Some ideas we use to form this solution:

- Assume we see the first 'B' in a particular row at column j1.

If we see another 'B' in the same row at column j2, then we can be certain that no cell on this row/column j1/column j2 can ever have a lonely pixel. - If there was exactly one 'B' in the row, we go through column j1 from the current row and below. Any 'B's we encounter mean that there can never be a lonely pixel on the rows that we see these pixels.

Essentially we have a set of possible rows and columns that could potentially have lonely pixels. Every time we see 'B's, we see if it's a lonely pixel (or eliminate potential rows/columns in the process).

```
def findLonelyPixel(self, picture):
m, n = len(picture), len(picture[0])
lonely_pixel_count = 0
invalid_rows, invalid_cols = [False]*m, [False]*n
for row in xrange(m):
# If this row has already been ininvalidated, we move on to the next row.
if invalid_rows[row]:
continue
count, col = 0, None
for j in xrange(n):
if picture[row][j] == 'B':
count, col = count+1, j
# If we have more than one 'B' on this row, then every column that has a 'B' is ininvalid
if count>1:
invalid_cols[col] = True
invalid_cols[j] = True
if count==1 and not invalid_cols[col]:
lonely = True
for i in xrange(row+1, m):
# If we see another 'B' on the rest of the column, every row with a 'B' is invalid.
if picture[i][col] == 'B':
invalid_rows[i] = True
lonely = False
if lonely:
lonely_pixel_count+=1
invalid_cols[col] = True
return lonely_pixel_count
```