Method and apparatus of tile-based belief propagation

The present application claims the benefit of U.S. Provisional Application No. 61/119,333 filed on Dec. 2, 2008, the complete subject matter of which is incorporated herein by reference in its entirety.

1. Field of the Invention

The present invention generally relates to image processing, and more particularly to tile-based belief propagation.

2. Description of the Prior Art

Energy (or cost) minimization on a Markov Random Field (MRF) is commonly applied to assign an optimal label to each node (pixel or block of pixels) of a scene representation in computer vision or image processing. A label stands for a local quantity of the state (or status) of the node. For example, the label may stand for the depth value of the node, or may stand for either foreground or background. There are two energy terms in the energy minimization: a data term E d and a smoothness term E s . The data term E d penalizes the inconsistency between the labels and the observed data. In other words, for example, the data term E d should be increased when the labels and the observed data are inconsistent and vice versa. The smoothness term E s favors the spatial coherence of the labels. In other words, for example, the smoothness term E s should be decreased when the neighboring labels are consistent and vice versa. The optimal labels {l p } are the labels that minimize the combination of these two energy terms,

{ l p } = arg ⁢ ⁢ min ⁢ { ∑ p ∈ P ⁢ E d ⁡ ( l p ) + ∑ ( p , q ) ∈ G ⁢ E s ⁡ ( l p , l p ) } ( 1 )

where P is the set of all nodes and G is a specified neighborhood, such as the 4-nearest neighboring pixels.

Many algorithms have been proposed for finding the optimal label assignment as formulated in the energy minimization. Among the algorithms, belief propagation (BP) has become a popular technique for solving computer vision problems, such as stereo estimation and image denoising. The belief propagation has high potential for hardware implementation due to its high degree of parallelism and regularity of memory access. However, the belief propagation requires large amounts of memory and bandwidth, therefore forbidding straightforward hardware implementation.

As the original belief propagation could not be effectively implemented in hardware, a need has arisen to propose a modified belief propagation which has similar performance but with much lower bandwidth and memory requirements than the original BP algorithm.

In view of the foregoing, it is an object of the present invention to provide a tile-based belief propagation, which is more suitable for hardware implementation than the original belief propagation due to the substantially reduced memory and bandwidth consumption.

According to one embodiment of the present invention, an image is first split into a number of tiles. Messages are then iteratively generated by a message computing device (such as a parallel processor) within each of the tiles, based on the messages from neighboring pixels to the tile at a previous iteration, wherein each message represents information of a state of the pixel. The generated messages for sending out of the tiles are stored, for example, in a memory. Labels are finally determined in a belief decision device based on the stored messages, wherein each label represents the state of the pixel.

FIG. 1 shows a flow diagram of a tile-based belief propagation (BP) according to one embodiment of the present invention;

FIG. 2A shows a portion of an image, in which each tile is made of B×B pixels;

FIG. 2B schematically shows messages around the tile;

FIG. 2C schematically shows messages M pq t being sent out of the tile;

FIG. 3A shows the tiles being processed in a raster scan order;

FIG. 3B shows the tiles being processed in an inverse-raster scan order;

FIG. 4 shows a simplified example in which the message M pq t at iteration t from p to q is constructed using the messages from neighbors to p at iteration t−1;

FIG. 5 shows a simplified example in which the node p collects all messages from the neighbors to determine the best label;

FIG. 6 shows an apparatus of the tile-based belief propagation (BP) according to one embodiment of the present invention;

FIG. 7A shows a coarse-to-fine technique for computing the message according to one embodiment of the present invention; and

FIG. 7B shows that each node in the level 1 corresponds to a block of 2×2 nodes in the level 1+1.

FIG. 1 shows a flow diagram of a tile-based belief propagation (BP) according to one embodiment of the present invention. The present invention may be applied in a variety of applications in image processing, such as, but not limited to, image denoising, stereo matching, motion estimation and depth generation. An exemplary pseudocode of the tile-based belief propagation is shown below.

pseudocode

Function {l p } ← TileBasedBP(E d , E s , B, T 0 , T i )

1   Initialize all message entities M pq 0 (l)=0

2   for t 0 =1, . . . ,T 0

3     loop through all tiles in a raster scan order

4       Load {M pq t−1 } for p ∉ C and q ε C; //C is the current

tile.

5       Load E d (l p ) for p ε C;

6       for t i =1, . . . ,T i

7         {M pq t } ← BPinOneTile({M pq t−1 }, E d , C);

8       Store {M pq t } for p ε C and q ∉ C;

9     loop through all tiles in an inverse-raster scan order

10       Load {M pq t−1 } for p ∉ C and q ε C;

11       Load E d (l p ) for p ε C;

12       for t i =1, . . . ,T i

13         {M pq t } ← BPinOneTile({M pq t−1 }, E d , C);

14       if (t 0 =T 0 ) Obtain {l p } for p ε C; //using Eq. (3);

15       else Store {M pq t } for p ε C and q ∉ C;

16   return {l p };

Function {M pq t } ← BPinOneTile({M pq t−1 }, E d , C)

17   Initialize M pq t (l)=0 for all p ε C and q ε C;

18     Update rightward message; //using Eq. (2);

19     Update leftward message;

20     Update downward message;

21     Update upward message;

22   return {M pq t };

According to the embodiment, in step 10 , the whole image is split into non-overlapping tiles of pixels. FIG. 2A shows a portion of an image, in which each tile is made of 4×4 pixels, while tile sizes other than 4×4 may be adapted as well. FIG. 2B schematically shows messages (i.e., the arrows) around the tile. The messages stand for information on the state (or status) of the outside world (that is, the pixels outside of the tile).

The pseudocode has a two-level structure: outer and inner iterations. In the outer iteration, the tiles are first processed in a raster scan order (beginning at line 3 of the pseudocode), and the tiles are then processed in an inverse-raster scan order (beginning at line 9 of the pseudocode). FIG. 3A shows the tiles being processed in the raster scan order (that is, from the top-left tile to the bottom-right tile), and FIG. 3B shows the tiles being processed in the inverse-raster scan order (that is, from the bottom-right tile to the top-left tile). It is appreciated that other scan orders may be adapted. For example, the tiles may be first processed in a vertically downward scan order from the left column to the right column, followed by a vertically upward scan order from the right column to the left column. Moreover, in certain situations, only partial tiles of the image are processed.

For each tile, the messages from other tiles (i.e., the arrows shown in FIG. 2B ), the smoothness term E s and the data term E d are loaded from the memory, and then a message computing operation is performed within the tile (in step 11 ) according to the following BP equation (2) (that is, the function BPinOneTile in the pseudocode).

M pq t ⁡ ( l p ) = min l ′ ∈ L ⁢ { E s ⁡ ( l q , l ′ ) + E d ⁡ ( l ′ ) + ∑ ( p , p ′ ) ∈ N p ⁢ \ ⁢ q ⁢ M p ′ ⁢ p t - 1 ⁡ ( l ′ ) } ( 2 )

where N p is the set of the neighbors of p.

Specifically, at iteration t, each node p sends the resultant message M pq t to its neighbor q. M pq t (1) encodes the opinion of p about assigning label 1 q to q. The message M pq t at iteration t from p to q is constructed using the messages from neighbors to p at iteration t−1. FIG. 4 shows a simplified example in which the message M pq t at iteration t from p to q is constructed using the messages (M rp t−1 , M sp t−1 and M up t−1 ) from neighbors (r, s and u) to p at iteration t−1.

After T i inner iterations (lines 6-7 of the pseudocode), the messages M pq t for sending out of the tile are stored (in step 12 ). FIG. 2C schematically shows the messages M pq t (i.e., the arrows) being sent out of the tile. The inner iterations act like a filtering operation that purifies the messages according to the data terms and the smoothness terms within the tile.

As the tiles are processed in the raster/inverse-raster scan order, the messages are thus iteratively propagated. At the T 0 outer iteration (that is, the end of the raster scan and the inverse-raster scan), the best labels are determined (in step 13 ) using the following equation (3) in line 14 of the pseudocode.

l p = arg ⁢ ⁢ min l ∈ L ⁢ { E d ⁡ ( l ) + ∑ ( p , p ′ ) ∈ N ⁡ ( p ) ⁢ M p ′ ⁢ p T ⁡ ( l ) } ( 3 )

where L is the set of all labels.

After enough iterations, say T (a number), the label of node p is determined based on the local likelihood (i.e., the data term E d ) and the messages M p′p T from the neighbors. FIG. 5 shows a simplified example in which the node p collects all messages from the neighbors (r, s, u and q) to determine the best label.

According to the embodiment, the BP has the following advantages for hardware implementation. First, it is highly parallel. In message passing, each node loads the messages from the previous iteration, operates independently, and generates new messages. Second, it only uses simple operations such as additions and comparisons. Third, the memory access is regular. If the message is updated sequentially, the required input data can be streamed into the processor with ease.

FIG. 6 shows apparatus 60 of the tile-based belief propagation (BP) according to one embodiment of the present invention. A message computing device 601 , preferably a parallel processor, generates message {M pq t } at iteration t according to the messages {M pq t−1 } from neighbors to p at iteration t−1, which are loaded from an (internal/external) memory 602 . According to the tile architecture, the operations of the function BPinOneTile in the pseudocode may be preferably performed in a parallel manner within the parallel processor or the message computing device 601 .

After T i inner iterations (lines 6-7 of the pseudocode), the messages {M pq t } for sending out of the tile are stored in the memory 602 . Subsequently, at the T 0 outer iteration, a belief decision device 603 determines the best labels {l p } based on the messages M p′p T from the neighbors. Finally, an output device 604 generates a label map (such as a depth map or a motion vector map) according to the determined labels {l p }.

Table 1 compares the memory and bandwidth consumption of the original belief propagation and the tile-based belief propagation of the present embodiment.

FIG. 7A shows a coarse-to-fine technique for computing the message according to one embodiment of the present invention. In the embodiment, level 2 has full resolution, level 1 has ¼ resolution, and level 0 has 1/16 resolution. Each node in level 1 corresponds to a block of 2×2 nodes in level 1+1, as shown in FIG. 7B . At the beginning, a coarse computing is performed to run BP on level 0 for the smallest number of iterations. Subsequently, a finer computing is performed on the (level 1) 2×2 nodes corresponding to a single node of level 0. Each message between adjacent nodes on level 0 is duplicated to two messages for the two adjacent pair of nodes on level 1 as shown in FIG. 7B . Finally, a finest computing is performed on the (level 2) 2×2 nodes corresponding to a single node of the level 1.

Although specific embodiments have been illustrated and described, it can be appreciated by those skilled in the art that various modifications may be made without departing from the scope of the present invention, which is intended to be limited solely by the appended claims.