Where Orientation Canonicalization Sits

Orientation canonicalization is a stage inside the multi-axis variance vector extraction pipeline that derives a digital artifact's unique identifier. It is not a standalone identity layer and it does not emit a canonical form of the content. Its purpose is narrow: to present the artifact's gradient orientation structure in a consistent rotational frame before the rest of the pipeline reads it, so that the resulting variance vector and unique identifier drift less under the minor rotational variation introduced by format conversion and resolution change.

The stage appears in two places in the disclosure. First, it canonicalizes the gradient orientation histogram that supplies the Z-axis of the nine-dimensional variance vector. Second, in the quadrant decomposition pipeline, an orientation canonicalization module conditionally rotates the whole normalized image before the four spatial quadrants are extracted. Both operate over gradient orientation and both feed downstream hashing rather than replacing it.

The Gradient Orientation Histogram

The Z-axis structural phase persistence vector encodes orientation and structural stability. The gradient histogram module computes a histogram of gradient magnitudes across eight angular bins spanning zero to pi radians, aggregated over all interior pixels of the normalized scalar field. Each bin accumulates the gradient magnitude associated with edges falling in that angular range, so the histogram describes how the artifact's edge energy is distributed across orientations.

The orientation canonicalization stage then rotates the histogram so that the dominant angular bin is positioned at index zero, producing a rotation-invariant representation of the artifact's edge orientation distribution. Because the dominant bin is always shifted back to the same starting index, a version of the same content rotated by a whole number of bins yields the same canonicalized histogram. The operation is performed on the histogram bins, not on the underlying pixels.

What the Canonicalized Histogram Feeds

Two of the three Z-axis components are derived from this histogram. The horizontal-vertical orientation bias is computed as the mean weight of the horizontal bins minus the mean weight of the vertical bins. The diagonal-axial bias is computed as the mean weight of the diagonal bins minus the mean weight of the axial bins. These two scalars summarize whether the artifact's edge energy concentrates along horizontal and vertical axes or along diagonals.

The third Z-axis component is a stability coefficient computed as one minus the absolute difference between the artifact's edge density and its normalized global variance, measuring the structural coherence between edge density and statistical variance. Edge density is the fraction of interior pixels whose gradient magnitude exceeds a threshold of 0.1, and the global variance is the full-image variance used as a proxy for information density. Together the three Z-axis components join the X-axis energy behavior vector and the Y-axis frequency compaction vector to form the nine-dimensional variance vector.

Conditional Image Rotation in the Quadrant Pipeline

In the quadrant decomposition pipeline, orientation canonicalization takes a second, spatial-domain form. The canonical normalization stage first rescales the input artifact to a 256-pixel by 256-pixel square canvas, computed by taking the ratio of the target dimension to the longest source edge, applying uniform scaling along both dimensions, and centering the scaled image on a black background fill, with image smoothing disabled to prevent anti-aliasing from introducing artificial variance signals. The orientation canonicalization module then computes the dominant gradient orientation of the normalized artifact by extracting the peak bin of an eight-bin gradient histogram over the full canonical image.

If the dominant orientation angle exceeds an absolute value of approximately 0.1 radians, corresponding to approximately 5.7 degrees, the artifact is rotated by that angle about the center of the canvas prior to quadrant extraction. If the dominant angle does not exceed that bound, no rotation is applied. This canonicalization presents artifacts that carry predominant orientation structure in a consistent spatial frame before spatial decomposition, reducing inter-format and inter-resolution unique identifier drift attributable to minor rotational variations. The four non-overlapping quadrants are then extracted, each fingerprinted independently, and the resulting quadrant hashes are sorted in lexicographic order so that the spatial fingerprint is itself rotation-invariant.

The Sixteen-Bin Variant in the Structure Signature

The structure signature, an optional component supporting recognition of logos, icons, and graphically sparse artifacts across background color changes and flat-fill variations, applies the same canonicalization idea at finer angular resolution. A sixteen-bin gradient histogram is computed over the full canonical image, with each bin accumulating gradient magnitude weighted by edge strength across all interior pixels, and the histogram is canonicalized by rotating to place the maximum-weight bin at index zero.

This gradient-only, rotation-canonicalized histogram is combined with edge density values computed at three gradient magnitude thresholds of 0.05, 0.10, and 0.15, together with the variance and peak of the normalized sixteen-bin histogram, to form a 21-dimensional structure vector. Because the structure vector is derived exclusively from spatial gradient information, it suppresses sensitivity to mean luminance and background fill, and the orientation canonicalization step is what places it in a consistent rotational frame.

Operation Over Any Normalized Scalar Field

Because the stage operates on a normalized scalar field rather than on pixels specifically, it carries over to non-image modalities without modification. For audio artifacts the scalar field is a normalized mel-spectrogram, for textual documents a token frequency grid, and for binary objects a reshaped byte matrix; in each case the gradient histogram and its orientation canonicalization operate over the scalar field in the same manner as for images.

For video artifacts the system operates at two levels, and at the frame level each frame is treated as a raster image artifact processed through the full image extraction pipeline, including canonical normalization and orientation canonicalization, before quadrant decomposition and optional structure and constellation signature computation. The canonicalized orientation signal is part of what the structural similarity evaluator and lineage construction later compare through cosine similarity over the variance vector.

Use in Screenshot Recapture Detection

The Z-axis orientation signal that canonicalization helps produce also carries a forensic signal. When a digital display renders an image and a camera or screen-capture device re-captures the rendered output, the sub-pixel geometry of the display, compression and dithering artifacts from the display pipeline, and the optical point-spread function of the capturing lens or sensor introduce a periodic spatial frequency structure in the luminance channel. These artifacts manifest in the Z-axis gradient histogram as elevated energy in the horizontal and vertical orientation bins relative to the diagonal bins, producing a horizontal-vertical bias score that is systematically elevated compared to the original digital artifact.

The screenshot recapture classifier evaluates this Z-axis horizontal-vertical bias against a policy-calibrated threshold and produces a recapture probability score. The method requires no reference to the original artifact and operates entirely from the structural features of the candidate artifact itself, which is meaningful only because the orientation bias is measured against the canonicalized histogram frame rather than against an arbitrary rotation of the input.

Disclosure Scope

The orientation canonicalization mechanism described here, comprising the rotation of a gradient orientation histogram to place its dominant bin at index zero, the conditional rotation of the normalized image about the canvas center when the dominant gradient orientation exceeds approximately 0.1 radians prior to quadrant extraction, the eight-bin Z-axis histogram and its derived horizontal-vertical and diagonal-axial bias components, and the sixteen-bin rotation-canonicalized histogram used in the structure signature, is disclosed in PCT International Application No. PCT/US26/28630. This article describes that disclosed mechanism using the specification's own terminology.

The scope extends to the application of the canonicalization over any normalized scalar field, including image, audio, textual, video-frame, and binary scalar fields, and to its use in reducing unique identifier drift across format conversion and resolution change and in supplying the orientation signal consumed by structural similarity comparison and screenshot recapture detection. It does not extend to mechanisms not disclosed in the specification, and the disclosed stage performs rotational canonicalization of gradient orientation in service of variance vector extraction, and nothing further.