EDIT
I actually got all this wrong, I was thinking of pytesseract, not python-tesseract.
If you go look at the API source (baseapi_mini.h) you'll see that there are some functions that sound very promising for what you're trying to do. The section you're interested in starts about line 500 or so.
char* GetUTF8Text();
/**
* Make a HTML-formatted string with hOCR markup from the internal
* data structures.
* page_number is 0-based but will appear in the output as 1-based.
*/
char* GetHOCRText(int page_number);
/**
* The recognized text is returned as a char* which is coded in the same
* format as a box file used in training. Returned string must be freed with
* the delete [] operator.
* Constructs coordinates in the original image - not just the rectangle.
* page_number is a 0-based page index that will appear in the box file.
*/
char* GetBoxText(int page_number);
/**
* The recognized text is returned as a char* which is coded
* as UNLV format Latin-1 with specific reject and suspect codes
* and must be freed with the delete [] operator.
*/
char* GetUNLVText();
/** Returns the (average) confidence value between 0 and 100. */
int MeanTextConf();
/**
* Returns all word confidences (between 0 and 100) in an array, terminated
* by -1. The calling function must delete [] after use.
* The number of confidences should correspond to the number of space-
* delimited words in GetUTF8Text.
*/
int* AllWordConfidences();
/**
* Applies the given word to the adaptive classifier if possible.
* The word must be SPACE-DELIMITED UTF-8 - l i k e t h i s , so it can
* tell the boundaries of the graphemes.
* Assumes that SetImage/SetRectangle have been used to set the image
* to the given word. The mode arg should be PSM_SINGLE_WORD or
* PSM_CIRCLE_WORD, as that will be used to control layout analysis.
* The currently set PageSegMode is preserved.
* Returns false if adaption was not possible for some reason.
*/
https://bitbucket.org/3togo/python-tesseract/src/9ce0abe168297513d648406be5482b52d38d883b/src/baseapi_mini.h?at=master
My original answer
In order to do that you're going to have to write your own wrapper.
python-tesseract is nice because it gets you up and running quickly, but it's not what I would call sophisticated. You can read the source and see how it works, but here's the synopsis:
Write the input image to a temp file
Call the tesseract command (from the command line) on that file
Return the results
So if you want to do anything special, this isn't going to work at all.
I had an application where I needed high performance and the time spent waiting for the file write to disk, waiting for tesseract to fire up and load the image and process it and whatnot was just too much.
If I remember correctly (I don't have access to the source anymore) I used ctypes to load up a tesseract process, set the image data and then call the GetHOCRText method. Then when I needed to process another image I didn't have to wait for tesseract to load up again, I just set the image data and called GetHOCRText again.
So that's not an exact solution to your problem, and it's definitely not a snippet of code you can use. But hopefully it'll help you make some progress towards your goal.
Here's another question about wrapping external libraries: Wrapping a C library in Python: C, Cython or ctypes?