Spatial Orthogonal Refinement (SOR)

• Spatial Orthogonal Refinement (SOR) is an overloaded term with domain-specific definitions that emphasize using orthogonal strategies to refine spatial features.
• In RGB-event tracking, SOR employs directional filters guided by local motion orientations to refine degraded RGB features with event-derived geometric anchors.
• In optics and computational geometry, SOR refines spatial fields by superposing orthogonal modes or adding grid planes to concentrate power or enable nonoverlapping unfoldings.

Searching arXiv for papers using the phrase “Spatial Orthogonal Refinement” and related usages. Spatial Orthogonal Refinement (SOR) is an overloaded term with distinct meanings across research domains. In contemporary computer vision, it denotes a modality-refinement mechanism for RGB-event visual object tracking in which orthogonal directional filters, guided by local motion orientations, extract motion-consistent structural responses from event streams and use them as geometric anchors to rectify degraded RGB features (Huang et al., 29 Mar 2026). In optical beam synthesis, the term has been used to frame a procedure for refining a beam’s spatial structure by coherently superposing orthogonal spatial modes with complex weights so as to concentrate power within a target region while controlling sidelobes (Xie et al., 2016). In computational geometry, it refers to the insertion of additional axis-aligned coordinate planes between the base grid planes of an orthogonal polyhedron, providing enough disjoint lanes to route a nonoverlapping unfolding path with only polynomially many orthogonal cuts (Damian et al., 2011). By contrast, in numerical linear algebra the acronym SOR almost universally denotes the Successive Over-Relaxation method rather than “Spatial Orthogonal Refinement,” a distinction explicitly noted in work on parallel SOR/ILU preconditioners for structured grids (Tavakoli, 2010).

1. Terminological scope and disciplinary usage

The term has no single canonical definition across arXiv literature. The most explicit contemporary use appears in “Spatial Orthogonal Refinement for Robust RGB-Event Visual Object Tracking,” where SOR is presented as the central module of SOR-Track for robust RGB-Event tracking under high-speed motion, motion blur, and low light (Huang et al., 29 Mar 2026). A separate optical usage frames the coherent superposition of orthogonal spatial modes with complex coefficients as Spatial Orthogonal Refinement, emphasizing localized power concentration and spatial shape control (Xie et al., 2016). A third usage appears in the description of the Delta-Unfolding algorithm for orthogonal polyhedra, where SOR denotes the quadratic insertion of additional coordinate planes between consecutive base planes (Damian et al., 2011).

This plurality of meanings is important because the acronym “SOR” is dominated in numerical analysis by Successive Over-Relaxation. That usage governs classical iterative schemes for solving sparse linear systems and preconditioning structured-grid problems (Tavakoli, 2010). Related analyses of random reordering in SOR-type methods, optimal relaxation parameters for Poisson problems, and adaptive relaxation control all preserve that numerical-linear-algebra meaning (Oswald et al., 2015, Darian, 17 Jan 2025, Miyatake et al., 2018). This suggests that “Spatial Orthogonal Refinement” should be interpreted as domain-specific nomenclature rather than a generally standardized acronym.

2. RGB-event tracking interpretation

In RGB-event visual object tracking, SOR is a refinement mechanism rather than a generic fusion operator. SOR-Track takes synchronized RGB frames and event representations accumulated over the exposure-matched time window $\Delta T$, extracts modality-specific features with a granular stem and a ViT backbone, and inserts the SOR module in the multimodal fusion stage to refine RGB features using event-derived directional anchors before classification and box regression (Huang et al., 29 Mar 2026).

The motivating premise is that conventional RGB cameras integrate light over finite exposure time, so fast motion produces blur that turns directional edges into low-pass, largely isotropic textures, while event cameras preserve high-frequency, anisotropic edge patterns aligned with motion and offer microsecond temporal resolution and high dynamic range greater than $120$ dB (Huang et al., 29 Mar 2026). SOR addresses the resulting structural discrepancy by explicitly leveraging directional geometric priors in event streams, rather than treating events as dense intensity-like inputs for black-box fusion.

At the module level, SOR estimates local motion orientations from event information, forms steerable orthogonal directional filters aligned to $\theta(x,y)$ and $\theta(x,y)+\pi/2$, computes directional responses, and uses those responses to asymmetrically modulate RGB features (Huang et al., 29 Mar 2026). The event accumulation and orientation-estimation pipeline is specified through the discrete event image

$$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$

the structure tensor

$$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$

and the orientation/confidence fields

$$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$

The steerable Gabor-like kernel is given by

$$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$

with orthogonal responses $R_{\parallel}=A*F(\cdot;\theta)$ and $R_{\perp}=A*F(\cdot;\theta+\pi/2)$ (Huang et al., 29 Mar 2026).

The asymmetric modulation step is central. The paper’s implementation defines

$120$0

so events modulate RGB but not vice versa (Huang et al., 29 Mar 2026). The stated rationale is that events provide physically reliable structural anchors under blur and HDR, whereas allowing RGB to modulate events could re-inject blur or noise. This makes SOR a one-way, geometry-aware correction mechanism.

The reported experimental setting uses the FE108 benchmark, a ViT backbone with MAE initialization, patch size $120$1, $120$2 orientations, template and search crops of $120$3 and $120$4, AdamW with weight decay $120$5, $120$6 epochs, batch size $120$7 on $120$8RTX 4090, learning rate $120$9 with backbone rate scaled by $\theta(x,y)$0, and step decay by $\theta(x,y)$1 at epoch $\theta(x,y)$2 (Huang et al., 29 Mar 2026). On FE108, SOR-Track is reported to improve over CEUTrack from AUC $\theta(x,y)$3, PR $\theta(x,y)$4, OP50 $\theta(x,y)$5, and OP75 $\theta(x,y)$6 to AUC $\theta(x,y)$7, PR $\theta(x,y)$8, OP50 $\theta(x,y)$9, and OP75 $\theta(x,y)+\pi/2$0, with the OP75 gain of $\theta(x,y)+\pi/2$1 emphasized as tighter-box improvement under blur and HDR (Huang et al., 29 Mar 2026).

Ablations further identify the granular stem as important. Replacing it with standard strided convolutions reduced performance from AUC $\theta(x,y)+\pi/2$2, PR $\theta(x,y)+\pi/2$3, NPR $\theta(x,y)+\pi/2$4, OP50 $\theta(x,y)+\pi/2$5, and OP75 $\theta(x,y)+\pi/2$6 to AUC $\theta(x,y)+\pi/2$7, PR $\theta(x,y)+\pi/2$8, NPR $\theta(x,y)+\pi/2$9, OP50 $$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$0, and OP75 $$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$1 (Huang et al., 29 Mar 2026). The paper interprets this as evidence that aggressive downsampling erases sparse event spikes and thin edges required for geometry-aware refinement. A plausible implication is that, in this formulation, SOR depends as much on preserving fine-scale event structure as on the orthogonality of the filters themselves.

3. Optical beam-structuring interpretation

In beam synthesis, Spatial Orthogonal Refinement denotes the refinement of a transverse optical field by combining orthogonal spatial basis functions with complex coefficients (Xie et al., 2016). The field is expanded as

$$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$2

with orthonormality

$$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$3

total power

$$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$4

and intensity $$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$5 (Xie et al., 2016).

The paper uses orbital angular momentum modes, i.e. Laguerre-Gaussian modes with radial index $$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$6, as the orthogonal basis. The general Laguerre-Gaussian mode is written as

$$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$7

and the OAM subset $$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$8 is orthogonal in $$A(x, y) = \sum_{i: t_i \in \Delta T} 1[x_i = x, y_i = y] \alpha(p_i),$$9 (Xie et al., 2016). The stated objective is to concentrate power within a target region $$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$0 while respecting total power and, where needed, sidelobe constraints:

$$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$1

where

$$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$2

For amplitude-and-phase control, maximizing $$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$3 subject to $$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$4 yields the principal eigenvector of $$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$5; for phase-only control, projected gradient ascent on the $$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$6-torus is proposed (Xie et al., 2016).

The mechanism is explicitly interference-based. At a point $$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$7,

$$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$8

and for fixed total power $$J(x, y) = \begin{bmatrix} \langle I_x^2\rangle & \langle I_x I_y\rangle \ \langle I_x I_y\rangle & \langle I_y^2\rangle \end{bmatrix},$$9, Cauchy-Schwarz gives

$$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$0

As more modes are included, the bound can increase, enabling higher localized intensity when phases are aligned (Xie et al., 2016). The paper emphasizes the corresponding trade-offs: improving concentration in $$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$1 generally raises sidelobes in $$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$2; larger mode sets increase control authority but also increase sensitivity to phase errors, modal cross-talk, and alignment; and higher $$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$3 diverges more rapidly during propagation (Xie et al., 2016).

Two realizations are described. The first is coherent combining of multiple OAM beams,

$$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$4

with orthogonal OAM modes as the constituent fields (Xie et al., 2016). The second is single-beam composite-mask encoding on a spatial light modulator, either via an off-axis hologram

$$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$5

with first-order pinhole filtering, or via double-phase encoding (Xie et al., 2016).

The quantitative results reported in the paper are specific. Localized power density gain (LPDG) is defined as

$$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$6

In simulation, using equal output size outperformed equal waist, and at a $$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$7 m link more than $$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$8 LPDG was achieved with $$\theta(x, y) = \frac{1}{2}\arctan\!\left(\frac{2\langle I_x I_y\rangle}{\langle I_x^2\rangle - \langle I_y^2\rangle + \epsilon}\right), \qquad c(x, y)=\frac{\lambda_{\max}-\lambda_{\min}}{\lambda_{\max}+\lambda_{\min}+\epsilon}.$$9 OAM modes (Xie et al., 2016). With OAM orders $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$0 to $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$1, a single-beam phase error of approximately $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$2 reduced LPDG from approximately $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$3 to approximately $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$4, while extinguishing one mode reduced it from approximately $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$5 to approximately $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$6 (Xie et al., 2016). In the single-beam SLM experiment with $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$7 OAM functions, aperture $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$8 mm, and distance $$F(x, y; \theta)=\exp\!\left(-\frac{x_\theta^2+\gamma^2 y_\theta^2}{2\sigma^2}\right)\cos\!\left(\frac{2\pi x_\theta}{\lambda}+\psi\right),$$9 m, the measured gain was approximately $R_{\parallel}=A*F(\cdot;\theta)$0 versus approximately $R_{\parallel}=A*F(\cdot;\theta)$1 in simulation (Xie et al., 2016).

This usage of SOR differs sharply from the RGB-event tracking formulation. The commonality is the exploitation of orthogonal structure and directional control, but the optimization targets, physical signals, and operators are entirely different. This suggests that “Spatial Orthogonal Refinement” functions more as a descriptive label than as a trans-domain formalism.

4. Orthogonal-polyhedra unfolding interpretation

In computational geometry, SOR is not a signal-processing or feature-modulation mechanism. It denotes the insertion of additional axis-aligned coordinate planes between the base coordinate planes through the vertices of an orthogonal polyhedron, thereby creating sufficient routing capacity for a nonoverlapping unfolding (Damian et al., 2011).

The setting is an orthogonal polyhedron $R_{\parallel}=A*F(\cdot;\theta)$2 homeomorphic to a sphere with $R_{\parallel}=A*F(\cdot;\theta)$3 vertices. Let $R_{\parallel}=A*F(\cdot;\theta)$4 be the union of all axis-aligned coordinate planes passing through at least one vertex, decomposed as $R_{\parallel}=A*F(\cdot;\theta)$5, $R_{\parallel}=A*F(\cdot;\theta)$6, and $R_{\parallel}=A*F(\cdot;\theta)$7 (Damian et al., 2011). Spatial Orthogonal Refinement supplements this base grid by inserting $R_{\parallel}=A*F(\cdot;\theta)$8 additional planes between every two consecutive planes of $R_{\parallel}=A*F(\cdot;\theta)$9 on each axis. If $R_{\perp}=A*F(\cdot;\theta+\pi/2)$0, then along axis $R_{\perp}=A*F(\cdot;\theta+\pi/2)$1 the refined set satisfies

$R_{\perp}=A*F(\cdot;\theta+\pi/2)$2

and summing over axes yields

$R_{\perp}=A*F(\cdot;\theta+\pi/2)$3

in the worst case (Damian et al., 2011).

The algorithmic context is the Delta-Unfolding algorithm. The polyhedron is sliced by $R_{\perp}=A*F(\cdot;\theta+\pi/2)$4-perpendicular planes through vertex $R_{\perp}=A*F(\cdot;\theta+\pi/2)$5-coordinates into slabs; slab side faces form bands; bands are connected by $R_{\perp}=A*F(\cdot;\theta+\pi/2)$6-beams; and these relations define an unfolding tree $R_{\perp}=A*F(\cdot;\theta+\pi/2)$7 (Damian et al., 2011). A thin spiral path $R_{\perp}=A*F(\cdot;\theta+\pi/2)$8 traverses a band, recursively diverting through children and returning without self-crossing. The central combinatorial idea is heavy-light decomposition on $R_{\perp}=A*F(\cdot;\theta+\pi/2)$9, with the rule “visit the heavy child last” (Damian et al., 2011). That rule suppresses repeated traversals of large subtrees.

The refinement is needed because the spiral induces many mutually parallel surface tracks. The paper proves that if $120$00 bounds the number of $120$01-induced segments on a top face in the subtree rooted at band $120$02, then

$120$03

from which $120$04 follows by induction (Damian et al., 2011). A perfect binary tree yields the tight example

$120$05

showing that the quadratic per-face bound is tight (Damian et al., 2011). The purpose of SOR is precisely to supply $120$06 disjoint tracks per gap so that these routes can be realized as orthogonal cut edges on the refined grid.

The main theorem states that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap using only polynomially many orthogonal cuts, specifically by cutting along the base grid together with $120$07 new planes between every consecutive pair of base planes on each axis (Damian et al., 2011). This improves on prior epsilon-unfolding, which required exponential refinement $120$08 per gap in the worst case (Damian et al., 2011). Here again, the term “Spatial Orthogonal Refinement” refers to a geometric construction rather than a general orthogonality principle in function space or feature space.

5. Contrast with Successive Over-Relaxation and related SOR literature

A recurring source of ambiguity is that SOR already has a dominant technical meaning in numerical linear algebra: Successive Over-Relaxation (Tavakoli, 2010). The standard iteration for a splitting $120$09 is

$120$10

with $120$11 reducing to Gauss-Seidel (Tavakoli, 2010). The term “Spatial Orthogonal Refinement” is therefore nonstandard in this literature.

This distinction matters because several arXiv papers develop sophisticated SOR theory while using the conventional meaning. Parallel structured-grid sweeping methods preserve the convergence behavior of sequential SOR/ILU through overlapping domain decomposition, multi-frontal sweeping, and small interface solves (Tavakoli, 2010). Randomized reordering improves asymptotic convergence bounds for SOR-type methods on Hermitian positive semidefinite systems by controlling triangular truncation under permutations (Oswald et al., 2015). For the Poisson equation on rectangular grids with unequal mesh sizes and mixed boundary conditions, explicit optimal-relaxation formulas are derived for point and line SOR, with the canonical relation

$120$12

appearing for several discretizations (Darian, 17 Jan 2025). Adaptive SOR methods based on the Wolfe conditions reinterpret $120$13 as a step size under the change of variables

$120$14

and update it without extra matrix-vector products (Miyatake et al., 2018).

The explicit clarification in the structured-grid parallelization paper is therefore significant: if one encounters “Spatial Orthogonal Refinement (SOR),” it should not be assumed to belong to the established numerical-linear-algebra SOR lineage (Tavakoli, 2010). A plausible implication is that any cross-domain reading of “SOR” requires immediate disambiguation by context.

6. Common structural themes and limits of unification

Despite their disciplinary separation, the three “Spatial Orthogonal Refinement” usages share a narrow structural resemblance. Each introduces additional orthogonal degrees of freedom to improve a spatial objective. In RGB-event tracking, orthogonal directional filters aligned with $120$15 and $120$16 expose motion-consistent event structure and refine RGB features (Huang et al., 29 Mar 2026). In optics, orthogonal spatial modes with complex weights enlarge the feasible interference pattern and allow constructive concentration within a target region (Xie et al., 2016). In orthogonal-polyhedra unfolding, additional orthogonal grid planes create enough independent routing tracks to realize a nonoverlapping strip decomposition (Damian et al., 2011).

Beyond that resemblance, the meanings diverge sharply. The computer-vision formulation is a learned multimodal refinement module with grouped dynamic convolution, GroupNorm, residual gating, and standard tracking losses

$120$17

(Huang et al., 29 Mar 2026). The optical formulation is a constrained quadratic optimization over complex modal coefficients, optionally using principal-eigenvector or projected-gradient methods (Xie et al., 2016). The geometric formulation is a combinatorial routing and refinement scheme governed by heavy-light decomposition and asymptotic track-count bounds (Damian et al., 2011).

Accordingly, any attempt to treat SOR as a unified theory would be inferential rather than textual. This suggests that the phrase currently functions as a context-sensitive label applied to domain-specific mechanisms that happen to rely on orthogonality and spatial refinement, rather than as a single mature concept with shared formal foundations across fields.