" is a sensitivity parameter. Your report should contain the following experiemnts:

- Compare livewire on 4 and 8 connected graph. Demonstarte the differences and explain them in the report.
- Compare the results for a range of values for contrast sensitivity parameter "sigma" in the edge-weighting function. Explain your impirical observations and justify a strategy for selecting "sigma".

PART II (Snake) The programming for this part requires mostly changing code in function "DP_move" (inside snake.cpp). Provided starter project makes random moves. Instead, you should implement Viterbi algorithm optimizing certain snake energies. You should experiment with different (pair-wise interaction) snakes as detailed below:

- Open and closed snakes should be handled (GUI closes a snake on a right click). You may set different default energies for these two cases. For example, open-ended snake could use "keep length" internal energy mode.
- Tune both "shrink" and "keep length" internal energy modes: "shrink" should use elastic term
while "keep_length" should use internal energy encouraging certain distance
*L*between control points (see class notes). Find a good way of selecting*L*automatically and describe it in your report. - Play with your snake's internal energy even before you introduce external/image energy. When only internal energy is present, your snake should develop into a smooth rounded contour (which converges to a dot in case of "SHRINK" ). Make sure to check your snake's internal energy operation before you turn its external energy on. Demonstrate examples for "SHRINK" and "KEEP LENGTH" in your report (GUI has a menu to choose this mode).
- Tune both "image gradients" and "distance transform" modes of the external energy (adapt GUI menu for this mode):
in the first case the internal energy should be based on the values of image gradients at each control point while the second
case should use the values of the
**generalized distance transform**. Your report should demonstrate examples where the two modes behave differently, and explain why.- Suggestion: precompute 2D table of the same size as the image for storing the results of computing image gradients
costs
*F(p)*at each pixel*p*(like node-costs in live-wire where low cost corresponded to large gradients). Then, you can compute another 2D array*D(p)*corresponding to the generalized distance transform of*F(p)*. Your snake should use either*F(p)*or*D(p)*according to the Extrenal Energy Mode (you can create any types of "modes" selectable from the drop-down-list, see`main.cpp`

). Note that Gradient and Distance Transform modes may require very different tuning of parameter`lambda`

controling relative weight of internal and external energies.

- Suggestion: precompute 2D table of the same size as the image for storing the results of computing image gradients
costs
- Compare performance of quadratic
*(v_i-v_(i-1))^2*and linear*abs(v_i-v_(i-1))*elastic terms. Explain your observations. - Analyse the effect of parameter
`alpha`

in the generalized distance map computation. Provide and explain results of empirical tests. - Implement interactive corrections via "nudging" (see class notes). Use distance transform to compute distances from a nudge point to all pixels in the image. "Snake.h" contains all necessary interface components ('add...Nudge' functions).
- Density of snake nodes (parameter
`dP`

) and/or their uneven distribution along the contour changes the balance between the internal and external energy terms. Find some example(s) where spacing of control points clearly affects the behaviour of the snake and report your results/analysis. Suggest some solution for eliminating such dependence on parameterization. - OPTIONAL PART (may get small bonus, do this only if really interested): implement an alternative method (GD-snake) for moving "snake" towards local minima based on
gradient-descent (energy derivatives) and compare it with DP-snake. For example, inside
`snake.cpp`

you can add a new function`GD_move()`

that can be called instead of`DP_move()`

when some "flag" is selected. Note that inside`GD_move`

you must use floating-point precision and select an additional parameter "dt".

`wire.cpp`

and `snake.cpp`

where you
can implementat all methods required to complete the tasks above. All functions in these files are called from `main`

according to GUI functionality
implemented in there. The provided GUI is in a "working" condition (compiles and runs). Livewire GUI is mainly designed to enter clicks and change some parameters. Main GUI features for the snake project are: left click = add snake nodes, right click = "close" the snake, key 's' = one iteration of
DP-snake, key 'c' = run iterations until snake convergence (local minima is found),
hit 'n'-key followed by a left (right) mouse click to add an attractive (repulsive) nudge.
`wire.cpp`

`snake.cpp`

and any other project files where you changed some code.
If you used special images, submit the corresponding image files.