TopoContour-Mamba

Topology-Guided Visual Serialization with Augmented Contour Trees

Abstract

Visual state-space models need a sequence before selective scanning, so the route decides which evidence is read early and which remains close to the final output. Most visual routes are fixed across images. We propose TopoContour-Mamba, a fully specified architecture that derives an image-specific route from a deterministic saliency field and 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. Uniform pilot points sample one Sobel field: the mean signed normal response selects one low-saliency read side for the whole contour, the smoothed response magnitude redistributes the fixed point budget, and its maximum fixes the common start/end point p0. Normal Mamba reads RGB samples from the first collision back to a tagged contour point. Two shared-weight Contour Mamba scans start at p0, traverse the same closed samples in opposite directions, and end on a tagged return to p0. A terminal contour reads both normal sides and uses a second pair of loops to combine them. All contours are encoded independently before a Tree Mamba aggregates their tagged outputs from low to high saliency. Splits copy one tagged summary, joins use permutation-invariant support-aware fusion, and terminal leaves are sorted by saliency measured on their actual reads for the final Mamba. The route is deterministic and uses no CNN feature stem. We give a complete algorithmic specification of its routes, token interfaces, boundary cases, defaults, and structural properties without claiming empirical performance.