Merge pull request #368 from oddkiva/maint-code-cleanup

MAINT: code cleanup.

python/oddkiva/sara/sfm/README.md

@@ -0,0 +1,2 @@
+The code in this folder are mostly a collection of results we reuse in the C++
+code.

python/oddkiva/sara/sfm/five_point_algorithm.py

@@ -1,18 +1,25 @@
-import sympy as sp
-from sympy.abc import x, y, z
+def calculate_E_matrix_constraints_from_5_point():
+    import sympy as sp
+    from sympy.abc import x, y, z
 
-# Solve the cubic polynomial.
-X = sp.MatrixSymbol('X', 3, 3)
-Y = sp.MatrixSymbol('Y', 3, 3)
-Z = sp.MatrixSymbol('Z', 3, 3)
-W = sp.MatrixSymbol('W', 3, 3)
+    # Solve the cubic polynomial.
+    #
+    # The essential matrix lives in the nullspace which is spanned by 4
+    # eigenvectors.
+    X = sp.MatrixSymbol('X', 3, 3)
+    Y = sp.MatrixSymbol('Y', 3, 3)
+    Z = sp.MatrixSymbol('Z', 3, 3)
+    W = sp.MatrixSymbol('W', 3, 3)
 
-# Form the symbolic matrix expression as reported in the paper.
-E = sp.Matrix(x * X + y * Y + z * Z + W)
+    # Form the symbolic matrix expression as reported in the paper.
+    E = sp.Matrix(x * X + y * Y + z * Z + W)
 
-essential_constraint = E * E.T * E - sp.Trace(E * E.T) * E
-rank_2_constraint = E.det()
+    # Form the first system of equations that the essential matrix must
+    # satisfy:
+    essential_constraint = E * E.T * E - sp.Trace(E * E.T) * E
 
-e = essential_constraint
+    # Form the second system of equations. The essential matrix has rank 2,
+    # therefore its determinant must be zero.
+    rank_2_constraint = E.det()
 
-import IPython; IPython.embed()
+    return essential_constraint, rank_2_constraint

python/oddkiva/sara/sfm/seven_point_algorithm.py

@@ -1,18 +1,21 @@
-import sympy as sp
+def calculate_F_matrix_rank_2_constraint_from_7_points():
+    import sympy as sp
 
-# Solve the cubic polynomial.
-F1 = sp.MatrixSymbol('F1', 3, 3)
-F2 = sp.MatrixSymbol('F2', 3, 3)
-α = sp.symbols('α')
+    # Solve the cubic polynomial.
+    F1 = sp.MatrixSymbol('F1', 3, 3)
+    F2 = sp.MatrixSymbol('F2', 3, 3)
+    α = sp.symbols('α')
 
-# Form the symbolic matrix expression as reported in the paper.
-F = sp.Matrix(F1 + α * F2)
+    # The fundamental matrix has rank 2.
+    # Necessarily its determinant must be 0.
+    #
+    # Form the symbolic matrix expression as reported in the paper.
+    F = sp.Matrix(F1 + α * F2)
 
-# Form the polynomial in the variable α.
-det_F, _ = sp.polys.poly_from_expr(F.det(), α)
+    # Form the polynomial in the variable α.
+    det_F, _ = sp.polys.poly_from_expr(F.det(), α)
 
-# Collect the coefficients "c[i]" as denoted in the paper.
-c = det_F.all_coeffs()
+    # Collect the coefficients "c[i]" as denoted in the paper.
+    c = det_F.all_coeffs()
 
-
-import IPython; IPython.embed()
+    return c