Temporal Texture Alignment (TTA)

Updated 11 July 2026

Temporal Texture Alignment is a framework that realigns evolving high-frequency textures in videos and time-series by correcting temporal mismatches and preserving detail.
Key methods include dynamic programming, variational DTW formulations, and learned diffeomorphic warping that handle both geometric and feature-space misalignments.
Empirical results demonstrate enhanced inter-frame stability in super-resolution and restoration tasks, with improved metrics and reduced texture flicker.

Temporal Texture Alignment (TTA) denotes the problem of bringing temporally evolving structure into correspondence when the same underlying content appears at different rates, under different feature transforms, or with motion-induced instability. In the sources considered here, the term is used explicitly in EvTexture++ for “precise inter-frame texture alignment” in video super-resolution (Kai et al., 11 Jun 2026). The broader literature suggests a wider technical category that includes reparameterization-invariant synchronization of time-parameterized motions (Tumpach et al., 2023), joint optimization of monotone temporal warping and global feature-space transforms (Vayer et al., 2020), learned diffeomorphic alignment and averaging of misaligned time series (Weber et al., 10 Feb 2025), iterative long-range frame alignment and texture-consistent aggregation for restoration (Zhou et al., 2021), temporally localized transition-texture representations (Leznik, 9 Mar 2026), and visually aligned temporal conditioning for text-to-audio generation (Mo et al., 2023). At the same time, the acronym is not stable across the literature: in “Test-time Correlation Alignment,” TTA denotes Test-Time Adaptation rather than Temporal Texture Alignment (You et al., 1 May 2025).

1. Scope and conceptual boundaries

The collected literature suggests that TTA is best understood as a family of alignment problems rather than a single standardized algorithm. One regime treats temporal mismatch as a nuisance reparameterization of a signal or curve. Another treats it as a correspondence problem between neighboring frames or propagated features, where alignment quality determines whether high-frequency texture is preserved or flickers over time. A third regime treats TTA as a representational problem: the goal is to construct features or images whose local temporal texture is sufficiently explicit that downstream matching or synchronization becomes feasible (Tumpach et al., 2023, Zhou et al., 2021, Leznik, 9 Mar 2026).

Within this spectrum, the strongest explicit use of the phrase occurs in event-driven video super-resolution. There, TTA is introduced because “large motions could degrade inter-frame temporal consistency, particularly in texture regions, leading to texture flickering,” and the purpose of the module is to estimate “event-guided texture-aware flow for precise inter-frame texture alignment” (Kai et al., 11 Jun 2026). This is narrower than generic motion alignment: the target is not merely geometric correspondence, but temporal stability of dense high-frequency detail.

A broader reading extends the same logic to any time-indexed feature sequence for which “same content, different rate” is a valid model. In that sense, TTA can include skeleton trajectories, multivariate time series, texture descriptors, pose embeddings, dynamic textures, or latent audiovisual features, provided temporal variability is primarily monotone and content-preserving (Tumpach et al., 2023, Vayer et al., 2020, Weber et al., 10 Feb 2025). This suggests that temporal texture is not restricted to literal image texture; it can also denote the structured evolution of features over time.

2. Geometric and variational formulations

A central mathematical formulation models an observed motion as a curve

$M:[0,1]\to \mathbb{R}^{3N},$

with temporal misalignment represented by an orientation-preserving diffeomorphism

$\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$

drawn from

$\operatorname{Diff}^{+}([0,1]).$

The group acts by reparameterization,

$\varphi\cdot f := f\circ \varphi,$

and the key claim is that reasonable alignment properties—reflexivity, symmetry, reparameterization inversion, $\operatorname{Diff}^{+}([0,1])$ -equivariance, and transitivity—imply a geometric structure in which the set of motions aligned to a template forms a slice to a principal fiber bundle for temporal reparameterizations (Tumpach et al., 2023). In this view, temporal alignment is not merely frame matching; it is a reparameterization-invariant projection onto a canonical representative of each orbit.

A related but more general variational formulation is DTW with global invariances. For time series $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ and $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ , the method defines

$\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$

or, in matrix form,

$\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$

Here temporal variability is modeled by an admissible monotone DTW path $\pi$ , while appearance variability is modeled by a latent global transform $\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 0 from a prescribed family $\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 1. The differentiable variant replaces the hard minimum over paths by softDTW (Vayer et al., 2020). This formulation is especially important for TTA because it makes explicit that temporal alignment and feature-space alignment can be inseparable: a poor feature transform corrupts the temporal path, and a poor temporal path corrupts estimation of the feature transform.

A third formulation is fully learned and diffeomorphic. DTAN assumes that each observed signal $\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 2 is a temporally warped version of an aligned latent signal $\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 3,

$\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 4

or equivalently,

$\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 5

with $\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 6. Joint alignment and averaging are posed as

$\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 7

The warp family is CPAB-based, hence monotonic, invertible, and diffeomorphic, and the paper introduces ICAE as a regularization-free alternative to explicit warp penalties (Weber et al., 10 Feb 2025). Across these formulations, the shared principle is that TTA is fundamentally a problem of quotienting out nuisance time parameterization while preserving structure that should remain aligned.

3. Algorithmic mechanisms

Classical dynamic programming remains one of the dominant algorithmic mechanisms. For two sequences of lengths $\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 8 and $\varphi:[0,1]\to[0,1], \qquad \varphi(0)=0,\ \varphi(1)=1,$ 9, one computes a local matching cost $\operatorname{Diff}^{+}([0,1]).$ 0 and then solves a monotone path problem with recurrence

$\operatorname{Diff}^{+}([0,1]).$ 1

with computational complexity $\operatorname{Diff}^{+}([0,1]).$ 2 (Tumpach et al., 2023). In the human-motion setting, this machinery is instantiated with several feature spaces: SRVT on trajectories of joints in $\operatorname{Diff}^{+}([0,1]).$ 3, Gram-matrix trajectories in the manifold of PSD matrices, curves on $\operatorname{Diff}^{+}([0,1]).$ 4, and curves on $\operatorname{Diff}^{+}([0,1]).$ 5. A major practical critique is that many such features are invariant to the full Euclidean group $\operatorname{Diff}^{+}([0,1]).$ 6, whereas the task may only warrant invariance closer to $\operatorname{Diff}^{+}([0,1]).$ 7; full invariance can remove vertical cues that are crucial for phase estimation (Tumpach et al., 2023).

That critique motivates anchored dynamic programming. The method detects exactly three keyframes on the racket arm—“the first frame with the highest $\operatorname{Diff}^{+}([0,1]).$ 8-coordinate,” “the first frame with the lowest $\operatorname{Diff}^{+}([0,1]).$ 9-coordinate,” and “the second frame with the highest $\varphi\cdot f := f\circ \varphi,$ 0-coordinate”—and forces the optimal warping path to pass through the corresponding anchor nodes, with a tolerance region around each node (Tumpach et al., 2023). The result is both more constrained and more efficient: admissible paths are pruned to those consistent with coarse stroke structure.

In restoration, the dominant mechanism is not DTW but iterative feature-space alignment with learned motion fields and deformable sampling. IAM decomposes a long-range alignment $\varphi\cdot f := f\circ \varphi,$ 1 into shared short-range sub-alignments

$\varphi\cdot f := f\circ \varphi,$ 2

and repeatedly refines the shared motion fields $\varphi\cdot f := f\circ \varphi,$ 3 instead of estimating them once. Aligned features are produced through deformable convolution,

$\varphi\cdot f := f\circ \varphi,$ 4

ARW then reweights aligned content according to both local reference similarity and inter-frame consistency, yielding

$\varphi\cdot f := f\circ \varphi,$ 5

after patchwise similarity weighting and consistency weighting relative to the aligned-frame average (Zhou et al., 2021). For TTA, the important point is that alignment and aggregation are separated: better correspondence is necessary, but residual uncertainty must still be downweighted.

EvTexture++ introduces an explicitly named Temporal Texture Alignment module inside a motion branch. It is a dual-stream MEMC design. The event stream estimates

$\varphi\cdot f := f\circ \varphi,$ 6

where $\varphi\cdot f := f\circ \varphi,$ 7 is a voxel grid built from temporally reversed events, $\varphi\cdot f := f\circ \varphi,$ 8 is a U-Net, and $\varphi\cdot f := f\circ \varphi,$ 9 bins are used in voxelization. In parallel, the RGB stream estimates

$\operatorname{Diff}^{+}([0,1])$ 0

with $\operatorname{Diff}^{+}([0,1])$ 1 instantiated as SpyNet. The two aligned features are fused by

$\operatorname{Diff}^{+}([0,1])$ 2

This design is texture-oriented rather than merely geometry-oriented: the event flow is described as preserving “sharper motion boundaries and richer textural details” than the smoother RGB flow (Kai et al., 11 Jun 2026).

Not all TTA-relevant work performs alignment directly. Some papers construct representations that make local temporal texture more explicit. TMTF is the clearest example. After quantizing a time series into $\operatorname{Diff}^{+}([0,1])$ 3 states $\operatorname{Diff}^{+}([0,1])$ 4, partitioning time into $\operatorname{Diff}^{+}([0,1])$ 5 contiguous chunks $\operatorname{Diff}^{+}([0,1])$ 6, and estimating a local transition matrix $\operatorname{Diff}^{+}([0,1])$ 7 in each chunk, the representation is defined by

$\operatorname{Diff}^{+}([0,1])$ 8

Because the matrix depends on $\operatorname{Diff}^{+}([0,1])$ 9 only through the row index, the resulting $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 0 image contains $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 1 horizontal bands whose textures encode chunk-local transition dynamics (Leznik, 9 Mar 2026). The paper states that TMTF is order-preserving in time and amplitude-agnostic, and that it degrades exactly to the standard MTF when

$\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 2

For TTA, this matters because it turns local dynamical regimes—persistence, mean reversion, upward trend, near-uniform randomness—into visually organized texture bands that can be matched downstream.

DiffAVA addresses a different setting: text-to-audio generation with visual alignment. Its core intervention is to replace the raw text condition in AudioLDM with a visually aligned text embedding. For each clip, audio $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 3, visual frames $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 4, and text prompt $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 5 are given; video features $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 6 are extracted by frozen X-CLIP, aggregated by a temporal transformer of depth $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 7, hidden dimension $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 8, and $\mathbf{x}\in\mathbb{R}^{T_x\times p_x}$ 9 attention heads, fused with CLAP text features $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 0 by a dual multi-modal residual network, and then used to condition a frozen latent diffusion model (Mo et al., 2023). The alignment is partly explicit, because the contrastive loss sums over temporal locations $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 1, but it remains largely implicit at generation time because the final condition is a compressed visual-aligned text embedding rather than direct per-time control. This places the method at the coarse-to-mid-level end of TTA: it improves temporal cross-modal consistency, but it does not establish precise event-level synchronization.

These representational and conditioning approaches emphasize that TTA need not always be solved by direct path optimization. An alternative is to build a signal space in which temporal texture is already localized, aligned conditioning is easier to learn, or local dynamics are separable enough for downstream matching.

5. Empirical evidence

The empirical record is heterogeneous because the literature spans motion alignment, restoration, event-driven super-resolution, and generic time-series alignment. Even so, several results recur: coarse anchors can make DTW-like alignment both more accurate and faster; iterative refinement and post-alignment weighting improve temporal detail preservation; and explicit texture-aware motion alignment reduces flicker in texture-rich videos.

Setting	Representative result	Source
Anchored dynamic programming	SRVT in $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 2: $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 3, 23s 227ms $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 4 $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 5, 7s 692ms; Moving Frames: $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 6, 23s 771ms $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 7 $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 8, 8s 184ms	(Tumpach et al., 2023)
IAM and ARW ablation	Baseline $\mathbf{y}\in\mathbb{R}^{T_y\times p_y}$ 9 +IAM+ $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 0: SR $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 1, Deblur $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 2, Denoise $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 3	(Zhou et al., 2021)
Motion-branch contribution in EvTexture++	Vid4 $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 4; REDS4 $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 5	(Kai et al., 11 Jun 2026)
Temporal consistency in EvTexture++	Vid4: TCC $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 6, tOF $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 7; REDS4: TCC $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 8, tOF $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \sum_{(i,j)\in\pi} d(\mathbf{x}_i, f(\mathbf{y}_j)),$ 9	(Kai et al., 11 Jun 2026)

In the geometric human-motion setting, the benchmark is unusually principled: a known reparameterization $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 0 is synthetically applied to a reference motion, and the alignment procedure is evaluated by whether it recovers $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 1. The mean $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 2-error over 7 experiments with frame counts between 50 and 185 then gives an exact synchronization measure rather than a subjective notion of visual plausibility (Tumpach et al., 2023). This evaluation philosophy is widely transferable.

In video restoration, the gains are most pronounced when motion corruption is severe. The paper reports that adding IAM yields $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 3 dB in video super-resolution, $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 4 dB in deblurring, and $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 5 dB in denoising over baseline, while adding ARW further improves those results to $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 6 dB, $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 7 dB, and $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 8 dB over baseline respectively (Zhou et al., 2021). The reported runtime on $\text{DTW-GI}(\mathbf{x}, \mathbf{y}) = \min_{f \in \mathcal{F},\; \pi \in \mathcal{A}(\mathbf{x}, \mathbf{y})} \left\langle \mathbf{W}_\pi, C(\mathbf{x}, f(\mathbf{y})) \right\rangle.$ 9 inputs rises only from 153 ms for the baseline to 170 ms for the full model.

For learned diffeomorphic alignment, the strongest evidence is breadth rather than one benchmark number. DTAN is evaluated on 128 UCR datasets, including 11 variable-length datasets, and the paper reports that ICAE-based variants outperform regularization-based alternatives while also enabling PCA on misaligned series. On the Trace dataset, the first principal component after alignment explains $\pi$ 0 of variance, whereas the first three principal components of the original data explain only $\pi$ 1 (Weber et al., 10 Feb 2025). This shows that removing temporal misalignment can substantially change the geometry of the resulting data manifold.

6. Limitations, misconceptions, and adjacent meanings

The literature makes clear that TTA is not a universal solution class. Most formulations assume monotone correspondence. In the geometric human-motion setting, the assumption is that the motions depict the same action and differ mainly by local accelerations and decelerations; the paper notes that this may fail when there are missing subactions, different topology of behavior, severe occlusions, or non-monotone temporal correspondences (Tumpach et al., 2023). DTW-GI is similarly strongest when feature differences are explained by a single global transform $\pi$ 2 and temporal differences by a monotone path $\pi$ 3; it is not designed for local time-varying appearance transforms or non-monotone event reordering (Vayer et al., 2020). DTAN inherits the same monotonicity bias through diffeomorphic CPAB warps (Weber et al., 10 Feb 2025).

Domain specificity is another recurrent constraint. The anchored-DP strategy in tennis is built around arm-elevation extrema and therefore does not transfer literally beyond that setting (Tumpach et al., 2023). TMTF is highly relevant to TTA as a representation, but it is not itself an alignment algorithm: it exposes temporally localized transition textures, yet it does not compute correspondences or warping paths (Leznik, 9 Mar 2026). DiffAVA improves coarse temporal consistency, but the paper does not provide direct synchronization metrics, exact temporal tokenization details, or an explicit event-level control interface into the diffusion model (Mo et al., 2023). EvTexture++ addresses inter-frame temporal consistency in texture regions, but the paper also states that the overall system assumes precise spatial alignment and identical resolution between event and RGB inputs, an assumption that may not hold in many practical camera setups (Kai et al., 11 Jun 2026).

A further misconception concerns nomenclature. The acronym TTA is overloaded. In “Test-time Correlation Alignment,” TTA means Test-Time Adaptation, and the method is a source-free second-order statistical alignment procedure that matches feature means and covariances through a linear transform rather than a temporal alignment method (You et al., 1 May 2025). This does not make the work irrelevant, but it places it outside the core meaning of Temporal Texture Alignment.

Taken together, these limitations suggest that TTA is most coherent when treated as a problem class centered on temporally structured correspondence under nuisance timing or motion variation. Within that class, the literature supports several distinct but compatible principles: model temporal mismatch as reparameterization, avoid invariances that erase phase cues, refine long-range correspondences rather than freezing them, separate alignment from aggregation reliability, and preserve localized temporal texture in the representation used for downstream matching.