Help me with this calculation that uses blockproc()

I have an input image of size 384x512 double. I applied blockproc() on this input image, with a blocksize of 20x20, and as a result I got new output image of size 58x77 double.

My question is "why is the output image size 58x77?"

Answer 1

[Walter Roberson]

With a 384 x 512 you do not have full blocks of 20 x 20 in either direction, so you will be operating on partial blocks on the edges.

Whatever operation you are doing is returning a 3 x 3 response for 20 x 20 blocks, but for the partial blocks it is returning 2 x 3 for the 4 x 20 partial blocks vertically, and 3 x 2 for the 20 x 12 the partial blocks horizontally, and 2 x 2 for the 4 x 12 partial corner block.

[TUSHAR MURATKAR]

@walter, can u pls explain this with a pictorial or numerical example

[Walter Roberson]

%I was slightly off on the above output description.

image_rows = 384;
image_columns = 512;
row_blocksize = 20;
column_blocksize = 20;
blockproc_output_rows = 58;
blockproc_output_columns = 77;

row_full_blocks = floor(image_rows/row_blocksize);
input_rows_used_for_full_blocks = row_blocksize * row_full_blocks;
row_partial_block_size = image_rows - input_rows_used_for_full_blocks;
outputs_per_full_row_block = floor(blockproc_output_rows ./ row_full_blocks);
output_rows_used_for_full_blocks = outputs_per_full_row_block * row_full_blocks;
leftover_blockproc_output_rows = blockproc_output_rows - output_rows_used_for_full_blocks;

column_full_blocks = floor(image_columns/column_blocksize);
input_columns_used_for_full_blocks = column_blocksize * column_full_blocks;
column_partial_block_size = image_columns - input_columns_used_for_full_blocks;
outputs_per_full_column_block = floor(blockproc_output_columns ./ column_full_blocks);
leftover_blockproc_output_columns = blockproc_output_columns - outputs_per_full_column_block * column_full_blocks;
output_columns_used_for_full_blocks = outputs_per_full_column_block * column_full_blocks;
leftover_blockproc_output_columns = blockproc_output_columns - output_columns_used_for_full_blocks;

fprintf('Image size is %d by %d\n', image_rows, image_columns);
fprintf('full input blocks are %d by %d\n', row_blocksize, column_blocksize);
fprintf('number of left-over input rows is %d; number of left-over input columns is %d\n', row_partial_block_size, column_partial_block_size);
fprintf('Output size is %d by %d\n', blockproc_output_rows, blockproc_output_columns);
fprintf('full output blocks are %d by %d\n', outputs_per_full_row_block, outputs_per_full_column_block);
fprintf('which uses up %d by %d of the output matrix\n', output_rows_used_for_full_blocks, output_columns_used_for_full_blocks);
fprintf('number of left-over output rows is %d; number of left-over output columns is %d\n', leftover_blockproc_output_rows, leftover_blockproc_output_columns);
fprintf('There are %d rows of output for each of the %d full input blocks with %d rows each\n', outputs_per_full_row_block, row_full_blocks, row_blocksize);
fprintf('There are %d rows of output for the one partial input block that was %d rows high\n', leftover_blockproc_output_rows, row_partial_block_size);
fprintf('There are %d columns of output for each of the %d full input blocks with %d columns each\n', outputs_per_full_column_block, column_full_blocks, column_blocksize);
fprintf('There are %d columns of output for the one partial input block that was %d columns wide\n', leftover_blockproc_output_columns, column_partial_block_size);

temp1 = sprintf('%2dx%2d ', row_blocksize, column_blocksize);
temp2 = [repmat(temp1, 1, column_full_blocks), sprintf('%2dx%2d\n', row_blocksize, column_partial_block_size)];
temp3 = repmat(temp2, 1, row_full_blocks);
temp4 = sprintf('%2dx%2d ', row_partial_block_size, column_blocksize);
temp5 = [repmat(temp4, 1, column_full_blocks), sprintf('%2dx%2d\n', row_partial_block_size, column_partial_block_size)];
fprintf('\nInput diagram:\n\n%s%s\n', temp3, temp5);

temp1 = sprintf('%2dx%2d ', outputs_per_full_row_block, outputs_per_full_column_block);
temp2 = [repmat(temp1, 1, column_full_blocks), sprintf('%2dx%2d\n', outputs_per_full_row_block, leftover_blockproc_output_columns)];
temp3 = repmat(temp2, 1, row_full_blocks);
temp4 = sprintf('%2dx%2d ', leftover_blockproc_output_rows, outputs_per_full_column_block);
temp5 = [repmat(temp4, 1, column_full_blocks), sprintf('%2dx%2d\n', leftover_blockproc_output_rows, leftover_blockproc_output_columns)];
fprintf('\nOutput diagram:\n\n%s%s\n', temp3, temp5);