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Main functions for applying Normalized Cut.
Code adapted from LOST: https://github.com/valeoai/LOST
"""
import torch
import torch.nn.functional as F
import numpy as np
from scipy.linalg import eigh
from scipy import ndimage
def ncut(feats, dims, scales, init_image_size, tau = 0, eps=1e-5, im_name='', no_binary_graph=False):
"""
Implementation of NCut Method.
Inputs
feats: the pixel/patche features of an image
dims: dimension of the map from which the features are used
scales: from image to map scale
init_image_size: size of the image
tau: thresold for graph construction
eps: graph edge weight
im_name: image_name
no_binary_graph: ablation study for using similarity score as graph edge weight
"""
cls_token = feats[0,0:1,:].cpu().numpy()
feats = feats[0,1:,:]
feats = F.normalize(feats, p=2)
A = (feats @ feats.transpose(1,0))
A = A.cpu().numpy()
if no_binary_graph:
A[A<tau] = eps
else:
A = A > tau
A = np.where(A.astype(float) == 0, eps, A)
d_i = np.sum(A, axis=1)
D = np.diag(d_i)
# Print second and third smallest eigenvector
_, eigenvectors = eigh(D-A, D, subset_by_index=[1,2])
eigenvec = np.copy(eigenvectors[:, 0])
# Using average point to compute bipartition
second_smallest_vec = eigenvectors[:, 0]
avg = np.sum(second_smallest_vec) / len(second_smallest_vec)
bipartition = second_smallest_vec > avg
seed = np.argmax(np.abs(second_smallest_vec))
if bipartition[seed] != 1:
eigenvec = eigenvec * -1
bipartition = np.logical_not(bipartition)
bipartition = bipartition.reshape(dims).astype(float)
# predict BBox
pred, _, objects,cc = detect_box(bipartition, seed, dims, scales=scales, initial_im_size=init_image_size[1:]) ## We only extract the principal object BBox
mask = np.zeros(dims)
mask[cc[0],cc[1]] = 1
return np.asarray(pred), objects, mask, seed, None, eigenvec.reshape(dims)
def detect_box(bipartition, seed, dims, initial_im_size=None, scales=None, principle_object=True):
"""
Extract a box corresponding to the seed patch. Among connected components extract from the affinity matrix, select the one corresponding to the seed patch.
"""
w_featmap, h_featmap = dims
objects, num_objects = ndimage.label(bipartition)
cc = objects[np.unravel_index(seed, dims)]
if principle_object:
mask = np.where(objects == cc)
# Add +1 because excluded max
ymin, ymax = min(mask[0]), max(mask[0]) + 1
xmin, xmax = min(mask[1]), max(mask[1]) + 1
# Rescale to image size
r_xmin, r_xmax = scales[1] * xmin, scales[1] * xmax
r_ymin, r_ymax = scales[0] * ymin, scales[0] * ymax
pred = [r_xmin, r_ymin, r_xmax, r_ymax]
# Check not out of image size (used when padding)
if initial_im_size:
pred[2] = min(pred[2], initial_im_size[1])
pred[3] = min(pred[3], initial_im_size[0])
# Coordinate predictions for the feature space
# Axis different then in image space
pred_feats = [ymin, xmin, ymax, xmax]
return pred, pred_feats, objects, mask
else:
raise NotImplementedError
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