Multi-Path Scanning Mechanism

• Multi-Path Scanning Mechanism is a set of techniques using multiple trajectories, beams, or scan orders to improve measurement accuracy and data separation.
• It is applied across structured light, mmWave, robotics, and network probing to address challenges like bimodal interference and adaptive scan ordering.
• The mechanism leverages methods such as dual-path scanning, trajectory design, and unmixing procedures to overcome hardware constraints and enhance system robustness.

Multi-path scanning mechanism denotes a class of scanning, probing, and acquisition strategies in which information is collected, propagated, or disambiguated through more than one path, beam, trajectory, or scan order. In the cited literature, the expression spans both adverse multi-path phenomena—such as bimodal optical multipath in structured-light phase measuring profilometry—and deliberately designed multi-path procedures, including dual-path state-space scans, two predetermined linear scans on a tilted movable plate, multi-beam 2D fiber scanning, hop-by-hop probing of load-balanced Internet paths, and alternating topological and geometric traverse planning for autonomous outdoor scanning (Zhang et al., 2017, Li et al., 18 Aug 2025, Kim et al., 13 Apr 2026, Tan et al., 2023, Vermeulen et al., 2018, Huang et al., 2020).

1. Domain scope and meanings of “path”

The literature assigns different technical meanings to the word “path,” and the mechanism depends on that meaning.

Domain	Path meaning	Stated objective
Structured light	Two light paths reaching one camera pixel	Separate the paths and make two separated depth measurements
mmWave beam alignment	A few resolvable paths with different AoDs	Minimize the expected value of the average transmission beamwidth
Shadow removal	Horizontal scanning and mask-aware adaptive scanning	Capture global features and improve structural continuity and fine-grained region modeling
Movable-antenna sensing	Two predetermined linear scans on a tilted plate	Estimate elevation and azimuth AoAs
Multi-beam OCT microscopy	Spiral and cycloid scan trajectories with synchronized fibers	Acquire images over a 2D field of view with a 1D actuator
Internet route tracing	Per-flow load-balanced paths	Discover all per-flow load-balanced paths
Outdoor robotic scanning	Dynamic visit paths between scanning goals	Maximize new surface coverage while minimizing travel cost

In the cited work, structured-light scanning treats multi-path as a radiometric and geometric mixing problem; mmWave sensing and Internet measurement treat it as a discovery problem over multiple propagation or routing branches; image restoration treats it as a scan-order design problem in feature space; microscopy and movable-antenna sensing treat it as a trajectory-design problem under hardware constraints; and outdoor robotics treats it as a path-planning problem under energy limits (Torkzaban et al., 2022, Li et al., 18 Aug 2025, Kim et al., 13 Apr 2026, Tan et al., 2023, Vermeulen et al., 2018, Huang et al., 2020).

This suggests that “multi-path scanning mechanism” is not a single canonical algorithm. A plausible implication is that the common substrate is the controlled use, separation, or fusion of multiple acquisition paths to improve visibility, discriminability, robustness, or efficiency.

2. Bimodal multipath in structured-light profilometry

Structured light illumination is an active 3-D scanning technique based on projecting and capturing a set of striped patterns and measuring the warping of the patterns as they reflect off a target object’s surface. As designed, each pixel in the camera sees exactly one pixel from the projector. The cited exception arises when the scanned surface has a complicated geometry with step edges and other discontinuities in depth, or where the target surface has specularities that reflect light away from the camera. These situations are referred to as multipath, where a given camera pixel receives light from multiple positions from the projector. In bimodal multipath, the camera pixel receives light from exactly two positions from the projector, which occurs when light bounces back from a reflective surface or along a step edge where the edge slices through a pixel so that the pixel sees both a foreground and background surface (Zhang et al., 2017).

The cited contribution presents a general mathematical model for the bimodal case in a phase measuring profilometry scanner. Its core operation is to measure the constructive and destructive interference between the two light paths and, by taking advantage of this cue, separate the paths and make two separated depth measurements. The work also reports validation with both simulation and a number of challenging real cases (Zhang et al., 2017).

In this setting, multi-path scanning is not a scan-planning strategy but a correction problem internal to the sensing physics. A common misconception is to equate “multi-path” only with multiple scanning trajectories. Here it instead denotes multiple optical contributions arriving at one detector sample, and the mechanism is an unmixing procedure that restores depth interpretability.

3. Dual-path scan ordering in state-space image restoration

In "D2-Mamba: Dual-Scale Fusion and Dual-Path Scanning with SSMs for Shadow Removal" (Li et al., 18 Aug 2025), the Dual-Path Mamba Group (DPMG) receives a feature map $X \in \mathbb{R}^{C \times H \times W}$ and a binary shadow mask $M \in \{0,1\}^{1 \times H \times W}$. It contains two parallel paths for context propagation. The Horizontal Scanning (HS) path performs a row-wise Z-shaped bidirectional scan, flattening the image into $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$ with $L = H \times W$, then applying a Mamba convolution,

$H_{\mathrm{seq}} = V * K_H,$

followed by a ConvMLP update,

$$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$

and reshaping back to $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$. The Mask-Aware Adaptive Scanning (MAS) path partitions $X$ into $s \times s$ blocks with $s=8$, computes blockwise mask means

$M \in \{0,1\}^{1 \times H \times W}$0

splits blocks into $M \in \{0,1\}^{1 \times H \times W}$1 and $M \in \{0,1\}^{1 \times H \times W}$2 using threshold $M \in \{0,1\}^{1 \times H \times W}$3, orders non-shadow blocks by a Greedy Boundary-contact Search and shadow blocks by a reversed spiral-in order, concatenates the two ordered lists, and applies a second Mamba-plus-ConvMLP path before reassembling $M \in \{0,1\}^{1 \times H \times W}$4.

The two path outputs are fused position-wise by a learned gate,

$M \in \{0,1\}^{1 \times H \times W}$5

with fused output

$M \in \{0,1\}^{1 \times H \times W}$6

The paper states that HS captures global features via horizontal scanning, while MAS dynamically groups blocks of the same type so that they remain adjacent in the SSM sequence, thereby preserving region-specific transformations. On SRD, the ablation reports $M \in \{0,1\}^{1 \times H \times W}$7 for HS only, $M \in \{0,1\}^{1 \times H \times W}$8 for MAS only, $M \in \{0,1\}^{1 \times H \times W}$9 for HS+MAS without DFMB, and $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$0 after adding DFMB. On ISTD, HS$$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$1MAS gives $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$2, slightly better than MAS$$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$3HS at $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$4. Each Mamba scan is stated to be $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$5 in time and memory, and the two paths can be launched in parallel on two streams (Li et al., 18 Aug 2025).

Here, the multi-path scanning mechanism is an ordering and fusion mechanism in token space rather than a physical scanner trajectory. This suggests that scan-path design can be used to encode region adjacency and transformation similarity, not only spatial coverage.

4. Physical trajectory design: movable antennas and single-axis multi-beam microscopy

In "Prior-Guided Movable Antenna Control for Agile Multi-Path Sensing (extended version)" (Kim et al., 13 Apr 2026), the receiver has a single antenna that can be mechanically moved over a rigid flat movable plate. The plate is first tilted in 3D by an Euler rotation $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$6, and the sensing target consists of $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$7 distinct non-line-of-sight signal paths with elevation and azimuth angles. When the movable antenna is at point $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$8, the extra propagation distance on path $$V = \mathrm{flatten\_rows}(X) \in \mathbb{R}^{C \times L}$$9 is

$L = H \times W$0

The framework has two steps. First, the plate orientation is optimized only once to maximize path visibility while preserving path discriminability, using Fisher information analysis and an SQP solution of an optimization over $L = H \times W$1. Second, only two predetermined linear scans are made on the tilted plate: one along the rotated $L = H \times W$2-axis and one along the $L = H \times W$3-axis. Spatial-smoothing MUSIC extracts up to $L = H \times W$4 dominant spatial frequency parameters from the two scan sequences, and a MAP pairing rule combines the data log-likelihood with a prior log-density induced by Gaussian priors on the global AoAs. The reported trade-off is explicit: the proposed method uses one plate tilt and $L = H \times W$5 positions, whereas exhaustive 2D scanning uses $L = H \times W$6 positions; the joint AoA RMSE of MAP with rotation closely tracks the Single-Path bound at $L = H \times W$7, is within $L = H \times W$8 at $L = H \times W$9, rotation yields a $H_{\mathrm{seq}} = V * K_H,$0–$H_{\mathrm{seq}} = V * K_H,$1 effective SNR gain over no-rotation schemes, and MAP outperforms purely data-driven SOMP pairing by $H_{\mathrm{seq}} = V * K_H,$2–$H_{\mathrm{seq}} = V * K_H,$3 (Kim et al., 13 Apr 2026).

A distinct physical mechanism appears in "Miniaturized 2D Scanning Microscopy with a Single 1D Actuation for Multi-Beam Optical Coherence Tomography" (Tan et al., 2023). There, a multi-beam fiber scanning platform generates multi-millimeter 2D scans with a 1D actuator by maximizing the mechanical coupling effect in its orthogonal axis. The bender–fiber system is modeled as two orthogonal second-order mass–spring–damper systems with linear mechanical coupling:

$H_{\mathrm{seq}} = V * K_H,$4

The scan circularity is

$H_{\mathrm{seq}} = V * K_H,$5

and tuning the clamping force in the major axis adjusts $H_{\mathrm{seq}} = V * K_H,$6 to achieve $H_{\mathrm{seq}} = V * K_H,$7 at resonance. Two 2D trajectories are implemented with a single-channel sinusoidal drive at $H_{\mathrm{seq}} = V * K_H,$8: a spiral scan generated by ramping the drive amplitude,

$H_{\mathrm{seq}} = V * K_H,$9

and a cycloid scan generated by constant-amplitude oscillation plus linear sample translation,

$$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$0

Three single-mode optical fibers with spacing $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$1 and cantilever lengths $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$2 are driven by one electrical channel, producing nominal resonance near $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$3. Reported performance includes a single-fiber FOV of $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$4 in spiral mode and $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$5 in cycloid mode, a combined three-beam mosaic of $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$6 in spiral mode and a strip longer than $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$7 by $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$8 in cycloid mode, $$z_t = \mathrm{Dropout}\!\left[W_2\,\mathrm{GELU}\!\left(\mathrm{DWConv}(W_1 h_t)\right)\right],$$9 lateral and axial resolution, and volume acquisition rates of $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$0 and $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$1, respectively (Tan et al., 2023).

Taken together, these two papers indicate a recurring design principle: hardware-limited systems can realize higher-dimensional scanning behavior through geometry, prior information, or mechanical coupling rather than through a matching increase in actuator dimensionality.

5. Beam-space and graph-space scanning under multi-path branching

In "Multi-user Beam Alignment in Presence of Multi-path" (Torkzaban et al., 2022), beam alignment for mmWave channels is formulated for users whose channels have up to $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$2 resolvable paths with different AoDs. A set of scanning beams $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$3, $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$4, is used in a probing phase; each user returns a $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$5-bit ACK/NACK sequence $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$6 indicating whether at least one path AoD falls in each beam; and a policy maps feedback sequences to transmission beams $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$7 with angular width $$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$8. The objective is to minimize the expected value of the average transmission beamwidth,

$$H_{\mathrm{out}} \in \mathbb{R}^{C \times H \times W}$$9

The paper proves that the set of contiguous scanning beams should have a special form, the Tulip Design, in which each beam intersects only its immediate neighbors modulo wrap-around. Under Tulip design, the problem reduces to optimization over a polytope in $X$0 with linear constraints, and the authors use a greedy algorithm. The paper distinguishes SD, BF, $X$1-SD, and $X$2-BF policies. For $X$3, $X$4, and a uniform AoD prior, the reported expected beamwidths are approximately $X$5 for SD, $X$6 for BF, $X$7 for 2-SD, and $X$8 for 2-BF. Under a truncated-Gaussian prior with mean $X$9 and $s \times s$0, SD and BF shrink further to $s \times s$1 and $s \times s$2. As $s \times s$3 grows from $s \times s$4 to $s \times s$5, all policies fall roughly as $s \times s$6, BF-type policies remain narrower than SD-type policies, and the gap widens with $s \times s$7 (Torkzaban et al., 2022).

In "Multilevel MDA-Lite Paris Traceroute" (Vermeulen et al., 2018), the scanning target is not angular space but the graph of per-flow load-balanced Internet routes. Classical MDA discovers all per-flow load-balanced paths by varying the packet flow identifier, using predetermined stopping points $s \times s$8, node control, and backward connectivity checks. MDA-Lite reduces overhead by assuming and testing that load balancing is uniform across interfaces and that diamonds are unmeshed. It adopts hop-by-hop rather than vertex-by-vertex probing, a light meshing test with parameter $s \times s$9, and a width-asymmetry test; if those assumptions fail, it switches to full MDA. For a hop with $s=8$0 equal-probability successors, the failure model remains

$s=8$1

and MDA-Lite uses the same stopping points as MDA. On canonical diamonds, it completes $s=8$2 discovery with approximately $s=8$3 fewer probes in uniform unmeshed cases. Over about $s=8$4 Internet measurements, MDA-Lite with $s=8$5 or $s=8$6 uses $s=8$7–$s=8$8 fewer packets in $s=8$9 of runs. Aggregate ratios relative to the first MDA run are reported as $M \in \{0,1\}^{1 \times H \times W}$00 vertices, $M \in \{0,1\}^{1 \times H \times W}$01 edges, and $M \in \{0,1\}^{1 \times H \times W}$02 packets for MDA-Lite $M \in \{0,1\}^{1 \times H \times W}$03, compared with $M \in \{0,1\}^{1 \times H \times W}$04 vertices, $M \in \{0,1\}^{1 \times H \times W}$05 edges, and $M \in \{0,1\}^{1 \times H \times W}$06 packets for single-flow-ID probing (Vermeulen et al., 2018).

These two mechanisms are analogous only at an abstract level. Both scan a combinatorial branching structure under a probing budget, but one scans beam overlap patterns in angular space and the other scans successor relationships in network hops. A plausible implication is that multi-path scanning often becomes a question of adaptive experiment design over a discrete hypothesis space rather than motion through Euclidean space.

6. Alternating topological and geometric path optimization in outdoor robotic scanning

"Autonomous Outdoor Scanning via Online Topological and Geometric Path Optimization" (Huang et al., 2020) formulates outdoor 3D acquisition as an energy-efficient discrete-continuous optimization of robot scanning paths. The robot carries a $M \in \{0,1\}^{1 \times H \times W}$07 LiDAR and maintains a point set $M \in \{0,1\}^{1 \times H \times W}$08, current pose $M \in \{0,1\}^{1 \times H \times W}$09, and an energy budget. The objective is to maximize new surface coverage while minimizing travel cost. Around the current pose, the method computes a guidance field over ground points using distance-based explorability,

$M \in \{0,1\}^{1 \times H \times W}$10

medial-axis-based explorability,

$M \in \{0,1\}^{1 \times H \times W}$11

and a smoothed observability-to-unknown term, combined as

$M \in \{0,1\}^{1 \times H \times W}$12

Local maxima of $M \in \{0,1\}^{1 \times H \times W}$13 define visit sites $M \in \{0,1\}^{1 \times H \times W}$14, and each site receives reward $M \in \{0,1\}^{1 \times H \times W}$15.

The discrete stage builds a complete graph over active sites and solves an Online TSP with per-edge cost–reward

$M \in \{0,1\}^{1 \times H \times W}$16

subject to the usual TSP constraints and the energy constraint

$M \in \{0,1\}^{1 \times H \times W}$17

The continuous stage refines the traverse path between consecutive sites by fitting a third-order B-spline,

$M \in \{0,1\}^{1 \times H \times W}$18

and maximizing the information gain

$M \in \{0,1\}^{1 \times H \times W}$19

where $M \in \{0,1\}^{1 \times H \times W}$20 is derived from local box-counting dimension. The algorithm alternates scan acquisition, site regeneration, active-set maintenance, Online TSP solution, B-spline refinement, and robot motion until the next planned tour would exceed the remaining battery capacity.

The reported evaluation covers $M \in \{0,1\}^{1 \times H \times W}$21 large synthetic scenes and $M \in \{0,1\}^{1 \times H \times W}$22 real-world outdoor areas of $M \in \{0,1\}^{1 \times H \times W}$23–$M \in \{0,1\}^{1 \times H \times W}$24. The method reaches $M \in \{0,1\}^{1 \times H \times W}$25 IoU coverage in approximately $M \in \{0,1\}^{1 \times H \times W}$26, whereas greedy frontier and random walk reach $M \in \{0,1\}^{1 \times H \times W}$27–$M \in \{0,1\}^{1 \times H \times W}$28 in the same time. Final travel distances are $M \in \{0,1\}^{1 \times H \times W}$29–$M \in \{0,1\}^{1 \times H \times W}$30, total scan times are $M \in \{0,1\}^{1 \times H \times W}$31–$M \in \{0,1\}^{1 \times H \times W}$32, travel is $M \in \{0,1\}^{1 \times H \times W}$33–$M \in \{0,1\}^{1 \times H \times W}$34 shorter than alternatives, integrated curvature is reduced by approximately $M \in \{0,1\}^{1 \times H \times W}$35, and the topological map update, TSP solve, fractal-dimension calculation, and path refinement run in real time on a laptop CPU (Huang et al., 2020).

Within this formulation, multi-path scanning appears at the platform level: the robot maintains multiple candidate visit paths, dynamically revises their rewards, and alternates topological selection with geometric refinement. This suggests that in large unbounded environments, a multi-path scanning mechanism is less about a fixed pattern than about preserving optionality among competing future traverses while respecting an explicit energy budget.