There is a special form for boolean formulas called "Conjunctive Normal Form" (CNF). A problem in this form consists of clauses connected with and operators, where each clause only contains variables connected with or operators. The variables can appear negated, but only variables can be directly negated, something like !(a && b) is not allowed. An example boolean formula in CNF form is:
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You look at a region of the image. If all the pixels are roughly the same color (below some threshold), you store the average color for the whole region as a single value. If the pixels vary too much, you split the region into four quadrants and try again.