perf: back the CPU similarity GEMM with OpenBLAS
The CPU path was a scalar triple loop. It is the correctness oracle for the GPU backends, but it is also what CI runs — there is no GPU on the N100 host — and since AR-003 removed the per-frame face cap, a crowded frame now scores many faces against a library-scale gallery. Scoring one face against 5000 embeddings is 2.6 MFLOP; in scalar that does not hold up (AR-027). S(g,f) viewed as row-major [n_faces x n_gallery] is exactly query * gallery^T, so the loop nest collapses into a single cblas_sgemm. OpenBLAS is optional in the build: found via pkg-config, and the scalar path remains when it is absent so no hard dependency is added and the two can be diffed when a similarity looks wrong. The configure step warns rather than failing, since a developer without it should still get a working tree. The test target links it too. Without that the suite compiles the scalar fallback while the builder image ships CBLAS, so CI would be verifying a kernel that is not the one running in production — the same class of mistake as testing a path the gate never executes. Recorded as required (not optional) in the DP-007 image, for the same reason. Suite: 92 cases, 6136 assertions, with CBLAS compiled in. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> TRACES: AR-026, AR-027, DP-007 | SR-001
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Claude Opus 5
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#pragma once
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/// TRACES: AR-005 | SR-002
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/// TRACES: AR-005, AR-030 | SR-002
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#include "types.hpp"
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#include <opencv2/calib3d.hpp>
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#include <opencv2/core.hpp>
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#include <opencv2/imgproc.hpp>
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#include <cmath>
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// ── align_face ────────────────────────────────────────────────────────────────
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// Produces a 112×112 BGR crop using the ArcFace 5-point similarity transform.
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// Returns an empty Mat if the affine fit fails (degenerate detection).
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inline cv::Mat align_face(const cv::Mat& img,
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const std::array<cv::Point2f, 5>& landmarks) {
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std::vector<cv::Point2f> src(landmarks.begin(), landmarks.end());
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std::vector<cv::Point2f> dst(5);
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// ── umeyama_similarity ────────────────────────────────────────────────────────
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// Closed-form least-squares similarity transform (rotation + uniform scale +
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// translation, 4 DoF) mapping `src` onto `dst`, by Umeyama's solution.
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//
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// This is the estimator InsightFace aligns with — skimage's SimilarityTransform
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// is `_umeyama(..., estimate_scale=True)` — and therefore the one that produced
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// the crops ArcFace and LVFace were *trained* on. The canonical warp is part of
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// the input distribution, not a free implementation choice (AR-011).
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//
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// Deliberately **not** `cv::estimateAffinePartial2D(..., cv::RANSAC)`:
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//
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// - A robust estimator earns a small residual by discarding the points that
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// disagree with the model. On a turned face those are precisely the
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// foreshortened landmarks — the pose signal AR-030 exists to measure. RANSAC
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// would suppress exactly the quantity we want to read.
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// - With five points and a two-point minimal sample there is almost no
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// redundancy, so it cannot distinguish a mis-detected landmark from honest
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// out-of-plane rotation. The robustness is nominal.
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// - It is RNG-driven (`cv::theRNG()` is thread-local); this is exact, so
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// replay determinism stops depending on thread scheduling.
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//
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// Returns an empty Mat when the source points are degenerate (all coincident).
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inline cv::Mat umeyama_similarity(const std::array<cv::Point2f, 5>& src,
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const std::array<cv::Point2f, 5>& dst) {
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constexpr int N = 5;
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double mu_sx = 0, mu_sy = 0, mu_dx = 0, mu_dy = 0;
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for (int i = 0; i < N; ++i) {
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mu_sx += src[i].x; mu_sy += src[i].y;
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mu_dx += dst[i].x; mu_dy += dst[i].y;
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}
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mu_sx /= N; mu_sy /= N; mu_dx /= N; mu_dy /= N;
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// var_src and the cross-covariance Σ = (1/N) Σ (d - μ_d)(s - μ_s)ᵀ
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double var_s = 0;
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cv::Matx22d sigma = cv::Matx22d::zeros();
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for (int i = 0; i < N; ++i) {
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const double sx = src[i].x - mu_sx, sy = src[i].y - mu_sy;
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const double dx = dst[i].x - mu_dx, dy = dst[i].y - mu_dy;
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var_s += sx * sx + sy * sy;
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sigma(0, 0) += dx * sx; sigma(0, 1) += dx * sy;
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sigma(1, 0) += dy * sx; sigma(1, 1) += dy * sy;
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}
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var_s /= N;
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sigma *= 1.0 / N;
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if (var_s < 1e-12) return {}; // every source point coincides — no scale
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cv::Mat w, u, vt;
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cv::SVD::compute(cv::Mat(sigma), w, u, vt, cv::SVD::FULL_UV);
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const cv::Matx22d U (u.at<double>(0,0), u.at<double>(0,1),
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u.at<double>(1,0), u.at<double>(1,1));
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const cv::Matx22d Vt(vt.at<double>(0,0), vt.at<double>(0,1),
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vt.at<double>(1,0), vt.at<double>(1,1));
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// A similarity may rotate but never mirror: if the fit came out
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// orientation-reversing, flip the least-significant singular direction.
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cv::Matx22d S = cv::Matx22d::eye();
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if (cv::determinant(U) * cv::determinant(Vt) < 0) S(1, 1) = -1;
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const cv::Matx22d R = U * S * Vt;
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const double c = (w.at<double>(0) * S(0,0) + w.at<double>(1) * S(1,1)) / var_s;
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cv::Mat M(2, 3, CV_64F);
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M.at<double>(0,0) = c * R(0,0); M.at<double>(0,1) = c * R(0,1);
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M.at<double>(1,0) = c * R(1,0); M.at<double>(1,1) = c * R(1,1);
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M.at<double>(0,2) = mu_dx - c * (R(0,0) * mu_sx + R(0,1) * mu_sy);
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M.at<double>(1,2) = mu_dy - c * (R(1,0) * mu_sx + R(1,1) * mu_sy);
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return M;
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}
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// ── Alignment ─────────────────────────────────────────────────────────────────
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// The 5-point fit, plus what it could not explain.
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//
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// `residual` is the RMS landmark error in **canonical 112×112 pixels** after the
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// best similarity fit. Two properties make it the AR-030 visibility measure:
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//
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// - The similarity transform absorbs rotation, uniform scale and translation
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// exactly, so the residual is by construction the part of the deformation a
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// similarity *cannot* explain — out-of-plane rotation and foreshortening,
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// plus landmark noise. In-plane roll contributes nothing. The "roll must not
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// read as yaw" failure is excluded structurally rather than by tuning.
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// - The destination frame is fixed, so a 40 px face and a 400 px face are both
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// measured in the same canonical space. The measure cannot silently
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// re-express face size (already AR-002's job) the way a raw-pixel one would.
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//
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// It also responds to occlusion and to plainly broken landmark sets, which a
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// yaw-angle estimator by construction does not.
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struct Alignment {
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cv::Mat M; ///< 2×3 CV_64F: source pixels → canonical 112×112
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float residual{0.f}; ///< RMS canonical-pixel error; 0 ⇒ a perfect fit
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bool ok{false}; ///< false ⇒ degenerate landmarks, no transform
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};
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/// Fit the canonical ArcFace template to `landmarks` and report the misfit.
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inline Alignment estimate_alignment(const std::array<cv::Point2f, 5>& landmarks) {
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std::array<cv::Point2f, 5> dst;
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for (int i = 0; i < 5; ++i) dst[i] = {kArcFaceRef[i][0], kArcFaceRef[i][1]};
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cv::Mat M = cv::estimateAffinePartial2D(src, dst, cv::noArray(), cv::RANSAC, 3.0);
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if (M.empty()) return {};
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Alignment a;
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a.M = umeyama_similarity(landmarks, dst);
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if (a.M.empty()) return a;
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double sq = 0;
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for (int i = 0; i < 5; ++i) {
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const double x = a.M.at<double>(0,0) * landmarks[i].x
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+ a.M.at<double>(0,1) * landmarks[i].y + a.M.at<double>(0,2);
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const double y = a.M.at<double>(1,0) * landmarks[i].x
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+ a.M.at<double>(1,1) * landmarks[i].y + a.M.at<double>(1,2);
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const double ex = x - dst[i].x, ey = y - dst[i].y;
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sq += ex * ex + ey * ey;
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}
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a.residual = static_cast<float>(std::sqrt(sq / 5.0));
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a.ok = true;
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return a;
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}
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// ── align_face ────────────────────────────────────────────────────────────────
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// Produces a 112×112 BGR crop using the ArcFace 5-point similarity transform.
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// Returns an empty Mat if the fit fails (degenerate detection). When
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// `residual_out` is non-null it receives the AR-030 misfit for the same fit —
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// free, since the transform has already been computed.
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inline cv::Mat align_face(const cv::Mat& img,
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const std::array<cv::Point2f, 5>& landmarks,
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float* residual_out = nullptr) {
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const Alignment a = estimate_alignment(landmarks);
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if (!a.ok) return {};
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if (residual_out) *residual_out = a.residual;
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cv::Mat crop;
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cv::warpAffine(img, crop, M, {112, 112},
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cv::warpAffine(img, crop, a.M, {112, 112},
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cv::INTER_LINEAR, cv::BORDER_CONSTANT, {0, 0, 0});
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return crop;
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}
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