LS report improved by Alison and JOSEF

1. During the fitting process, there are 4 groups of coefficient optimised.

    During the fitting process,  4 groups of coefficient are optimised. (more direct, more informative )

2. In every step, ESO optimises one group parameters, and all the other parameters are regarded as constants. So the computational intensity is reduced in every group.

    问题在于，说第一句话的时候，读者并不知道你要干什么，有点茫然。直到读者读到So以后，才知道要干什么。为了使读者一直抓住思路，改为：

    To reduce the computational intensity, in every step, ESO optimises one group parameters, and all the other parameters are regarded as constants.

3. First..Then...After that...Then... Finally

    First..Then...After that...Next... Finally, 保持多样性，不要重复用词

4. The head pose has to be first estimated , and then (两个连词重复) the modelcouldbe projected to the correct location in the image plane.

    After the head pose is estimated ,  the model can be projected to the correct location in the image plane.

5. Because w is a nonlinear projection, so the optimisation cannot be conducted by solving linear system.  (不可同时用)

    Because w is a nonlinear projection,  the optimisation cannot be conducted by solvinga linear system.

6. In this work, (work is too general)

     In this study

7. Because the landmarks are very sparse feature, leading to a really low dimensional searching space, the optimisation isreally fast. 重复

    Because the landmarks are very sparse feature, leading to a rather low dimensional searching space, the optimisation is really fast. 

8. Until the end of this section, (until 指的是时间)

    In this section so far / up to this point in this section

9. The regularisation term used in this work is  based on the shape probability density of the training samples. So the regularisation trades off the landmark fitting and the prior probability density. 不能直接看出两句的联系

   As the regularisation term used in this work is  based on the shape probability density of the training samples,  the regularisation trades off the landmark fitting and the prior probability density. 

   As 用在开头比BECAUSE好

   After the first iteration, all the illumination parameters have been estimated, so the cost function becomes

   After the first iteration, as all the illumination parameters have been estimated,  the cost function becomes   

10. But it is observed that  在写作中，BUT不放在开头

      However,...

11. It is easy to get  the closed-form solution...

      the closed-form solution can be obtained. There  is, it is...  句型都不直接，最好用被动替换

 12. From Figure 2, the images ...

       Figure 2 demonstrates that    直接

13. ... ,which means that...

      ...., indicating that

 14. It is not hard to find that the illumination is well recovered.    

        Clearly, the illumination is well recovered.    简单直接

15. Different from the existing methods,

       In contrast to the existing methods, 

16. self-collected database--> local database

17. It is easy to over-fit->It tends to overfit

18. extremely rotated pose images->extreme pose images

19. MFF,,,,In this work, we proposed ESO.

      MFF...However MFF still has number of shortcomings, which we address in this paper. In this work, we proposed ESO.

20. A brief introduction of 3DMM --> a brief introduction to 3DMM

21. They use a simplified affine camera, which cannot model the perspective distortion. We use a perspective camera, which can model the perspective distortion.

      They use a simplified affine camera, which cannot model the perspective distortion.By contrast, this distortion can be modelled by our perspective camera.

 22. ICIA only models shape and texture, it could not estimate illumination.

       ICIA models only shape and texture, and so cannotestimate illumination. (could 是过去时， 注意连词)

23. The fitting is faster than with the SNO, but the performance is similar to SNO.

      The fitting is faster than the SNO, but with similar performance.

24. the state-of-the-art methods

       state-of-the-art methods

25. The regularisation term is important for avoid being overfitted.

       The regularisation term is important to avoid overfitting.

26. ..., because the fitting was trapped into a local minima. That is the problem of the gradient-based methods.

      ..., because the fitting was trapped into a local minima, characteristic behaviour of  the gradient-based methods.

27. The reconstruction errors of MFF are X1,X2 and X3 respectively. However, such errors for ESO are Y1,Y2 and Y3.

      The reconstruction errors of MFF are X1,X2 and X3 respectively, compared with Y1,Y2 and Y3 for ESO.

28. It is also noted that...

       Note that...

29. So far, the MFF achieves the best face recognition rate.

      To date, .....

30.  In common with [8], ESO estimates ... with closed-form solutions.

31. ESO achieves comparable face recognition rate compared to state-of-the-art methods, however, ESO is much more efficient.

       ESO achieves comparable face recognition rate compared to state-of-the-art methods, while being much more efficient.

32. In order to compare

      To compare, 简单明了

33. .......... It means..........

      ...........This means........  前后衔接更好

34. In order to make fair comparisons, we use the same 3DMM, landmarks and optimal regularisation parameter setting strategy. Only the fitting methods are different.  

To make fair comparisons, we use the same 3DMM, landmarks and optimal regularisation parameter setting strategy.The only difference is the fitting methods.  强调

35. The methods are very time-consuming. In contrast, the non-iterative methods only use landmarks to recover alpha. Not surprisingly, it is very efficient. 

      In contrast to these methods, which are very time-consuming, the non-iterative methods only use landmarks to recover alpha, and consequently very efficient.

36. These parameters are grouped into 5 groups.

      These parameters are grouped into 5 categories.

37. Different from the previous work

      In contrast to the previous work, 预期更强

38. ICIA  assumes that the initial parameters  are close to the optimum. Thisassumption cannot be satisfied in the real world. 

      The assumption of ICIA, namely/specifically, the initial parameters  are close to the optimum, cannot be satisfied in the real world. 

39. Besides-> Apart from, as well as, in addition to