A quantitative measure of aesthetic is actually difficult to define?
A question I’ve been wondering for so long is how are we able to distinguish something that is visually aesthetic from otherwise?
I think the specific application case I was exploring was creating an algorithm that generates a GOL starting point that converges in finite-time an aesthetically pleasing image.
Ofcourse to design such an algorithm one must question what it means to be aesthetically pleasing.
There are things that immediately stand out like the presence of symmetries, soft curves, recurring patterns. But it’s hard to assign a number to this.
Leon Gatys et al worked on an adjacent problem; How do we transfer the style of one image to another without losing structure [1].
They realised that different layers in a VGG convnet preserve different aspects of the same image.
Which led to a criterion involving a weighted sum of the squared difference in the structure-relevant feature maps and the squared difference between the gram matrix of the style preserving Feature maps.
\[ G_{ij}^l = \sum_k{F_{ik}^lF_{jk}^l} \]which is essentially the flattened Feature map (along the H x W dimensions) multiplied by itself to produce $G \isin \mathbb{R}^{C\times C}$ where C is the number of channels.
\[ E_l = \frac{1}{4N^2_lM^2_l} \sum_{i,j}(G^l_{ij} - A^l_{ij})^2 \] \[ \mathcal{L}_{content}(p, x, l) = \frac{1}{2}\sum_{ij}(F_{ij}^l - P^l_{ij})^2 \] \[ \mathcal{L}_{style}(a, x) = \sum_{l}w_l E_l \] \[ \mathcal{L_{total}} = \alpha\mathcal{L_{content}} + \beta\mathcal{L_{style}} \]