Image Processing Techniques for Assessing Contractility in Isolated Adult Cardiac Myocytes

Table 1

𝑁⇐100	number of iterations (%)
𝜀⇐1/255	regularization parameter (%)
𝜎⇐1	Gaussian kernel's width (%)
𝑑⇐2	dimensionality of problem (%)
𝑢(𝐱,0)⇐𝑢0(𝐱),onΩ	set initial condition (%)
∇𝑢0⇐[(𝑢0)𝑥(𝑢0)𝑦]^T	estimate gradients (%)
𝑐1⇐corr(𝑢,𝑓)	performance measure (%)
𝑐1⇐corr(𝑢,𝑢0)	correlation measure (%)
for  𝑖=1 to N do
𝑢𝜎=𝐺𝜎∗𝑢	convolve image with Gaussian kernel (%)
𝜎^2=var(𝑢)−var(𝑢𝜎)	estimate variance of the noise (%)
∇𝑢⇐[𝑢𝑥𝑢𝑦]^T	estimate gradients (%)
|∇𝑢|⇐𝑢^2𝑥+𝑢^2𝑦	magnitude of the gradients (%)
1𝑔⇐𝑢^2𝑥+𝑢^2𝑦+𝜀	diffusivity function (%)
⟨𝑔⋅∇𝑢,𝐧⟩⇐0, on 𝜕Ω	set boundary conditions (%)
1Λ=−2𝜎^2[𝑢𝑥(𝑢𝑥−(𝑢0)𝑥)+𝑢𝑦(𝑢𝑦−(𝑢0)𝑦)]	forcing term parameter (%)
𝜙=|∇𝑢|∇⋅(𝑔⋅∇𝑢)−Λ(𝑢−𝑢0)	diffusion term (%)
𝜀𝛿𝑡(𝐱)=51+(−𝜀2𝑑5)(max(|∇𝑢|)−|∇𝑢|)max(|∇𝑢|)	time-step (%)
𝑢⇐𝑢+𝛿𝑡𝜙	evolve the image (%)
𝑐𝑖+1⇐corr(𝑢,𝑓)	update performance measure (%)
𝑐𝑖+1⇐corr(𝑢,𝑢0)	update correlation measure (%)
𝑐̂𝑖+1⇐𝜕^2𝑐𝑖+1	stopping criterion (%)
if  𝜕𝑐̂𝑖+1≤0 then
𝑣=𝑢	save best image if condition is met (%)
end if
end for