diff --git a/libweston/color-lcms/color-curve-segments.c b/libweston/color-lcms/color-curve-segments.c
index 51aae583e..95e30f6ed 100644
--- a/libweston/color-lcms/color-curve-segments.c
+++ b/libweston/color-lcms/color-curve-segments.c
@@ -676,3 +676,58 @@ get_parametric_curveset_params(struct weston_compositor *compositor,
 
 	return true;
 }
+
+/** Create a matrix stage equivalent to the CurveSet stage.
+ *
+ * A tabulated curve segment with 2 samples is equivalent to a matrix
+ * (scaling and offset), ignoring possible input clamping and allowing
+ * extrapolation.
+ *
+ * \param context_id The matrix stage is created in this context.
+ * \param stage An arbitrary stage, can be NULL.
+ * \return A new matrix stage equivalent to the given (CurveSet) stage, or
+ * NULL otherwise.
+ */
+cmsStage *
+lcms_matrix_stage_from_curve(cmsContext context_id, cmsStage *stage)
+{
+	const _cmsStageToneCurvesData *data;
+	cmsFloat64Number Matrix[3 * 3] = {}; /* row-major */
+	cmsFloat64Number Offset[3];
+	unsigned i;
+
+	if (!stage || cmsStageType(stage) != cmsSigCurveSetElemType)
+		return NULL;
+
+	data = cmsStageData(stage);
+	if (data->nCurves != 3)
+		return NULL;
+
+	for (i = 0; i < 3; i++) {
+		const cmsCurveSegment *seg;
+		bool clamped_input;
+		double y0, y1, k;
+
+		seg = get_defining_curve_segment(data->TheCurves[i], &clamped_input);
+		if (!seg)
+			return NULL;
+
+		/* Type 0 is tabulated. */
+		if (seg->Type != 0)
+			return NULL;
+
+		if (seg->nGridPoints != 2)
+			return NULL;
+
+		y0 = seg->SampledPoints[0];
+		y1 = seg->SampledPoints[1];
+
+		/* y = k * x + Offset */
+
+		k = (y1 - y0) / (seg->x1 - seg->x0);
+		Offset[i] = y0 - k * seg->x0;
+		Matrix[3 * i + i] = k;
+	}
+
+	return cmsStageAllocMatrix(context_id, 3, 3, Matrix, Offset);
+}
diff --git a/libweston/color-lcms/color-curve-segments.h b/libweston/color-lcms/color-curve-segments.h
index adb20dab4..b761a3264 100644
--- a/libweston/color-lcms/color-curve-segments.h
+++ b/libweston/color-lcms/color-curve-segments.h
@@ -39,6 +39,9 @@ get_parametric_curveset_params(struct weston_compositor *compositor,
 			       float curveset_params[3][MAX_PARAMS_LCMS_PARAM_CURVE],
 			       bool *clamped_input);
 
+cmsStage *
+lcms_matrix_stage_from_curve(cmsContext context_id, cmsStage *stage);
+
 void
 curveset_print(cmsStage *stage, struct weston_log_scope *scope);
 
@@ -64,6 +67,12 @@ get_parametric_curveset_params(struct weston_compositor *compositor,
 	return false;
 }
 
+cmsStage *
+lcms_matrix_stage_from_curve(cmsContext ContextID, cmsStage *stage)
+{
+	return NULL;
+}
+
 static inline void
 curveset_print(cmsStage *stage, struct weston_log_scope *scope)
 {
diff --git a/libweston/color-lcms/color-transform.c b/libweston/color-lcms/color-transform.c
index 6f4ba3b8c..d3c20c048 100644
--- a/libweston/color-lcms/color-transform.c
+++ b/libweston/color-lcms/color-transform.c
@@ -387,6 +387,30 @@ merge_curvesets(cmsPipeline **lut, cmsContext context_id)
 	return modified;
 }
 
+static void
+linear_curvesets_to_matrices(cmsPipeline **lut, cmsContext context_id)
+{
+	cmsPipeline *pipe;
+	cmsStage *elem;
+	cmsStage *matrix;
+
+	pipe = cmsPipelineAlloc(context_id, 3, 3);
+	abort_oom_if_null(pipe);
+
+	elem = cmsPipelineGetPtrToFirstStage(*lut);
+	for (; elem; elem = cmsStageNext(elem)) {
+		matrix = lcms_matrix_stage_from_curve(context_id, elem);
+		if (matrix) {
+			cmsPipelineInsertStage(pipe, cmsAT_END, matrix);
+		} else {
+			cmsPipelineInsertStage(pipe, cmsAT_END, cmsStageDup(elem));
+		}
+	}
+
+	cmsPipelineFree(*lut);
+	*lut = pipe;
+}
+
 static const struct weston_color_tf_info *
 lcms_curve_matches_any_tf(struct weston_compositor *compositor,
 			  uint32_t lcms_curve_type, bool clamped_input,
@@ -1013,6 +1037,8 @@ lcms_optimize_pipeline(cmsPipeline **lut, cmsContext context_id)
 {
 	bool cont_opt;
 
+	linear_curvesets_to_matrices(lut, context_id);
+
 	/**
 	 * This optimization loop will delete identity stages. Deleting
 	 * identity matrix stages is harmless, but deleting identity