refactor: Update affinity matrix calculation and dependencies

- Replaced the `linear_sum_assignment` import from `scipy.optimize` with `hungarian_algorithm` from `optax` to enhance performance in affinity matrix calculations.
- Introduced a new `AffinityResult` class to encapsulate results of affinity computations, including trackings and detections, improving the structure of the affinity calculation process.
- Removed deprecated functions and debug print statements to streamline the codebase.
- Updated `pyproject.toml` and `uv.lock` to include `optax` as a dependency, ensuring compatibility with the new implementation.
- Refactored imports and type hints for better organization and consistency across the codebase.

app/tracking/__init__.py

@@ -2,8 +2,10 @@ from dataclasses import dataclass
 from datetime import datetime
 from typing import (
     Any,
+    Callable,
     Generator,
     Optional,
+    Sequence,
     TypeAlias,
     TypedDict,
     TypeVar,
@@ -14,7 +16,11 @@ from typing import (
 import jax
 import jax.numpy as jnp
 from beartype import beartype
-from jaxtyping import Array, Float, jaxtyped
+from beartype.typing import Mapping, Sequence
+from jax import Array
+from jaxtyping import Array, Float, Int, jaxtyped
+
+from app.camera import Detection
 
 
 @jaxtyped(typechecker=beartype)
@@ -67,3 +73,30 @@ class Tracking:
         # Step 2 – pure JAX math
         # ------------------------------------------------------------------
         return self.keypoints + velocity * delta_t_s
+
+
+@jaxtyped(typechecker=beartype)
+@dataclass
+class AffinityResult:
+    """
+    Result of affinity computation between trackings and detections.
+    """
+
+    matrix: Float[Array, "T D"]
+    trackings: Sequence[Tracking]
+    detections: Sequence[Detection]
+    indices_T: Int[Array, "T"]  # pylint: disable=invalid-name
+    indices_D: Int[Array, "D"]  # pylint: disable=invalid-name
+
+    def tracking_detections(
+        self,
+    ) -> Generator[tuple[float, Tracking, Detection], None, None]:
+        """
+        iterate over the best matching trackings and detections
+        """
+        for t, d in zip(self.indices_T, self.indices_D):
+            yield (
+                self.matrix[t, d].item(),
+                self.trackings[t],
+                self.detections[d],
+            )