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| -rw-r--r-- | fg21sim/utils/rotate.py | 131 |
1 files changed, 131 insertions, 0 deletions
diff --git a/fg21sim/utils/rotate.py b/fg21sim/utils/rotate.py new file mode 100644 index 0000000..b89365c --- /dev/null +++ b/fg21sim/utils/rotate.py @@ -0,0 +1,131 @@ +# Copyright (c) 2016 Weitian LI <liweitianux@live.com> +# MIT license + +""" +Image (only gray-scale image, i.e., matrix) rotate utilities. + +References +---------- +- Leptonica: Rotation + http://www.leptonica.com/rotation.html +- Image rotation by MATLAB without using imrotate + https://stackoverflow.com/a/19687481/4856091 + https://stackoverflow.com/a/19689081/4856091 +""" + + +import numpy as np +import numba as nb + + +@nb.jit([nb.float64[:, :](nb.int64[:, :], nb.float64, nb.boolean, + nb.boolean, nb.float64), + nb.float64[:, :](nb.float64[:, :], nb.float64, nb.boolean, + nb.boolean, nb.float64)], + nopython=True) +def rotate_center(imgin, angle, interp=True, reshape=True, fill_value=0.0): + """Rotate the input image (only gray-scale image currently supported) + by a given angle about its center. + + Parameters + ---------- + imgin : 2D `~numpy.ndarray` + Input gray-scale image to be rotated + angle : float + Rotation angle (unit: [ degree ]) + interp : bool, optional + Use the area mapping of the 4 closest input pixels (``interp=True``), + which is also the same as "bilinear interpolation", + or use the nearest neighbor (``interp=False``) for rotated pixels. + reshape : bool, optional + Whether adapt the output shape so that the input image is contained + completely in the output? + fill_value : float, optional + Value used to fill pixels in the rotated image that corresponding + pixels outside the boundaries of the input image. + """ + nrow, ncol = imgin.shape + # Rotation transformation image + angle = np.deg2rad(angle) + mrotate = np.zeros((2, 2), dtype=np.float64) + mrotate[0, 0] = np.cos(angle) + mrotate[0, 1] = np.sin(angle) + mrotate[1, 0] = -np.sin(angle) + mrotate[1, 1] = np.cos(angle) + # Determine the shape of rotated image + corner00 = np.array((0, 0)) + corner01 = np.array((0, ncol-1)) + corner10 = np.array((nrow-1, 0)) + corner11 = np.array((nrow-1, ncol-1)) + corners = np.vstack((corner00, corner01, corner10, corner11)) + if reshape: + dest = np.dot(corners.astype(np.float64), mrotate) + # XXX: ``numba`` does not support ``np.max()`` with arguments + minc = np.min(dest[:, 0]) + minr = np.min(dest[:, 1]) + maxc = np.max(dest[:, 0]) + maxr = np.max(dest[:, 1]) + nr = int(maxr - minr + 0.5) + nc = int(maxc - minc + 0.5) + else: + # Constraint to be same shape + nr = nrow + nc = ncol + imgout = np.ones((nr, nc)) * fill_value + # + # Calculate the offset, for easier transformation of rotated pixels + # back to input image. + # + # NOTE: + # Notations: + # P_out : (r_out, c_out) a pixel in the output rotated image + # C_out : center position of the output rotated image + # P_in : (r_in, c_in) a pixel in the input image + # C_in : center position of the input image + # R : rotation matrix + # R_T : transposed rotation matrix + # The rotation relation between pixel pair is (about the center): + # (P_in - C_in) * R = P_out - C_out + # Then: + # (P_in - C_in) = (P_out - C_out) * R_T + # And then: + # P_in = C_in + (P_out-C_out) * R_T = P_out*R_T + (C_in - C_out*R_T) + # Thus can define the "offset" as: + # offset = C_in - C_out * R_T + # Then the transformation back to input image is simply given by: + # P_in = P_out * R_T + offset + # + center_in = np.array((nrow/2.0 - 0.5, ncol/2.0 - 0.5)) + center_out = np.array((nr/2.0 - 0.5, nc/2.0 - 0.5)) + mrotate_T = mrotate.transpose() + offset = center_in - np.dot(center_out, mrotate_T) + # Map pixels of the rotated image to the input image + for rr in range(nr): + for cc in range(nc): + p_out = np.array((rr, cc)) + p_in = np.dot(p_out.astype(np.float64), mrotate_T) + offset + if np.all((p_in > corner00) & (p_in < corner11)): + # Calculate the pixel value for the rotated image + if interp: + # Use area mapping of the 4 closest input pixels + idx_rf, idx_cf = np.floor(p_in).astype(np.int64) + idx_rc, idx_cc = np.ceil(p_in).astype(np.int64) + # Calculate the overlapping areas + p_r, p_c = p_in + p4_area = np.array([(idx_rc - p_r) * (idx_cc - p_c), + (idx_rc - p_r) * (p_c - idx_cf), + (p_r - idx_rf) * (idx_cc - p_c), + (p_r - idx_rf) * (p_c - idx_cf)]) + p4_val = np.array((imgin[idx_rf, idx_cf], + imgin[idx_rf, idx_cc], + imgin[idx_rc, idx_cf], + imgin[idx_rc, idx_cc])) + p_val = np.sum(p4_area * p4_val) + else: + # Use the nearest neighbor as the rotated value + idx_r = round(p_in[0]) + idx_c = round(p_in[1]) + p_val = imgin[idx_r, idx_c] + # + imgout[rr, cc] = p_val + return imgout |