A sequential attention interface with a dense reward function for mitosis detection

Abstract

The work aims to develop a fast detection method for instances of mitosis in breast cell sections, which needs time-consuming and labor-intensive searches. The system consists of two sequential processes. The first involves data pre-processing to avoid confusing images transferring to the successive detection procedure from wasteful computations. The input data is filtered using the blue ratio threshold to remove unnecessary background information and increase the color difference between the target and the non-target. Cropped images of suspicious candidates are classified as mitotic or non-mitotic employing a hard attention model, which only grapes the fine trained features locally and detailly instead of the entire picture. There is less computational complexity in terms of efficiency and performance because there are fewer parameters and smaller image sizes, so the proposed classification system outperforms traditional models, such as LEnet-5 and VGG-19, for the benchmarked data set provided in the TPAC2016 competition data sets. The proposed method is also compared to other methods listed on a ranking table for the ICPR2012 competition using its official test data set.

Appendices

Appendix

The loss function consists of three sub-losses from a classifier for accuracy. The critic-network in the Locator predicts the returns for each round. The actor-network in the Locator accounts for the policy gradient. For TensorFlow, these three loss functions are used to update the weights in a gradient descent manner.

Hybird loss function

$$\begin{aligned} \text {Hybird Loss = Classification Loss + Critic Loss - Actor loss} \end{aligned}$$

(A.1)

Classification loss–using cross-entropy

$$\begin{aligned} \text {Classification Loss} = \sum _{b=1}^{B}\frac{cross\_entropy\big (LOGIT_{b, c}, LABEL_{b, c}\big )}{B} \end{aligned}$$

(B.1)

where $cross\_entropy = -[ylog{\hat{y}}+(1-y)log(1-{\hat{y}})]$; $y = LOGIT[0]$ and ${\hat{y}} = LABEL[0]$. LOGIT is the output of a Classifier with softmax and LABEL is a single encoder from the initial label, where b denotes data from the batch and c denotes the class is it.

Critic loss–using mean square error

$$\begin{aligned} \text {Critic Loss} = \sum _{i=1}^{N}\frac{\big (R_{b,t}-BL_{b,t}\big )}{B \times T} \end{aligned}$$

(C.1)

where $R_{b,t}$ is a reward from a Classifier, $BL_{b,t}$ is the prediction of the critic, B is the batch size, T is the number of glimpses.

Actor loss–using Policy gradient

$$\begin{aligned}&\text {Actor loss} {\bar{R}}_{\theta } = \sum _{\tau } R(\tau )p_{\theta }(\tau ) \nonumber \\ \Rightarrow&\nabla {\bar{R}}_{\theta } = \sum _{\tau } R(\tau ) \nabla p_{\theta }(\tau ) \nonumber \\&= \sum _{\tau } R(\tau ) p_{\theta }(\tau ) \frac{\nabla p_{\theta }(\tau )}{p_{\theta }(\tau )} \nonumber \\&= \sum _{\tau } R(\tau ) p_{\theta }(\tau ) \nabla log p_{\theta }(\tau ) \nonumber \\&= E_{\tau \sim p_{\theta }(\tau )} [R(\tau ) \nabla log p_{\theta }(\tau )] \nonumber \\&\approx \frac{1}{N}\sum _{n=1}^{N}R(\tau ^n) \nabla log p_{\theta }(\tau ^n) \nonumber \\&= \frac{1}{N}\sum _{n=1}^{N} \sum _{t=1}^{T_n}R(\tau ^n) \nabla log p_{\theta }(a_t^n|s_t^n) \end{aligned}$$

(D.1)

$$\begin{aligned} \mathbf {The Policy Gradient}:&\nonumber \\ \nabla {\bar{R}}_{\theta }&\approx \frac{1}{B \times T} \sum _{b=1}^{B} \sum _{t=1}^{T}(R_{b,t}-BL_{b,t}) \nabla log p_{\theta }(a_t^b|s_t^b) \end{aligned}$$

(D.2)