void levinson_durbin(
scalar R[], /* order+1 autocorrelation coeff */
scalar lpcs[], /* order+1 LPC's */
int order /* order of the LPC analysis */
)
{
scalar a[order+1][order+1];
scalar sum, e, k;
int i,j; /* loop variables */
scalar ZERO = fl_to_numb(0.0);
e = R[0]; /* Equation 38a, Makhoul */
for(i=1; i<=order; i++) {
sum = ZERO;
for(j=1; j<=i-1; j++)
sum = s_add(sum, s_mul(a[i-1][j],R[i-j]));
k = s_mul(-1.0, s_div(s_add(R[i], sum),e)); /* Equation 38b, Makhoul */
if (s_abs(k) > fl_to_numb(1.0))
k = ZERO;
a[i][i] = k;
for(j=1; j<=i-1; j++)
a[i][j] = s_add(a[i-1][j] , s_mul(k,a[i-1][i-j])); /* Equation 38c, Makhoul */
e = s_mul(e, s_sub(fl_to_numb(1.0),s_mul(k,k))); /* Equation 38d, Makhoul */
}
for(i=1; i<=order; i++)
lpcs[i] = a[order][i];
lpcs[0] = fl_to_numb(1.0);
}
void find_aks(
scalar Sn[], /* Nsam samples with order sample memory */
scalar a[], /* order+1 LPCs with first coeff 1.0 */
int Nsam, /* number of input speech samples */
int order, /* order of the LPC analysis */
scalar *E /* residual energy */
)
{
scalar Wn[LPC_MAX_N]; /* windowed frame of Nsam speech samples */
scalar R[order+1]; /* order+1 autocorrelation values of Sn[] */
int i;
assert(Nsam < LPC_MAX_N);
hanning_window(Sn,Wn,Nsam);
autocorrelate(Wn,R,Nsam,order);
levinson_durbin(R,a,order);
*E = fl_to_numb(0.0);
for(i=0; i<=order; i++)
*E = s_add(*E , s_mul(a[i],R[i]));
if (*E < fl_to_numb(0.0)) {
#ifdef MATH_Q16_16
*E = 1;
#else
*E = powf(2, -16);//fl_to_numb(1E-12); For debuging purposes.
#endif
}
}
void synthesis_filter(
scalar res[], /* Nsam input residual (excitation) samples */
scalar a[], /* LPCs for this frame of speech samples */
int Nsam, /* number of speech samples */
int order, /* LPC order */
scalar Sn_[] /* Nsam output synthesised speech samples */
)
{
int i,j; /* loop variables */
/* Filter Nsam samples */
for(i=0; i<Nsam; i++) {
Sn_[i] = s_mul(res[i],a[0]);
for(j=1; j<=order; j++)
Sn_[i] = s_sub(Sn_[i], s_mul(Sn_[i-j],a[j]));
}
}
void hanning_window(
scalar Sn[], /* input frame of speech samples */
scalar Wn[], /* output frame of windowed samples */
int Nsam /* number of samples */
)
{
int i; /* loop variable */
scalar HALF = fl_to_numb(0.5);
scalar PI2_ = fl_to_numb(2*PI);
scalar Nsam_ = int_to_numb(Nsam-1);
for(i=0; i<Nsam; i++){
scalar sc_cos = s_mul(HALF,s_cos(s_mul( PI2_, s_div(fl_to_numb((float)i),Nsam_))));
scalar sc_a = s_sub(HALF, sc_cos);
Wn[i] = s_mul(Sn[i], sc_a);
}
}
void weight(
scalar ak[], /* vector of order+1 LPCs */
scalar gamma, /* weighting factor */
int order, /* num LPCs (excluding leading 1.0) */
scalar akw[] /* weighted vector of order+1 LPCs */
)
{
int i;
for(i=1; i<=order; i++)
akw[i] = s_mul(ak[i],s_powf(gamma,fl_to_numb((float)i)));
}
void *nlp_create(
int m /* analysis window size */
)
{
NLP *nlp;
int i;
assert(m <= PMAX_M);
nlp = (NLP*)malloc(sizeof(NLP));
if (nlp == NULL)
return NULL;
nlp->m = m;
scalar PI2_ = fl_to_numb(2*PI);
scalar DEC_ = int_to_numb(m/DEC - 1);
scalar HALF = fl_to_numb(.5);
scalar ZERO = fl_to_numb(0.0);
scalar a, b, c;
for(i=0; i<m/DEC; i++) {
a = s_div(s_mul(PI2_, int_to_numb(i) ) , DEC_);
b = s_mul(HALF,s_cos(a));
nlp->w[i] = s_sub(HALF, b);
//nlp->w[i] = 0.5 - 0.5*cosf(2*PI*i/(m/DEC-1));
}
for(i=0; i<PMAX_M; i++)
nlp->sq[i] = ZERO;
nlp->mem_x = ZERO;
nlp->mem_y = ZERO;
for(i=0; i<NLP_NTAP; i++)
nlp->mem_fir[i] = ZERO;
nlp->fft_cfg = kiss_fft_alloc (PE_FFT_SIZE, 0, NULL, NULL);
assert(nlp->fft_cfg != NULL);
return (void*)nlp;
}
void de_emp(
scalar Sn_de[], /* output frame of speech samples */
scalar Sn[], /* input frame of speech samples */
scalar *mem, /* Sn[-1]single sample memory */
int Nsam /* number of speech samples to use */
)
{
int i;
scalar BETA_ = fl_to_numb(BETA);
for(i=0; i<Nsam; i++) {
Sn_de[i] = s_add(Sn[i] , s_mul(BETA_, mem[0]));
mem[0] = Sn_de[i];
}
}
void inverse_filter(
scalar Sn[], /* Nsam input samples */
scalar a[], /* LPCs for this frame of samples */
int Nsam, /* number of samples */
scalar res[], /* Nsam residual samples */
int order /* order of LPC */
)
{
int i,j; /* loop variables */
for(i=0; i<Nsam; i++) {
res[i] = fl_to_numb(0.0);
for(j=0; j<=order; j++)
res[i] = s_add(res[i] , s_mul(Sn[i-j],a[j]));
}
}
void autocorrelate(
scalar Sn[], /* frame of Nsam windowed speech samples */
scalar Rn[], /* array of P+1 autocorrelation coefficients */
int Nsam, /* number of windowed samples to use */
int order /* order of LPC analysis */
)
{
int i,j; /* loop variables */
scalar Zero = fl_to_numb(0.0);
for(j=0; j<order+1; j++) {
Rn[j] = Zero;
for(i=0; i<Nsam-j; i++)
Rn[j] = s_add(Rn[j] , s_mul(Sn[i],Sn[i+j]));
}
}
/* Add a weak learner h to the strong classifier H */
void addWeak( int posCount, int negCount, int blockCount, int selectTable[],
float ***POS, float ***NEG, Matrix *posWeight, Matrix *negWeight, Ada *strong, int *hUsed ) {
/* For all possible features (Bid, Fid) */
int Iid, Bid, Fid;
Matrix posCorrect, negCorrect, ONES; /* classification correctness matrices */
Matrix bestPosCorrect, bestNegCorrect;
float bestError = 1.f;
int bestBid, bestFid;
short bestParity;
float bestDecision;
float alpha;
float normalize;
#if SHOWAVGERROR
float avgError = 1.f;
int round = 0;
#endif
ones( &posCorrect, 1, posCount, 1 );
ones( &negCorrect, 1, posCount, 1 );
ones( &ONES, 1, posCount, 1 );
#if 0
/* Show the data weight */
full_dump( posWeight, "posWeight", ALL, FLOAT );
full_dump( negWeight, "negWeight", ALL, FLOAT );
#endif
printf( "Add a weak classifier\n" );
for ( Bid = 0; Bid < blockCount; Bid++ ) {
for ( Fid = 0; Fid < FEATURE_COUNT; Fid++ ) {
float POS_mean = 0.f, NEG_mean = 0.f;
float decision;
float error = 0.f;
short parity = +1; /* default: ... NEG_mean ... | ... POS_mean ... */
/* [0] Initilize the matrices: Restore to all 1's */
full_assign( &ONES, &posCorrect, ALL, ALL );
full_assign( &ONES, &negCorrect, ALL, ALL );
/* [1] Compute the POS & NEG mean feature value */
for ( Iid = 0; Iid < posCount; Iid++ ) {
POS_mean += POS[ Iid ][ Bid ][ Fid ];
NEG_mean += NEG[ selectTable[ Iid ] ][ Bid ][ Fid ];
}
POS_mean /= posCount;
NEG_mean /= posCount;
/* default decision threshold: avg of POS_mean and NEG_mean */
decision = ( POS_mean + NEG_mean ) / 2.f;
if ( POS_mean < NEG_mean ) {
parity = -1; /* toggle: ... POS_mean ... | ... NEG_mean ... */
}
#if 0
printf( "Bid: %d, Fid: %d, POS_mean: %f, NEG_mean: %f\n", Bid, Fid, POS_mean, NEG_mean );
#endif
/* [2] Classification and compute the WEIGHTED error rate */
for ( Iid = 0; Iid < posCount; Iid++ ) {
/* positive & wrong */
if ( parity * POS[ Iid ][ Bid ][ Fid ] < parity * decision ) {
error += posWeight->data[ 0 ][ 0 ][ Iid ];
posCorrect.data[ 0 ][ 0 ][ Iid ] = -1.f;
}
/* negative & wrong */
if ( parity * NEG[ selectTable[ Iid ] ][ Bid ][ Fid ] > parity * decision ) {
error += negWeight->data[ 0 ][ 0 ][ Iid ];
negCorrect.data[ 0 ][ 0 ][ Iid ] = -1.f;
}
}
#if SHOWAVGERROR
printf( "Weighted error rate: %f\n", error );
#endif
/* record the best h */
if ( error < bestError ) {
copy( &posCorrect, &bestPosCorrect );
copy( &negCorrect, &bestNegCorrect );
bestError = error;
bestBid = Bid;
bestFid = Fid;
bestParity = parity;
bestDecision = decision;
}
#if SHOWAVGERROR
round++;
avgError += error;
#endif
} /* end of loop Fid */
} /* end of loop Bid */
#if SHOWAVGERROR
avgError /= round;
printf( "Avg. weighted error rate: %f\n", avgError );
#endif
printf( "\nBest weighted error rate: %f, Bid: %d, Fid: %d\n", bestError, bestBid, bestFid );
/* make sure that best error rate < 0.5 (random guessing) */
if ( bestError >= 0.5 ) {
error( "addWeak(): Best error rate is above 0.5!" );
}
#if 0
full_dump( &bestPosCorrect, "bestPosCorrect", ALL, INT );
full_dump( &bestNegCorrect, "bestNegCorrect", ALL, INT );
#endif
/* [3] Record the best parameters, then determine the alpha weight for this weak classifier. */
strong[ *hUsed ].Bid = bestBid;
strong[ *hUsed ].Fid = bestFid;
strong[ *hUsed ].parity = bestParity;
strong[ *hUsed ].decision = bestDecision;
alpha = logf( ( 1.f - bestError ) / bestError ) / 2.f;
strong[ *hUsed ].alpha = alpha;
printf( "alpha%d: %f\n", *hUsed, alpha );
/* [4] Update the data weight */
s_mul( &bestPosCorrect, -alpha );
s_mul( &bestNegCorrect, -alpha );
s_expRaise( &bestPosCorrect );
s_expRaise( &bestNegCorrect );
e_mul( &bestPosCorrect, posWeight, posWeight );
e_mul( &bestNegCorrect, negWeight, negWeight );
normalize = m_sum( posWeight ) + m_sum( negWeight );
s_mul( posWeight, 1.f / normalize );
s_mul( negWeight, 1.f / normalize );
(*hUsed)++;
/* free memory space */
freeMatrix( &posCorrect ); freeMatrix( &negCorrect );
freeMatrix( &bestPosCorrect ); freeMatrix( &bestNegCorrect );
}
/* learn AdaBoost stage A[i,j] */
void learnA( int posCount, int negCount, int blockCount, int *rejectCount, bool rejected[],
float ***POS, float ***NEG, Ada *H, float *F_current, float d_minA, float f_maxA, FILE *fout ) {
int selectTable[ posCount ]; /* image selection table */
int imgCount = posCount * 2;
float initialW = 1.f / (float)imgCount;
Matrix posWeight, negWeight; /* data weight in AdaBoost */
int hAllocated = 10;
int hUsed = 0;
int Iid, t;
float f_local = 1.f;
float threshold = 0.f; /* threshold of the strong classifier A[i,j], should be recorded */
Matrix posResult, negResult;
ones( &posWeight, 1, posCount, 1 );
ones( &negWeight, 1, posCount, 1 );
H = (Ada *)malloc( hAllocated * sizeof( Ada ) );
zeros( &posResult, 1, posCount, 1 );
zeros( &negResult, 1, posCount, 1 );
/* Initialize the data weight */
s_mul( &posWeight, initialW );
s_mul( &negWeight, initialW );
/* [0] Randomly select NEG examples from the bootstrap set
* Report an error if NEG images are not enough
*/
if ( posCount + (*rejectCount) > negCount ) {
fprintf( fout, "Warning: Not enough NEG images.\n" );
error( "learnA(): Not enough NEG images." );
}
select_neg( posCount, negCount, rejected, selectTable );
while ( f_local > f_maxA ) {
int fpCount; /* false positive count */
float d_local = 0.f;
/* [1] Add a weak learner h to the strong classifier A[i,j] */
/* Use realloc() if H is full */
if ( hUsed == hAllocated ) {
hAllocated *= 2;
printf( "call realloc()\n" );
H = (Ada*)realloc( H, hAllocated * sizeof( Ada ) );
}
addWeak( posCount, negCount, blockCount, selectTable,
POS, NEG, &posWeight, &negWeight, H, &hUsed );
threshold = 0.f; /*** Adjust by the threshold ONLY WHEN NECESSARY ***/
float minPosResult = 0.f; /* minimum value of the positive result */
int detect = 0; /* detection count */
fpCount = 0;
/* [2.1] Use the H(x) so far to trial-classify
* H(x) = sign( sum[alpha_t * h_t(x)] )
* Process the POS and NEG together in one loop
*/
for ( Iid = 0; Iid < posCount; Iid++ ) {
float posTemp = 0.f;
float negTemp = 0.f;
for ( t = 0; t < hUsed; t++ ) {
int Bid = H[ t ].Bid;
int Fid = H[ t ].Fid;
short parity = H[ t ].parity;
float decision = H[ t ].decision;
float alpha = H[ t ].alpha;
/* determine that positive is positive */
if ( parity * POS[ Iid ][ Bid ][ Fid ] >= parity * decision ) {
posTemp += alpha;
}
/* determine that positive is negative */
else {
posTemp -= alpha;
}
/* determine that negative is positive */
if ( parity * NEG[ selectTable[ Iid ] ][ Bid ][ Fid ] >= parity * decision ) {
negTemp += alpha;
}
/* determine that negative is negative */
else {
negTemp -= alpha;
}
} /* end of loop "t" */
/* Record into posResult or negResult, and collect min( posResult ) */
posResult.data[ 0 ][ 0 ][ Iid ] = posTemp;
negResult.data[ 0 ][ 0 ][ Iid ] = negTemp;
if ( posTemp < minPosResult ) {
minPosResult = posTemp;
}
} /* end of loop "Iid" */
#if 0
full_dump( &posResult, "posResult", ALL, FLOAT );
full_dump( &negResult, "negResult", ALL, FLOAT );
#endif
#if 1
/* count for detections and false positives */
for ( Iid = 0; Iid < posCount; Iid++ ) {
if ( posResult.data[ 0 ][ 0 ][ Iid ] >= 0.f ) {
detect++;
}
if ( negResult.data[ 0 ][ 0 ][ Iid ] >= 0.f ) {
fpCount++;
}
}
d_local = (float)detect / (float)posCount;
printf( "Before modify threshold:\n Detection rate: %f ( %d / %d )\n", d_local, detect, posCount );
/* [3] Calculate f_local of H(x) */
f_local = (float)fpCount / (float)posCount;
printf( " False positive rate: %f ( %d / %d )\n", f_local, fpCount, posCount );
#endif
/* [2.2] Modify the threshold of H(x) to fulfill d_minA
* If min( posResult ) < 0, then let
* result = result - min( posResult ) so that all POS data are
* determined as positive, i.e., detection rate = 100%
*/
if ( minPosResult < 0.f ) {
threshold = minPosResult;
s_add( &posResult, -threshold );
s_add( &negResult, -threshold );
}
printf( "threshold: %f\n", threshold );
#if 0
full_dump( &posResult, "posResult", ALL, FLOAT );
full_dump( &negResult, "negResult", ALL, FLOAT );
#endif
/* count for detections and false positives */
detect = 0;
fpCount = 0;
for ( Iid = 0; Iid < posCount; Iid++ ) {
if ( posResult.data[ 0 ][ 0 ][ Iid ] >= 0.f ) {
detect++;
}
if ( negResult.data[ 0 ][ 0 ][ Iid ] >= 0.f ) {
fpCount++;
}
}
d_local = (float)detect / (float)posCount;
printf( " After modify threshold:\n Detection rate: %f ( %d / %d )\n", d_local, detect, posCount );
//assert( d_local >= d_minA );
/* [3] Calculate f_local of H(x) */
f_local = (float)fpCount / (float)posCount;
printf( "False positive rate: %f ( %d / %d )\n", f_local, fpCount, posCount );
} /* end of loop "f_local > f_maxA" */
*F_current *= f_local;
printf( "\nWeak learners used: %d\n", hUsed );
printf( "Overall false positive rate: %f\n", *F_current );
/* [4] Put in the "rejection list" the negative images rejected by H(x) */
for ( Iid = 0; Iid < posCount; Iid++ ) {
if ( negResult.data[ 0 ][ 0 ][ Iid ] < 0.f ) {
rejected[ selectTable[ Iid ] ] = true;
(*rejectCount)++;
}
}
printf( "Rejected %d negative images in total.\n", *rejectCount );
getchar();
/* [5] Output H(x) information to file */
fprintf( fout, "%d %f\n", hUsed, threshold );
for ( t = 0; t < hUsed; t++ ) {
fprintf( fout, "%d %d %d %f %f\n",
H[ t ].Bid, H[ t ].Fid, H[ t ].parity, H[ t ].decision, H[ t ].alpha );
}
/* Free memory space */
freeMatrix( &posWeight );
freeMatrix( &negWeight );
free( H );
freeMatrix( &posResult );
freeMatrix( &negResult );
}