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comparison: src/AlgorithmFB.jl

src/AlgorithmFB.jl

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1 ####################################################################
2 # Predictive online PDPS for optical flow with known velocity field
3 ####################################################################
4
5 __precompile__()
6
7 module AlgorithmFB
8
9 identifier = "fb_known"
10
11 using Printf
12
13 using AlgTools.Util
14 import AlgTools.Iterate
15 using ImageTools.Gradient
16
17 using ..OpticalFlow: Image,
18 ImageSize,
19 flow!
20
21 #########################
22 # Iterate initialisation
23 #########################
24
25 function init_rest(x::Image)
26 imdim=size(x)
27
28 y = zeros(2, imdim...)
29 Δx = copy(x)
30 Δy = copy(y)
31 ỹ = copy(y)
32 y⁻ = copy(y)
33
34 return x, y, Δx, Δy, ỹ, y⁻
35 end
36
37 function init_iterates(xinit::Image)
38 return init_rest(copy(xinit))
39 end
40
41 function init_iterates(dim::ImageSize)
42 return init_rest(zeros(dim...))
43 end
44
45 ############
46 # Algorithm
47 ############
48
49 function solve( :: Type{DisplacementT};
50 dim :: ImageSize,
51 iterate = AlgTools.simple_iterate,
52 params::NamedTuple) where DisplacementT
53
54 ################################
55 # Extract and set up parameters
56 ################################
57
58 α, ρ = params.α, params.ρ
59 τ₀, τ̃₀ = params.τ₀, params.τ̃₀
60
61 R_K² = ∇₂_norm₂₂_est²
62 τ̃ = τ̃₀/R_K²
63 τ = τ₀
64
65 ######################
66 # Initialise iterates
67 ######################
68
69 x, y, Δx, Δy, ỹ, y⁻ = init_iterates(dim)
70 init_data = (params.init == :data)
71
72 ####################
73 # Run the algorithm
74 ####################
75
76 v = iterate(params) do verbose :: Function,
77 b :: Image,
78 v_known :: DisplacementT,
79 🚫unused_b_next :: Image
80
81 ##################
82 # Prediction step
83 ##################
84
85 if init_data
86 x .= b
87 init_data = false
88 else
89 # Δx is a temporary storage variable of correct dimensions
90 flow!(x, v_known, Δx)
91 end
92
93 ##################################################################
94 # We need to do forward–backward step on min_x |x-b|^2/2 + α|∇x|.
95 # The forward step is easy, the prox requires solving the predual
96 # problem of a problem similar to the original.
97 ##################################################################
98
99 @. x = x-τ*(x-b)
100
101 ##############
102 # Inner FISTA
103 ##############
104
105 t = 0
106 # Move step length from proximal quadratic term into L1 term.
107 α̃ = α*τ
108 @. ỹ = y
109 for i=1:params.fb_inner_iterations
110 ∇₂ᵀ!(Δx, ỹ)
111 @. Δx .-= x
112 ∇₂!(Δy, Δx)
113 @. y⁻ = y
114 @. y = (ỹ - τ̃*Δy)/(1 + τ̃*ρ/α̃)
115 proj_norm₂₁ball!(y, α̃)
116 t⁺ = (1+√(1+4*t^2))/2
117 @. ỹ = y+((t-1)/t⁺)*(y-y⁻)
118 t = t⁺
119 end
120
121 ∇₂ᵀ!(Δx, y)
122 @. x = x - Δx
123
124 ################################
125 # Give function value if needed
126 ################################
127 v = verbose() do
128 ∇₂!(Δy, x)
129 value = norm₂²(b-x)/2 + α*γnorm₂₁(Δy, ρ)
130 value, x, [NaN, NaN], nothing
131 end
132
133 v
134 end
135
136 return x, y, v
137 end
138
139 end # Module
140
141

Mercurial Repository: PredictPDPS

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