Fully Convolutional Networks for Semantic Segmentation

1. Training the whole image is more efficient and equally effective.

When these receptive fields overlap significantly, both
feedforward computation and backpropagation are much
more efficient when computed layer-by-layer over an entire
image instead of independently patch-by-patch.

2.Shift-and-stitch Filter Dilation

Dense predictions can be obtained from coarse outputs by
stitching together outputs from shifted versions of the
input. If the output is downsampled by a factor of f, shift
the input x pixels to the right and y pixels down, once for
every x; y such that 0 < x, y < f. Process each of these $f^2$
inputs, and interlace the outputs so that the predictions correspond
to the pixels at the centers of their receptive fields.
(如果下采样系数为$f$, 将输入分别向右和下平移x和y个单位，0<=x,
y< $f$, 将生成的$f^2$)个输出合成在一起作为输出，这样输出的每个像素点都指向他们感受野的中心）
A trike to do so:
Consider a layer (convolution or pooling) with input stride s, and a subsequent convolution layer with filter
weights fij (eliding the irrelevant feature dimensions). Setting
the earlier layer’s input stride to one upsamples its output
by a factor of s. However, convolving the original filter
with the upsampled output does not produce the same
result as shift-and-stitch, because the original filter only sees
a reduced portion of its (now upsampled) input. To produce
the same result, dilate (or “rarefy”) the filter by forming

$$f'_{ij}=\Big\{\begin{array}\ f_{i/s, j/s} \quad & if \ s\ divides\ both\ i\ and\ j\\ 0\quad & otherwise \end{array} $$
(with i and j zero-based). Reproducing the full net output of
shift-and-stitch involves repeating this filter enlargement
layer-by-layer until all subsampling is removed. (In practice,
this can be done efficiently by processing subsampled
versions of the upsampled input.)
使用空洞卷积使生成的特征谱

1.F. Yu and V. Koltun, “Multi-scale context aggregation by dilated
convolutions,” in Proc. Int. Conf. Learn. Represent., 2016.