feature/issue-11/implement-hausdorff-features

pyproject.toml

@@ -10,7 +10,8 @@ readme = "README.md"
 requires-python = ">=3.12"
 dependencies = [
   "pandas>=2.2.3",
-  "pydantic>=2.11.1"
+  "pydantic>=2.11.1",
+  "scipy>=1.15.2"
 ]
 
 [dependency-groups]

src/graphomotor/core/models.py

@@ -10,13 +10,13 @@ class Spiral(BaseModel):
     """A class representing a spiral drawing, encapsulating both raw data and metadata.
 
     Attributes:
-        data: DataFrame containing drawing data with required columns
-            (line_number, x, y, UTC_Timestamp, seconds)
+        data: DataFrame containing drawing data with required columns (line_number, x,
+            y, UTC_Timestamp, seconds).
         metadata: Dictionary containing metadata about the spiral:
-            - id: Unique identifier for the participant
-            - hand: Hand used ('Dom' for dominant, 'NonDom' for non-dominant)
-            - task: Task name
-            - start_time: Start time of drawing
+            - id: Unique identifier for the participant,
+            - hand: Hand used ('Dom' for dominant, 'NonDom' for non-dominant),
+            - task: Task name,
+            - start_time: Start time of drawing.
     """
 
     model_config = ConfigDict(arbitrary_types_allowed=True)

src/graphomotor/features/__init__.py

@@ -0,0 +1 @@
+""".. include:: ../../README.md"""  # noqa: D415

src/graphomotor/features/distance.py

@@ -0,0 +1,120 @@
+"""Feature extraction module for distance-based metrics in spiral drawing data."""
+
+import numpy as np
+from scipy import stats
+from scipy.spatial import distance
+
+from graphomotor.core import models
+
+
+def _segment_data(data: np.ndarray, start_prop: float, end_prop: float) -> np.ndarray:
+    """Extract segment of data based on given proportion range.
+
+    Args:
+        data: Data to segment.
+        start_prop: Start proportion, [0-1).
+        end_prop: End proportion, (0-1].
+
+    Returns:
+        Segmented data.
+    """
+    if not (0 <= start_prop < end_prop <= 1):
+        raise ValueError(
+            "Proportions must be between 0 and 1, "
+            "and start_prop must be less than end_prop"
+        )
+    num_samples = len(data)
+    start_idx = int(start_prop * num_samples)
+    end_idx = int(end_prop * num_samples)
+    return data[start_idx:end_idx]
+
+
+def calculate_hausdorff_metrics(
+    spiral: models.Spiral, reference_spiral: np.ndarray
+) -> dict:
+    """Calculate Hausdorff distance metrics for a spiral object.
+
+    This function computes multiple features based on the Hausdorff distance between a
+    drawn spiral and a reference (ideal) spiral, as described in [1]. Implementation
+    is based on the original R script provided with the publication. The Hausdorff
+    distance measures the maximum distance of a set to the nearest point in the other
+    set. This metric and its derivatives capture various aspects of the spatial
+    relationship between the drawn and reference spirals. Calculated features include:
+        - hausdorff_distance_maximum: The maximum of the directed Hausdorff distances
+            between the data points and the reference data points,
+        - hausdorff_distance_sum: The sum of the directed Hausdorff distances,
+        - hausdorff_distance_sum_per_second: The sum of the directed Hausdorff distances
+            divided by the total drawing duration,
+        - hausdorff_distance_interquartile_range: The interquartile range of the
+            directed Hausdorff distances,
+        - hausdorff_distance_start_segment_maximum_normalized: The maximum of the
+            directed Hausdorff distances between the beginning segment (0% to 25%) of
+            data points and the beginning segment of reference data points divided by
+            the number of data points in the beginning segment,
+        - hausdorff_distance_end_segment_maximum_normalized: The maximum of the directed
+            Hausdorff distances in the ending segment (75% to 100%) of data points and
+            the ending segment of reference data points divided by the number of data
+            points in the ending segment,
+        - hausdorff_distance_middle_segment_maximum: The maximum of the directed
+            Hausdorff distances in the middle segment (15% to 85%) of data points and
+            the ending segment of reference data points (this metric is not divided by
+            the number of data points in the middle segment unlike previous ones),
+        - hausdorff_distance_middle_segment_maximum_per_second: The maximum of the
+            directed Hausdorff distances in the middle segment divided by the total
+            drawing duration.
+
+    Args:
+        spiral: Spiral object with drawing data.
+        reference_spiral: Reference spiral data for comparison.
+
+    Returns:
+        Dictionary containing Hausdorff distance-based features.
+
+    References:
+        [1] Messan, Komi S et al. “Assessment of Smartphone-Based Spiral Tracing in
+            Multiple Sclerosis Reveals Intra-Individual Reproducibility as a Major
+            Determinant of the Clinical Utility of the Digital Test.” Frontiers in
+            medical technology vol. 3 714682. 1 Feb. 2022, doi:10.3389/fmedt.2021.714682
+    """
+    spiral_data = np.column_stack((spiral.data["x"].values, spiral.data["y"].values))
+
+    total_duration = spiral.data["seconds"].iloc[-1]
+
+    start_segment_data = _segment_data(spiral_data, 0.0, 0.25)
+    end_segment_data = _segment_data(spiral_data, 0.75, 1.0)
+    mid_segment_data = _segment_data(spiral_data, 0.15, 0.85)
+
+    start_segment_ref = _segment_data(reference_spiral, 0.0, 0.25)
+    end_segment_ref = _segment_data(reference_spiral, 0.75, 1.0)
+    mid_segment_ref = _segment_data(reference_spiral, 0.15, 0.85)
+
+    haus_dist = [
+        distance.directed_hausdorff(spiral_data, reference_spiral)[0],
+        distance.directed_hausdorff(reference_spiral, spiral_data)[0],
+    ]
+    haus_dist_start = [
+        distance.directed_hausdorff(start_segment_data, start_segment_ref)[0],
+        distance.directed_hausdorff(start_segment_ref, start_segment_data)[0],
+    ]
+    haus_dist_end = [
+        distance.directed_hausdorff(end_segment_data, end_segment_ref)[0],
+        distance.directed_hausdorff(end_segment_ref, end_segment_data)[0],
+    ]
+    haus_dist_mid = [
+        distance.directed_hausdorff(mid_segment_data, mid_segment_ref)[0],
+        distance.directed_hausdorff(mid_segment_ref, mid_segment_data)[0],
+    ]
+
+    return {
+        "hausdorff_distance_maximum": np.max(haus_dist),
+        "hausdorff_distance_sum": np.sum(haus_dist),
+        "hausdorff_distance_sum_per_second": np.sum(haus_dist) / total_duration,
+        "hausdorff_distance_interquartile_range": stats.iqr(haus_dist),
+        "hausdorff_distance_start_segment_maximum_normalized": np.max(haus_dist_start)
+        / len(start_segment_data),
+        "hausdorff_distance_end_segment_maximum_normalized": np.max(haus_dist_end)
+        / len(end_segment_data),
+        "hausdorff_distance_middle_segment_maximum": np.max(haus_dist_mid),
+        "hausdorff_distance_middle_segment_maximum_per_second": np.max(haus_dist_mid)
+        / total_duration,
+    }

src/graphomotor/utils/reference_spiral.py

@@ -0,0 +1,99 @@
+"""Generate a reference spiral with equidistant points along its arc length."""
+
+import numpy as np
+from scipy import integrate, optimize
+
+_SPIRAL_CENTER_X = 50
+_SPIRAL_CENTER_Y = 50
+_SPIRAL_START_RADIUS = 0
+_SPIRAL_GROWTH_RATE = 1.075
+_SPIRAL_START_ANGLE = 0
+_SPIRAL_END_ANGLE = 8 * np.pi
+_SPIRAL_NUM_POINTS = 10000
+
+
+def _arc_length_integrand(t: float) -> float:
+    """Calculate the differential arc length at angle t for an Archimedean spiral.
+
+    Args:
+        t: Angle parameter.
+
+    Returns:
+        Differential arc length value.
+    """
+    r_t = _SPIRAL_START_RADIUS + _SPIRAL_GROWTH_RATE * t
+    return np.sqrt(r_t**2 + _SPIRAL_GROWTH_RATE**2)
+
+
+def _calculate_arc_length(theta: float) -> float:
+    """Calculate the arc length of the spiral from _SPIRAL_START_ANGLE to theta.
+
+    Args:
+        theta: The angle in radians.
+
+    Returns:
+        The arc length of the spiral from _SPIRAL_START_ANGLE to theta.
+    """
+    return integrate.quad(
+        lambda t: _arc_length_integrand(t), _SPIRAL_START_ANGLE, theta
+    )[0]
+
+
+def _find_theta_for_arc_length(target_arc_length: float) -> float:
+    """Find the theta value for a given arc length using numerical root finding.
+
+    Args:
+        target_arc_length: Target arc length.
+
+    Returns:
+        Angle theta corresponding to the arc length.
+    """
+    solution = optimize.root_scalar(
+        lambda theta: _calculate_arc_length(theta) - target_arc_length,
+        bracket=[_SPIRAL_START_ANGLE, _SPIRAL_END_ANGLE],
+    )
+    return solution.root
+
+
+def generate_reference_spiral() -> np.ndarray:
+    """Generate a reference spiral with equidistant points along its arc length.
+
+    This function creates an Archimedean spiral with points distributed at equal arc
+    length intervals. The generated spiral serves as a standardized reference template
+    for feature extraction algorithms that compare user-drawn spirals with an ideal
+    form.
+
+    The algorithm works by:
+        1. Computing the total arc length for the entire spiral,
+        2. Creating equidistant target arc length values,
+        3. For each target arc length, finding the corresponding theta value that
+           produces that arc length using numerical root finding,
+        4. Converting these theta values to Cartesian coordinates.
+
+    Mathematical formulas used:
+        - Spiral equation: r(θ) = a + b·θ
+        - Arc length differential: ds = √(r(θ)² + b²) dθ
+        - Arc length from 0 to θ: s(θ) = ∫₀ᶿ √(r(t)² + b²) dt
+        - Cartesian coordinates: x = cx + r·cos(θ), y = cy + r·sin(θ)
+
+    Parameters used:
+        - Center coordinates: (cx, cy) = (_SPIRAL_CENTER_X, _SPIRAL_CENTER_Y)
+        - Start radius: a = _SPIRAL_START_RADIUS
+        - Growth rate: b = _SPIRAL_GROWTH_RATE
+        - Total rotation: θ = _SPIRAL_END_ANGLE - _SPIRAL_START_ANGLE
+        - Number of points: N = _SPIRAL_NUM_POINTS
+
+    Returns:
+        Array with shape (N, 2) containing Cartesian coordinates of the spiral points.
+    """
+    total_arc_length = _calculate_arc_length(_SPIRAL_END_ANGLE)
+
+    arc_length_values = np.linspace(0, total_arc_length, _SPIRAL_NUM_POINTS)
+
+    theta_values = np.array([_find_theta_for_arc_length(s) for s in arc_length_values])
+
+    r_values = _SPIRAL_START_RADIUS + _SPIRAL_GROWTH_RATE * theta_values
+    x_values = _SPIRAL_CENTER_X + r_values * np.cos(theta_values)
+    y_values = _SPIRAL_CENTER_Y + r_values * np.sin(theta_values)
+
+    return np.column_stack((x_values, y_values))

tests/conftest.py

@@ -3,9 +3,13 @@
 import datetime
 import pathlib
 
+import numpy as np
 import pandas as pd
 import pytest
 
+from graphomotor.core import models
+from graphomotor.utils import reference_spiral
+
 
 @pytest.fixture
 def sample_data() -> pathlib.Path:
@@ -35,3 +39,21 @@ def valid_spiral_metadata() -> dict[str, str | datetime.datetime]:
             tz=datetime.timezone.utc,
         ),
     }
+
+
+@pytest.fixture
+def valid_spiral(
+    valid_spiral_data: pd.DataFrame,
+    valid_spiral_metadata: dict[str, str | datetime.datetime],
+) -> models.Spiral:
+    """Create a valid Spiral object."""
+    return models.Spiral(
+        data=valid_spiral_data,
+        metadata=valid_spiral_metadata,
+    )
+
+
+@pytest.fixture
+def ref_spiral() -> np.ndarray:
+    """Create a reference spiral for testing."""
+    return reference_spiral.generate_reference_spiral()

tests/unit/test_distance.py

@@ -0,0 +1,52 @@
+"""Test cases for distance.py functions."""
+
+import numpy as np
+import pytest
+
+from graphomotor.core import models
+from graphomotor.features import distance
+
+
+def test_segment_data_valid() -> None:
+    """Test that the data is segmented correctly."""
+    data = np.array([[i, i] for i in range(100)])
+
+    segment = distance._segment_data(data, 0.1, 0.3)
+    assert len(segment) == 20
+    assert segment[0][0] == 10
+    assert segment[-1][0] == 29
+
+
+def test_segment_data_invalid() -> None:
+    """Test that invalid percentages raise a ValueError."""
+    data = np.array([[i, i] for i in range(100)])
+
+    with pytest.raises(
+        ValueError,
+        match=(
+            "Proportions must be between 0 and 1, "
+            "and start_prop must be less than end_prop"
+        ),
+    ):
+        distance._segment_data(data, 0.6, 0.5)
+
+
+def test_calculate_hausdorff_metrics(
+    valid_spiral: models.Spiral, ref_spiral: np.ndarray
+) -> None:
+    """Test that each Hausdorff metric is calculated."""
+    metrics = distance.calculate_hausdorff_metrics(valid_spiral, ref_spiral)
+
+    expected_metrics = {
+        "hausdorff_distance_maximum",
+        "hausdorff_distance_sum",
+        "hausdorff_distance_sum_per_second",
+        "hausdorff_distance_interquartile_range",
+        "hausdorff_distance_start_segment_maximum_normalized",
+        "hausdorff_distance_end_segment_maximum_normalized",
+        "hausdorff_distance_middle_segment_maximum",
+        "hausdorff_distance_middle_segment_maximum_per_second",
+    }
+
+    assert set(metrics.keys()) == expected_metrics
+    assert all(isinstance(value, float) for value in metrics.values())

tests/unit/test_reference_spiral.py

@@ -0,0 +1,34 @@
+"""Test cases for reference_spiral.py functions."""
+
+import numpy as np
+
+from graphomotor.utils import reference_spiral
+
+
+def test_generate_reference_spiral() -> None:
+    """Test the generation of a reference spiral."""
+    expected_mean_arc_length = reference_spiral._calculate_arc_length(
+        reference_spiral._SPIRAL_END_ANGLE
+    ) / (reference_spiral._SPIRAL_NUM_POINTS - 1)
+
+    spiral = reference_spiral.generate_reference_spiral()
+    arc_lengths = np.linalg.norm(spiral[1:] - spiral[:-1], axis=1)
+    mean_arc_length = np.mean(arc_lengths)
+
+    assert isinstance(spiral, np.ndarray)
+    assert spiral.shape == (reference_spiral._SPIRAL_NUM_POINTS, 2)
+    assert np.array_equal(
+        spiral[0],
+        [reference_spiral._SPIRAL_CENTER_X, reference_spiral._SPIRAL_CENTER_Y],
+    )
+    assert np.allclose(
+        spiral[-1],
+        [
+            reference_spiral._SPIRAL_CENTER_X
+            + reference_spiral._SPIRAL_GROWTH_RATE * reference_spiral._SPIRAL_END_ANGLE,
+            reference_spiral._SPIRAL_CENTER_Y,
+        ],
+        atol=1e-8,
+    )
+    assert np.allclose(arc_lengths, mean_arc_length, rtol=1e-3)
+    assert np.isclose(mean_arc_length, expected_mean_arc_length, rtol=1e-6)