. 2018 Dec 6;7:e40224. doi: 10.7554/eLife.40224

Table 2. Components of the registration potential function.

	Term	Description	Form
1	$F_{e} (x; x_{0}, E)$	Penalizes changes in the distances between neighboring vertices in the mesh.	$\frac{H_{e} (x; x_{0}, E) + G_{e} (x; x_{0}, E)}{\| E \|}$
2	$F_{ϑ} (x; x_{0}, Θ)$	Penalizes the changes in t he angles of the triangles in the mesh.	$\frac{H_{ϑ} (x; x_{0}, Θ) + G_{ϑ} (x; x_{0}, Θ)}{\| Θ \|}$
3	$F_{p} (x; x_{0}, P)$	Penalizes any change in the positions of the vertices on the perimeter of the map.	$\frac{1}{2} \sum_{u \in P} {(x)}_{u} - {(x_{0})}_{u}^{2}$
4	$F_{φ} (x; Φ)$	Decreases as a retinotopic vertex u approaches its anchor-point y in the retinotopy model.	$\frac{\sum_{(u, y, σ, w) \in Φ} w \exp (- \frac{{(x)}_{u} - y}{2 σ^{2}})}{\| Φ \|}$
5	$H_{e} (x; x_{0}, E)$	Harmonic component of the edge-length deviation penalty $F_{e} (x; x_{0}, E)$ .	$\frac{1}{2} \sum_{(u, v) \in E} {(r_{x} (u, v) - r_{x_{0}} (u, v))}^{2}$
6	$G_{e} (x; x_{0}, E)$	Infinite-well component of the edge-length deviation penalty $F_{e} (x; x_{0}, E)$ .	$\frac{1}{2} \sum_{(u, v) \in E} ({(\sqrt{\frac{r_{x_{0}} (u, v) - q_{0}}{r_{x} (u, v) - q_{0}}} - 1)}^{2} + {(\sqrt{\frac{q_{1} - r_{x_{0}} (u, v)}{q_{1} - r_{x} (u, v)}} - 1)}^{2})$
7	$H_{ϑ} (x; x_{0}, Θ)$	Harmonic component of the angle deviation penalty $F_{ϑ} (x; x_{0}, Θ)$ . $F_{p} (x; x_{0}, P)$	$\frac{1}{2} \sum_{(a, b, c) \in Θ} {(α_{x} (a, b, c) - α_{x_{0}} (a, b, c))}^{2}$
8	$G_{ϑ} (x; x_{0}, Θ)$	Infinite-well component of the angle deviation penalty $F_{ϑ} (x; x_{0}, Θ)$ .	$\frac{1}{2} \sum_{(a, b, c) \in Θ} ({(\sqrt{\frac{α_{x_{0}} (a, b, c)}{α_{x} (a, b, c)}} - 1)}^{2} + {(\sqrt{\frac{π - α_{x_{0}} (a, b, c)}{π - α_{x} (a, b, c)}} - 1)}^{2})$