TopoContour-Mamba: Topology-Guided Visual Serialization with Augmented Contour Trees

AbstractVisual state-space models need a sequence before selectivescanning, so the route decides which evidence is read earlyand which remains close to the final output. Most visualroutes are fixed across images. We propose TopoContourMamba, a fully specified architecture that derives animage-specific route from a deterministic saliency fieldand reads raw image samples along that route. A full contour tree supplies valid continuation, split, join, source,and terminal events; only useful regular contours are inserted into a sparse execution tree. Each retained contour receives a perimeter-based point budget. Uniformpilot points sample one Sobel field: the mean signed normal response selects one low-saliency read side for thewhole contour, the smoothed response magnitude redistributes the fixed point budget, and its maximum fixesthe common start/end point p0. Normal Mamba readsRGB samples from the first collision back to a taggedcontour point. Two shared-weight Contour Mamba scansstart at p0, traverse the same closed samples in oppositedirections, and end on a tagged return to p0. A terminalcontour reads both normal sides and uses a second pairof loops to combine them. All contours are encoded independently before a Tree Mamba aggregates their taggedoutputs from low to high saliency. Splits copy one taggedsummary, joins use permutation-invariant support-awarefusion, and terminal leaves are sorted by saliency measured on their actual reads for the final Mamba. Theroute is deterministic and uses no CNN feature stem. Wegive a complete algorithmic specification of its routes, token interfaces, boundary cases, defaults, and structuralproperties without claiming empirical performance.